Applicability of self-consistent mean-field theory
International Nuclear Information System (INIS)
Guo Lu; Sakata, Fumihiko; Zhao Enguang
2005-01-01
Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case
Mean-field theory and self-consistent dynamo modeling
International Nuclear Information System (INIS)
Yoshizawa, Akira; Yokoi, Nobumitsu
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Mean fields and self consistent normal ordering of lattice spin and gauge field theories
International Nuclear Information System (INIS)
Ruehl, W.
1986-01-01
Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)
A self-consistent mean field theory for diffusion in alloys
International Nuclear Information System (INIS)
Nastar, M.; Barbe, V.
2007-01-01
Starting from a microscopic model of the atomic transport via vacancies and interstitials in alloys, a self-consistent mean field (SCMF) kinetic theory yields the phenomenological coefficients L ij . In this theory, kinetic correlations are accounted for through a set of effective interactions within a non-equilibrium distribution function of the system. The introduction of a master equation describing the evolution with time of the distribution function and its moments leads to general self-consistent kinetic equations. The L ij of a face centered cubic alloy are calculated using the kinetic equations of Nastar (M. Nastar, Philos. Mag., 2005, 85, 3767, ref. 1) derived from a microscopic broken bond model of the vacancy jump frequency. A first approximation leads to an analytical expression of the L ij and a second approximation to a better agreement with the Monte Carlo simulations. A change of sign of the L ij is studied as a function of the microscopic parameters of the jump frequency. The L ij of a cubic centered alloy obtained for the complex diffusion mechanism of the dumbbell configuration of the interstitial are used to study the effect of an on-site rotation of the dumbbell on the transport. (authors)
Kalikmanov, V.I.; De Leeuw, S.W.
2002-01-01
We propose a self-consistent mean-field lattice-gas theory of intercalation compounds based on effective interactions between interstitials in the presence of the host atoms. In addition to short-range screened Coulomb repulsions, usually discussed in the lattice gas models, the present theory takes
Odd-even mass differences from self-consistent mean field theory
International Nuclear Information System (INIS)
Bertsch, G. F.; Bertulani, C. A.; Nazarewicz, W.; Schunck, N.; Stoitsov, M. V.
2009-01-01
We survey odd-even nuclear binding energy staggering using density functional theory with several treatments of the pairing interaction including the BCS, Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami approximation. We calculate the second difference of binding energies and compare the results with 443 measured neutron energy differences in isotope chains and 418 measured proton energy differences in isotone chains. The particle-hole part of the energy functional is taken as the SLy4 Skyrme parametrization, and the pairing part of the functional is based on a contact interaction with possible density dependence. An important feature of the data, reproduced by the theory, is the sharp gap quenching at magic numbers. With the strength of the interaction as a free parameter, the theory can reproduce the data to an rms accuracy of about 0.25 MeV. This is slightly better than a single-parameter phenomenological description but slightly poorer than the usual two-parameter phenomenological form c/A α . The following conclusions can be made about the performance of common parametrization of the pairing interaction: (i) there is a weak preference for a surface-peaked neutron-neutron pairing, which might be attributable to many-body effects, (ii) a larger strength is required in the proton pairing channel than in the neutron pairing channel, and (iii) pairing strengths adjusted to the well-known spherical isotope chains are too weak to give a good overall fit to the mass differences
Wieser, R
2017-05-04
A self-consistent mean field theory is introduced and used to investigate the thermodynamics and spin dynamics of an S = 1 quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. In addition, the spin dynamics of a magnetic Skyrmion is described by solving the time dependent Schrödinger equation with additional damping term. The Skyrmion annihilation process driven by an electric field is used to compare the trajectories of the quantum mechanical simulation with a semi-classical description for the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.
Directory of Open Access Journals (Sweden)
Aliza B Rubenstein
2017-06-01
Full Text Available Multispecificity-the ability of a single receptor protein molecule to interact with multiple substrates-is a hallmark of molecular recognition at protein-protein and protein-peptide interfaces, including enzyme-substrate complexes. The ability to perform structure-based prediction of multispecificity would aid in the identification of novel enzyme substrates, protein interaction partners, and enable design of novel enzymes targeted towards alternative substrates. The relatively slow speed of current biophysical, structure-based methods limits their use for prediction and, especially, design of multispecificity. Here, we develop a rapid, flexible-backbone self-consistent mean field theory-based technique, MFPred, for multispecificity modeling at protein-peptide interfaces. We benchmark our method by predicting experimentally determined peptide specificity profiles for a range of receptors: protease and kinase enzymes, and protein recognition modules including SH2, SH3, MHC Class I and PDZ domains. We observe robust recapitulation of known specificities for all receptor-peptide complexes, and comparison with other methods shows that MFPred results in equivalent or better prediction accuracy with a ~10-1000-fold decrease in computational expense. We find that modeling bound peptide backbone flexibility is key to the observed accuracy of the method. We used MFPred for predicting with high accuracy the impact of receptor-side mutations on experimentally determined multispecificity of a protease enzyme. Our approach should enable the design of a wide range of altered receptor proteins with programmed multispecificities.
International Nuclear Information System (INIS)
Hattori, Kazumasa
2010-01-01
We investigate a two-orbital Anderson lattice model with Ising orbital intersite exchange interactions on the basis of a dynamical mean field theory combined with the static mean field approximation of intersite orbital interactions. Focusing on Ce-based heavy-fermion compounds, we examine the orbital crossover between two orbital states, when the total f-electron number per site n f is ∼1. We show that a 'meta-orbital' transition, at which the occupancy of two orbitals changes steeply, occurs when the hybridization between the ground-state f-electron orbital and conduction electrons is smaller than that between the excited f-electron orbital and conduction electrons at low pressures. Near the meta-orbital critical end point, orbital fluctuations are enhanced and couple with charge fluctuations. A critical theory of meta-orbital fluctuations is also developed by applying the self-consistent renormalization theory of itinerant electron magnetism to orbital fluctuations. The critical end point, first-order transition, and crossover are described within Gaussian approximations of orbital fluctuations. We discuss the relevance of our results to CeAl 2 , CeCu 2 Si 2 , CeCu 2 Ge 2 , and related compounds, which all have low-lying crystalline-electric-field excited states. (author)
Self-consistent mean-field models for nuclear structure
International Nuclear Information System (INIS)
Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
2003-01-01
The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications
Exotic nuclei in self-consistent mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Buervenich, T.; Reinhard, P.-G.; Maruhn, J. A.; Greiner, W.
1999-01-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei with emphasis on neutron-rich tin isotopes and superheavy nuclei. (c) 1999 American Institute of Physics
Self-consistent normal ordering of gauge field theories
International Nuclear Information System (INIS)
Ruehl, W.
1987-01-01
Mean-field theories with a real action of unconstrained fields can be self-consistently normal ordered. This leads to a considerable improvement over standard mean-field theory. This concept is applied to lattice gauge theories. First an appropriate real action mean-field theory is constructed. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean-field theory are derived. (author). 4 refs
A self-consistent mean-field approach to the dynamical symmetry breaking
International Nuclear Information System (INIS)
Kunihiro, Teiji; Hatsuda, Tetsuo.
1984-01-01
The dynamical symmetry breaking phenomena in the Nambu and Jona-Lasimio model are reexamined in the framework of a self-consistent mean-field (SCMF) theory. First, we formulate the SCMF theory in a lucid manner based on a successful decomposition of the Lagrangian into semiclassical and residual interaction parts by imposing a condition that ''the dangerous term'' in Bogoliubov's sense should vanish. Then, we show that the difference of the energy density between the super and normal phases, the correct expression of which the original authors failed to give, can be readily obtained by applying the SCMF theory. Futhermore, it is shown that the expression thus obtained is identical to that of the effective potential (E.P.) given by the path-integral method with an auxiliary field up to the one loop order in the loop expansion, then one finds a new and simple way to get the E.P. Some numerical results of the E.P. and the dynamically generated mass of fermion are also shown. As another demonstration of the powerfulness of the SCMF theory, we derive, in the Appendix, the energy density of the O(N)-phi 4 model including the higher order corrections in the sense of large N expansion. (author)
Translationally invariant self-consistent field theories
International Nuclear Information System (INIS)
Shakin, C.M.; Weiss, M.S.
1977-01-01
We present a self-consistent field theory which is translationally invariant. The equations obtained go over to the usual Hartree-Fock equations in the limit of large particle number. In addition to deriving the dynamic equations for the self-consistent amplitudes we discuss the calculation of form factors and various other observables
Self-consistent mean field forces in turbulent plasmas: Current and momentum relaxation
International Nuclear Information System (INIS)
Hegna, C.C.
1997-08-01
The properties of turbulent plasmas are described using the two-fluid equations. Under some modest assumptions, global constraints for the turbulent mean field forces that act on the ion and electron fluids are derived. These constraints imply a functional form for the parallel mean field forces in the Ohm's law and the momentum balance equation. These forms suggest that the fluctuations attempt to relax the plasma to a state where both the current and the bulk plasma momentum are aligned along the mean magnetic field with proportionality constants that are global constants. Observations of flow profile evolution during discrete dynamo activity in reversed field pinch experiments are interpreted
International Nuclear Information System (INIS)
Nastar, M.
2008-01-01
When an alloy is irradiated, atomic transport can occur through the two types of defects which are created: vacancies and interstitials. Recent developments of the self-consistent mean field (SCMF) kinetic theory could treat within the same formalism diffusion due to vacancies and interstitials in a multi-component alloy. It starts from a microscopic model of the atomic transport via vacancies and interstitials and yields the fluxes with a complete Onsager matrix of the phenomenological coefficients. The jump frequencies depend on the local environment through a 'broken bond model' such that the large range of frequencies involved in concentrated alloys is produced by a small number of thermodynamic and kinetic parameters. Kinetic correlations are accounted for through a set of time-dependent effective interactions within a non-equilibrium distribution function of the system. The different approximations of the SCMF theory recover most of the previous diffusion models. Recent improvements of the theory were to extend the multi-frequency approach usually restricted to dilute alloys to diffusion in concentrated alloys with jump frequencies depending on local concentrations and to generalize the formalism first developed for the vacancy diffusion mechanism to the more complex diffusion mechanism of the interstitial in the dumbbell configuration. (author)
Self consistent field theory of virus assembly
Li, Siyu; Orland, Henri; Zandi, Roya
2018-04-01
The ground state dominance approximation (GSDA) has been extensively used to study the assembly of viral shells. In this work we employ the self-consistent field theory (SCFT) to investigate the adsorption of RNA onto positively charged spherical viral shells and examine the conditions when GSDA does not apply and SCFT has to be used to obtain a reliable solution. We find that there are two regimes in which GSDA does work. First, when the genomic RNA length is long enough compared to the capsid radius, and second, when the interaction between the genome and capsid is so strong that the genome is basically localized next to the wall. We find that for the case in which RNA is more or less distributed uniformly in the shell, regardless of the length of RNA, GSDA is not a good approximation. We observe that as the polymer-shell interaction becomes stronger, the energy gap between the ground state and first excited state increases and thus GSDA becomes a better approximation. We also present our results corresponding to the genome persistence length obtained through the tangent-tangent correlation length and show that it is zero in case of GSDA but is equal to the inverse of the energy gap when using SCFT.
The nuclear N-body problem and the effective interaction in self-consistent mean-field methods
International Nuclear Information System (INIS)
Duguet, Thomas
2002-01-01
This work deals with two aspects of mean-field type methods extensively used in low-energy nuclear structure. The first study is at the mean-field level. The link between the wave-function describing an even-even nucleus and the odd-even neighbor is revisited. To get a coherent description as a function of the pairing intensity in the system, the utility of the formalization of this link through a two steps process is demonstrated. This two-steps process allows to identify the role played by different channels of the force when a nucleon is added in the system. In particular, perturbative formula evaluating the contribution of time-odd components of the functional to the nucleon separation energy are derived for zero and realistic pairing intensities. Self-consistent calculations validate the developed scheme as well as the derived perturbative formula. This first study ends up with an extended analysis of the odd-even mass staggering in nuclei. The new scheme allows to identify the contribution to this observable coming from different channels of the force. The necessity of a better understanding of time-odd terms in order to decide which odd-even mass formulae extracts the pairing gap the most properly is identified. These terms being nowadays more or less out of control, extended studies are needed to make precise the fit of a pairing force through the comparison of theoretical and experimental odd-even mass differences. The second study deals with beyond mean-field methods taking care of the correlations associated with large amplitude oscillations in nuclei. Their effects are usually incorporated through the GCM or the projected mean-field method. We derive a perturbation theory motivating such variational calculations from a diagrammatic point of view for the first time. Resuming two-body correlations in the energy expansion, we obtain an effective interaction removing the hard-core problem in the context of configuration mixing calculations. Proceeding to a
Time independent mean-field theory
International Nuclear Information System (INIS)
Negele, J.W.
1980-02-01
The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures
Mean-field theory for a ferroelectric transition
International Nuclear Information System (INIS)
Dobry, A.; Greco, A.; Stachiotti, M.
1990-01-01
For the treatment of anharmonic models of solids presenting structural transitions, a commonly used approximation is that of self-consistent phonons. Rather than the usual site decoupling, this mean-field theory is based on decoupling of modes in reciprocal space. A self-consistent phonon approximation for the non-linear polarizability model is developed in this work. The model describes the dynamical properties of ferroelectric materials. Phase diagrams as a function of relevant model parameters are presented. An analysis is made of critical behaviour and it is shown that the approximation leads to the same anomalies found in other models. (Author). 9 refs., 3 figs
Parquet equations for numerical self-consistent-field theory
International Nuclear Information System (INIS)
Bickers, N.E.
1991-01-01
In recent years increases in computational power have provided new motivation for the study of self-consistent-field theories for interacting electrons. In this set of notes, the so-called parquet equations for electron systems are derived pedagogically. The principal advantages of the parquet approach are outlined, and its relationship to simpler self-consistent-field methods, including the Baym-Kadanoff technique, is discussed in detail. (author). 14 refs, 9 figs
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Mean-field theory and solitonic matter
International Nuclear Information System (INIS)
Cohen, T.D.
1989-01-01
Finite density solitonic matter is considered in the context of quantum field theory. Mean-field theory, which provides a reasonable description for single-soliton properties gives rise to a crystalline description. A heuristic description of solitonic matter is given which shows that the low-density limit of solitonic matter (the limit which is presumably relevant for nuclear matter) does not commute with the mean-field theory limit and gives rise to a Fermi-gas description of the system. It is shown on the basis of a formal expansion of simple soliton models in terms of the coupling constant why one expects mean-field theory to fail at low densities and why the corrections to mean-field theory are nonperturbative. This heuristic description is tested against an exactly solvable 1+1 dimensional model (the sine-Gordon model) and found to give the correct behavior. The relevance of these results to the program of doing nuclear physics based on soliton models is discussed. (orig.)
Band mixing effects in mean field theories
International Nuclear Information System (INIS)
Kuyucak, S.; Morrison, I.
1989-01-01
The 1/N expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model (IBM). Conversely, comparison with the exact IBM results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the E2 transitions among the ground, β and γ bands are incomplete for the spin dependent terms and it is essential to include band mixing effect for a correct (Mikhailov) analysis of E2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the sd and sdg boson models. 17 refs., 7 figs., 8 tabs
Quantitative verification of ab initio self-consistent laser theory.
Ge, Li; Tandy, Robert J; Stone, A D; Türeci, Hakan E
2008-10-13
We generalize and test the recent "ab initio" self-consistent (AISC) time-independent semiclassical laser theory. This self-consistent formalism generates all the stationary lasing properties in the multimode regime (frequencies, thresholds, internal and external fields, output power and emission pattern) from simple inputs: the dielectric function of the passive cavity, the atomic transition frequency, and the transverse relaxation time of the lasing transition.We find that the theory gives excellent quantitative agreement with full time-dependent simulations of the Maxwell-Bloch equations after it has been generalized to drop the slowly-varying envelope approximation. The theory is infinite order in the non-linear hole-burning interaction; the widely used third order approximation is shown to fail badly.
Relativistic mean field theory for unstable nuclei
International Nuclear Information System (INIS)
Toki, Hiroshi
2000-01-01
We discuss the properties of unstable nuclei in the framework of the relativistic mean field (RMF) theory. We take the RMF theory as a phenomenological theory with several parameters, whose form is constrained by the successful microscopic theory (RBHF), and whose values are extracted from the experimental values of unstable nuclei. We find the outcome with the newly obtained parameter sets (TM1 and TMA) is promising in comparison with various experimental data. We calculate systematically the ground state properties of even-even nuclei up to the drip lines; about 2000 nuclei. We find that the neutron magic shells (N=82, 128) at the standard magic numbers stay at the same numbers even far from the stability line and hence provide the feature of the r-process nuclei. However, many proton magic numbers disappear at the neutron numbers far away from the magic numbers due to the deformations. We discuss how to describe giant resonances for the case of the non-linear coupling terms for the sigma and omega mesons in the relativistic RPA. We mention also the importance of the relativistic effect on the spin observables as the Gamow-Teller strength and the longitudinal and transverse spin responses. (author)
A self-consistent theory of the magnetic polaron
International Nuclear Information System (INIS)
Marvakov, D.I.; Kuzemsky, A.L.; Vlahov, J.P.
1984-10-01
A finite temperature self-consistent theory of magnetic polaron in the s-f model of ferromagnetic semiconductors is developed. The calculations are based on the novel approach of the thermodynamic two-time Green function methods. This approach consists in the introduction of the ''irreducible'' Green functions (IGF) and derivation of the exact Dyson equation and exact self-energy operator. It is shown that IGF method gives a unified and natural approach for a calculation of the magnetic polaron states by taking explicitly into account the damping effects and finite lifetime. (author)
Multiconfigurational self-consistent reaction field theory for nonequilibrium solvation
DEFF Research Database (Denmark)
Mikkelsen, Kurt V.; Cesar, Amary; Ågren, Hans
1995-01-01
electronic structure whereas the inertial polarization vector is not necessarily in equilibrium with the actual electronic structure. The electronic structure of the compound is described by a correlated electronic wave function - a multiconfigurational self-consistent field (MCSCF) wave function. This wave......, open-shell, excited, and transition states. We demonstrate the theory by computing solvatochromatic shifts in optical/UV spectra of some small molecules and electron ionization and electron detachment energies of the benzene molecule. It is shown that the dependency of the solvent induced affinity...
DEFF Research Database (Denmark)
Lerchner, Alexander; Sterner, G.; Hertz, J.
2006-01-01
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn, with a numerical procedure for solving the mean-field equations quantitatively. With our treatment, one can determine self-consistently both the firing rates and the firing correlations...
Doubly self-consistent field theory of grafted polymers under simple shear in steady state
International Nuclear Information System (INIS)
Suo, Tongchuan; Whitmore, Mark D.
2014-01-01
We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkman equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities
Nonequilibrium dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Nonequilibrium dynamical mean-field theory
International Nuclear Information System (INIS)
Eckstein, Martin
2009-01-01
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Classification of networks of automata by dynamical mean field theory
International Nuclear Information System (INIS)
Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.
1990-01-01
Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)
Self-consistent T-matrix theory of superconductivity
Czech Academy of Sciences Publication Activity Database
Šopík, B.; Lipavský, Pavel; Männel, M.; Morawetz, K.; Matlock, P.
2011-01-01
Roč. 84, č. 9 (2011), 094529/1-094529/13 ISSN 1098-0121 R&D Projects: GA ČR GAP204/10/0212; GA ČR(CZ) GAP204/11/0015 Institutional research plan: CEZ:AV0Z10100521 Keywords : superconductivity * T-matrix * superconducting gap * restricted self-consistency Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.691, year: 2011
Nuclear response beyond mean field theory
International Nuclear Information System (INIS)
Brand, M.G.E.; Allaart, K.; Dickhoff, W.H.
1990-01-01
An extension of the RPA equations is derived, with emphasis on the relation between the single-particle Green function and the polarization propagator. Including second order self-energy contributions the resulting particle-hole interaction includes the coupling to two-particle-two-hole (2p2h) states and the resulting response satisfies relevant conservation laws. This aspect of the theory is shown to be essential to obtain reliable and meaningful results for excitation strengths and to avoid ghost solutions. This method is applied to electromagnetic and charge exchange excitations in 48 Ca up to 100 MeV. A G-matrix interaction based on meson exchange is used which takes care of short-range correlations. The results compare favourably with measured excitation strengths and electromagnetic form factors both at low energy as well as in the giant resonance region. Remaining discrepancies point in the direction of further strength reduction due to short-range correlations as well as a possible stronger coupling to 2p2h states at low energy. (orig.)
Thermodynamically self-consistent theory for the Blume-Capel model.
Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G
2001-04-01
We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.
General variational many-body theory with complete self-consistency for trapped bosonic systems
International Nuclear Information System (INIS)
Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.
2006-01-01
In this work we develop a complete variational many-body theory for a system of N trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue--generally integro-differential--equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or MCHB(M), where M specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states
Modification of linear response theory for mean-field approximations
Hütter, M.; Öttinger, H.C.
1996-01-01
In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the
Some approximate calculations in SU2 lattice mean field theory
International Nuclear Information System (INIS)
Hari Dass, N.D.; Lauwers, P.G.
1981-12-01
Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)
Dynamical Mean Field Approximation Applied to Quantum Field Theory
Akerlund, Oscar; Georges, Antoine; Werner, Philipp
2013-12-04
We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...
Mean-field theory of nuclear structure and dynamics
International Nuclear Information System (INIS)
Negele, J.W.
1982-01-01
The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission
Self-consistent theory of normal-to-superconducting transition
International Nuclear Information System (INIS)
Radzihovsky, L.; Chicago Univ., IL
1995-01-01
I study the normal-to-superconducting (NS) transition within the Ginzburg-Landau (GL) model, taking into account the fluctuations in the m-component complex order parameter ψ α and the vector potential A in the arbitrary dimension d, for any m. I find that the transition is of second order and that the previous conclusion of the fluctuation-driven first-order transition is a possible artifact of the breakdown of the ε-expansion and the inaccuracy of the 1/m-expansion for physical values ε = 1, m 1. I compute the anomalous η(d, m) exponent at the NS transition, and find η(3, 1) ∼ -0.38. In the m → ∞ limit, η(d, m) becomes exact and agrees with the 1/m-expansion. Near d = 4 the theory is also in good agreement with the perturbative ε-expansion results for m > 183 and provides a sensible interpolation formula for arbitrary d and m. (orig.)
Self-consistent field theory of polymer-ionic molecule complexation.
Nakamura, Issei; Shi, An-Chang
2010-05-21
A self-consistent field theory is developed for polymers that are capable of binding small ionic molecules (adsorbates). The polymer-ionic molecule association is described by Ising-like binding variables, C(i) ((a))(kDelta)(=0 or 1), whose average determines the number of adsorbed molecules, n(BI). Polymer gelation can occur through polymer-ionic molecule complexation in our model. For polymer-polymer cross-links through the ionic molecules, three types of solutions for n(BI) are obtained, depending on the equilibrium constant of single-ion binding. Spinodal lines calculated from the mean-field free energy exhibit closed-loop regions where the homogeneous phase becomes unstable. This phase instability is driven by the excluded-volume interaction due to the single occupancy of ion-binding sites on the polymers. Moreover, sol-gel transitions are examined using a critical degree of conversion. A gel phase is induced when the concentration of adsorbates is increased. At a higher concentration of the adsorbates, however, a re-entrance from a gel phase into a sol phase arises from the correlation between unoccupied and occupied ion-binding sites. The theory is applied to a model system, poly(vinyl alcohol) and borate ion in aqueous solution with sodium chloride. Good agreement between theory and experiment is obtained.
Symplectic manifolds, coadjoint orbits, and Mean Field Theory
International Nuclear Information System (INIS)
Rosensteel, G.
1986-01-01
Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit
Mean field with corrections in lattice gauge theory
International Nuclear Information System (INIS)
Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.
1981-12-01
A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)
Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems
International Nuclear Information System (INIS)
Lévêque, Camille; Madsen, Lars Bojer
2017-01-01
We develop an ab initio time-dependent wavefunction based theory for the description of a many-body system of cold interacting bosons. Like the multi-configurational time-dependent Hartree method for bosons (MCTDHB), the theory is based on a configurational interaction Ansatz for the many-body wavefunction with time-dependent self-consistent-field orbitals. The theory generalizes the MCTDHB method by incorporating restrictions on the active space of the orbital excitations. The restrictions are specified based on the physical situation at hand. The equations of motion of this time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory are derived. The similarity between the formal development of the theory for bosons and fermions is discussed. The restrictions on the active space allow the theory to be evaluated under conditions where other wavefunction based methods due to exponential scaling in the numerical effort cannot, and to clearly identify the excitations that are important for an accurate description, significantly beyond the mean-field approach. For ground state calculations we find it to be important to allow a few particles to have the freedom to move in many orbitals, an insight facilitated by the flexibility of the restricted-active-space Ansatz . Moreover, we find that a high accuracy can be obtained by including only even excitations in the many-body self-consistent-field wavefunction. Time-dependent simulations of harmonically trapped bosons subject to a quenching of their noncontact interaction, show failure of the mean-field Gross-Pitaevskii approach within a fraction of a harmonic oscillation period. The TD-RASSCF theory remains accurate at much reduced computational cost compared to the MCTDHB method. Exploring the effect of changes of the restricted-active-space allows us to identify that even self-consistent-field excitations are mainly responsible for the accuracy of the method. (paper)
Lerchner, A; Hertz, J; Ahmadi, M
2004-01-01
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stim...
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
A mean field theory of coded CDMA systems
International Nuclear Information System (INIS)
Yano, Toru; Tanaka, Toshiyuki; Saad, David
2008-01-01
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems
A mean field theory of coded CDMA systems
Energy Technology Data Exchange (ETDEWEB)
Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp
2008-08-15
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.
General Relativistic Mean Field Theory for rotating nuclei
Energy Technology Data Exchange (ETDEWEB)
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Nuclear collective vibrations in extended mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-07-01
The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)
Self-consistent Random Phase Approximation applied to a schematic model of the field theory
International Nuclear Information System (INIS)
Bertrand, Thierry
1998-01-01
The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small-perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion-collisions are discussed briefly. (orig.)
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly. (orig.)
Nonlinear mean field theory for nuclear matter and surface properties
International Nuclear Information System (INIS)
Boguta, J.; Moszkowski, S.A.
1983-01-01
Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)
Self-consistent Ginzburg-Landau theory for transport currents in superconductors
DEFF Research Database (Denmark)
Ögren, Magnus; Sørensen, Mads Peter; Pedersen, Niels Falsig
2012-01-01
We elaborate on boundary conditions for Ginzburg-Landau (GL) theory in the case of external currents. We implement a self-consistent theory within the finite element method (FEM) and present numerical results for a two-dimensional rectangular geometry. We emphasize that our approach can in princi...... in principle also be used for general geometries in three-dimensional superconductors....
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.
1981-01-01
A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures
Probabilistic theory of mean field games with applications
Carmona, René
2018-01-01
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...
Fictive impurity approach to dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Fuhrmann, A.
2006-10-15
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Fictive impurity approach to dynamical mean field theory
International Nuclear Information System (INIS)
Fuhrmann, A.
2006-10-01
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Self-consistent cluster theory for systems with off-diagonal disorder
International Nuclear Information System (INIS)
Kaplan, T.; Leath, P.L.; Gray, L.J.; Diehl, H.W.
1980-01-01
A self-consistent cluster theory for elementary excitations in systems with diagonal, off-diagonal, and environmental disorder is presented. The theory is developed in augmented space where the configurational average over the disorder is replaced by a ground-state matrix element in a translationally invariant system. The analyticity of the resulting approximate Green's function is proved. Numerical results for the self-consistent single-site and pair approximations are presented for the vibrational and electronic properties of disordered linear chains with diagonal, off-diagonal, and environmental disorder
Renormalization in self-consistent approximation schemes at finite temperature I: theory
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-07-01
Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)
The application of mean field theory to image motion estimation.
Zhang, J; Hanauer, G G
1995-01-01
Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.
Spin and orbital exchange interactions from Dynamical Mean Field Theory
Energy Technology Data Exchange (ETDEWEB)
Secchi, A., E-mail: a.secchi@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands); Lichtenstein, A.I., E-mail: alichten@physnet.uni-hamburg.de [Universitat Hamburg, Institut für Theoretische Physik, Jungiusstraße 9, D-20355 Hamburg (Germany); Katsnelson, M.I., E-mail: m.katsnelson@science.ru.nl [Radboud University, Institute for Molecules and Materials, 6525 AJ Nijmegen (Netherlands)
2016-02-15
We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii–Moriya interaction and other symmetric terms such as dipole–dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms. - Highlights: • We give formulas for the exchange interaction tensor in strongly correlated systems. • Interactions are written in terms of electronic Green's functions and self-energies. • The method is suitable for a Dynamical Mean Field Theory implementation. • No quenching of the orbital magnetic moments is assumed. • Spin and orbital contributions to magnetism can be computed separately.
Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
Rohringer, G.; Hafermann, H.; Toschi, A.; Katanin, A. A.; Antipov, A. E.; Katsnelson, M. I.; Lichtenstein, A. I.; Rubtsov, A. N.; Held, K.
2018-04-01
Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.
Screening effects in a polyelectrolyte brush: self-consistent-field theory
Zhulina, E.B.; Klein Wolterink, J.; Borisov, O.V.
2000-01-01
We have developed an analytical self-consistent-field (SCF) theory describing conformations of weakly charged polyelectrolyte chains tethered to the solid-liquid interface and immersed in a solution of low molecular weight salt. Depending on the density of grafting of the polyelectrolytes to the
Martínez-Veracoechea, Francisco J.; Escobedo, Fernando A.
2009-01-01
A combination of particle-based simulations and self-consistent field theory (SCFT) is used to study the stabilization of multiple ordered bicontinuous phases in blends of a diblock copolymer (DBC) and a homopolymer. The double-diamond phase (DD
Similarities between Prescott Lecky's theory of self-consistency and Carl Rogers' self-theory.
Merenda, Peter F
2010-10-01
The teachings of Prescott Lecky on the self-concept at Columbia University in the 1920s and 1930s and the posthumous publications of his book on self-consistency beginning in 1945 are compared with the many publications of Carl Rogers on the self-concept beginning in the early 1940s. Given that Rogers was a graduate student at Columbia in the 1920s and 1930s, the striking similarities between these two theorists, as well as claims attributed to Rogers by Rogers' biographers and writers who have quoted Rogers on his works relating to self-theory, strongly suggest that Rogers borrowed from Lecky without giving him the proper credit. Much of Rogers' writings on the self-concept included not only terms and concepts which were original with Lecky, but at times these were actually identical.
Non-local correlations within dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Li, Gang
2009-03-15
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Non-local correlations within dynamical mean field theory
International Nuclear Information System (INIS)
Li, Gang
2009-03-01
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
International Nuclear Information System (INIS)
Cafiero, Mauricio; Gonzalez, Carlos
2005-01-01
We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials
Quantum Critical Point revisited by the Dynamical Mean Field Theory
Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei
Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. Our results reveal a substantial difference with the calculations based on the Spin-Fermion model which indicates that the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor. The authors are supported by Center for Computational Design of Functional Strongly Correlated Materials and Theoretical Spectroscopy under DOE Grant DE-FOA-0001276.
Quantum critical point revisited by dynamical mean-field theory
Xu, Wenhu; Kotliar, Gabriel; Tsvelik, Alexei M.
2017-03-01
Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. We use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. By comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.
Quantum critical point revisited by dynamical mean-field theory
International Nuclear Information System (INIS)
Xu, Wenhu; Kotliar, Gabriel; Rutgers University, Piscataway, NJ; Tsvelik, Alexei M.
2017-01-01
Dynamical mean-field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. We characterize the QCP by a universal scaling form of the self-energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low-energy kink and the high-energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high-energy antiferromagnetic paramagnons. Here, we use the frequency-dependent four-point correlation function of spin operators to calculate the momentum-dependent correction to the electron self-energy. Furthermore, by comparing with the calculations based on the spin-fermion model, our results indicate the frequency dependence of the quasiparticle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.
Relativistic mean field theory for deformed nuclei with pairing correlations
International Nuclear Information System (INIS)
Geng, Lisheng; Toki, Hiroshi; Sugimoto, Satoru; Meng, Jie
2003-01-01
We develop a relativistic mean field (RMF) description of deformed nuclei with pairing correlations in the BCS approximation. The treatment of the pairing correlations for nuclei whose Fermi surfaces are close to the threshold of unbound states needs special attention. With this in mind, we use a delta function interaction for the pairing interaction to pick up those states whose wave functions are concentrated in the nuclear region and employ the standard BCS approximation for the single-particle states obtained from the BMF theory with deformation. We apply the RMF + BCS method to the Zr isotopes and obtain a good description of the binding energies and the nuclear radii of nuclei from the proton drip line to the neutron drip line. (author)
Multiagent model and mean field theory of complex auction dynamics
Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng
2015-09-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.
Multiagent model and mean field theory of complex auction dynamics
International Nuclear Information System (INIS)
Chen, Qinghua; Wang, Yougui; Huang, Zi-Gang; Lai, Ying-Cheng
2015-01-01
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena. (paper)
Sine-Gordon mean field theory of a Coulomb gas
Energy Technology Data Exchange (ETDEWEB)
Diehl, Alexandre; Barbosa, Marcia C.; Levin, Yan
1997-12-31
Full text. The Coulomb gas provides a paradigm for the study of various models of critical phenomena. In particular, it is well known that the two dimensional (2 D). Coulomb gas can be directly used to study the superfluidity transition in {sup 4} He films, arrays of Josephson junctions, roughening transition, etc. Not withstanding its versatility, our full understanding of the most basic model of Coulomb gas, namely an ensemble of hard spheres carrying either positive or negative charges at their center, is still lacking. It is now well accepted that at low density the two dimensional plasma of equal number of positive and negative particles undergoes a Kosterlitz-Thouless (KT) metal insulator transition. This transition is of an infinite order and is characterized by a diverging Debye screening length. As the density of particles increases, the validity of the KT theory becomes questionable and the possibility of the KT transition being replaced by some kind of first order discontinuity has been speculated for a long time. In this work sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean-field free energy is constructed and the corresponding phase diagrams in two and three dimensions are obtained. When analyzed in terms of chemical potential, the sine-Gordon theory predicts the phase diagram topologically identical to the Monte Carlo simulations and a recently developed Debye-Huckel-Bjerrum theory. In 2D, we find that the infinite-order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole insulating phase is mapped onto zero density. (author)
Self-consistent theory of hadron-nucleus scattering. Application to pion physics
International Nuclear Information System (INIS)
Johnson, M.B.
1980-01-01
The requirement of using self-consistent amplitudes to evaluate microscopically the scattering of strongly interacting particles from nuclei is developed. Application of the idea to a simple model of pion-nucleus scattering is made. Numerical results indicate that the expansion of the optical potential converges when evaluated in terms of fully self-consistent quantities. A comparison of the results to a recent determination of the spreading interaction in the phenomenological isobar-hole model shows that the theory accounts for the sign and magnitude of the real and imaginary part of the spreading interaction with no adjusted parameters. The self-consistnt theory has a strong density dependence, and the consequences of this for pion-nucleus scattering are discussed. 18 figures, 1 table
Self-consistent theory of finite Fermi systems and radii of nuclei
International Nuclear Information System (INIS)
Saperstein, E. E.; Tolokonnikov, S. V.
2011-01-01
Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ ch (r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.
Self-consistent theory of charged current neutrino-nucleus reactions
Energy Technology Data Exchange (ETDEWEB)
Paar, Nils; Marketin, Tomislav; Vretenar, Dario [Physics Department, Faculty of Science, University Zagreb (Croatia); Ring, Peter [Physik-Department, Technischen Universitaet Muenchen, D-85748 Muenchen (Germany)
2009-07-01
A novel theoretical framework has been introduced for description of neutrino induced reactions with nuclei. The properties of target nuclei are determined in a self-consistent way using relativistic mean-field framework based on effective Lagrangians with density dependent meson-nucleon vertex functions. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described in the relativistic Hartree-Bogolyubov model, and the relevant transitions to excited nuclear states are calculated in the proton-neutron relativistic quasiparticle random phase approximation. This framework has been employed in studies of charged-current neutrino reactions involving nuclei of relevance for neutrino detectors, r-process nuclei, and neutrino-nucleus cross sections averaged over measured neutrino fluxes and supernova neutrino distributions.
International Nuclear Information System (INIS)
Kuchinskii, E. Z.; Nekrasov, I. A.; Sadovskii, M. V.
2008-01-01
The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition
Superheavy nuclei in the relativistic mean-field theory
International Nuclear Information System (INIS)
Lalazissis, G.A.; Ring, P.; Gambhir, Y.K.
1996-01-01
We have carried out a study of superheavy nuclei in the framework of the relativistic mean-field theory. Relativistic Hartree-Bogoliubov (RHB) calculations have been performed for nuclei with large proton and neutron numbers. A finite-range pairing force of Gogny type has been used in the RHB calculations. The ground-state properties of very heavy nuclei with atomic numbers Z=100-114 and neutron numbers N=154-190 have been obtained. The results show that in addition to N=184 the neutron numbers N=160 and N=166 exhibit an extra stability as compared to their neighbors. For the case of protons the atomic number Z=106 is shown to demonstrate a closed-shell behavior in the region of well deformed nuclei about N=160. The proton number Z=114 also indicates a shell closure. Indications for a doubly magic character at Z=106 and N=160 are observed. Implications of shell closures on a possible synthesis of superheavy nuclei are discussed. (orig.)
Mean-field theory of meta-learning
International Nuclear Information System (INIS)
Plewczynski, Dariusz
2009-01-01
We discuss here the mean-field theory for a cellular automata model of meta-learning. Meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents that acquire and process incoming information using various types, or different versions, of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share the opposite classification outcome can be observed in the system. Therefore, the probability of selecting a proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are built from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents
Regular and chaotic dynamics in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.
1997-01-01
Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society
Multichain Mean-Field Theory of Quasi-One-Dimensional Quantum Spin Systems
International Nuclear Information System (INIS)
Sandvik, A.W.
1999-01-01
A multichain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C 0 is modeled by a number of neighboring chains C δ , δ=±1, hor-ellipsis,± , with the edge chains C ±n coupled to a staggered field. Using a quantum Monte Carlo method, the effective (2n+1) -chain Hamiltonian is solved self-consistently for n up to 4 . The results are compared with simulation results for the original Hamiltonian on large rectangular lattices. Both methods show that the staggered magnetization M for small interchain couplings α behaves as M∼√(α) enhanced by a multiplicative logarithmic correction. copyright 1999 The American Physical Society
Quark mean field theory and consistency with nuclear matter
International Nuclear Information System (INIS)
Dey, J.; Tomio, L.; Dey, M.; Frederico, T.
1989-01-01
1/N c expansion in QCD (with N c the number of colours) suggests using a potential from meson sector (e.g. Richardson) for baryons. For light quarks a σ field has to be introduced to ensure chiral symmetry breaking ( χ SB). It is found that nuclear matter properties can be used to pin down the χ SB-modelling. All masses, M Ν , m σ , m ω are found to scale with density. The equations are solved self consistently. (author)
Elizondo-Aguilera, L. F.; Zubieta Rico, P. F.; Ruiz-Estrada, H.; Alarcón-Waess, O.
2014-11-01
A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, Fl m ,l m(k ,t ) and Flm ,l m S(k ,t ) , are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density nl m(k ,t ) and the translational (α =T ) and rotational (α =R ) current densities jlm α(k ,t ) . Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by Sl m ,l m(k ) . Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γT and γR, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O
2014-11-01
A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
Self-consistent field theory of polymer-ionic molecule complexation
Nakamura, Issei; Shi, An-Chang
2010-01-01
A self-consistent field theory is developed for polymers that are capable of binding small ionic molecules (adsorbates). The polymer-ionic molecule association is described by Ising-like binding variables, C_(i)^(a)(kΔ)(= 0 or 1), whose average determines the number of adsorbed molecules, nBI. Polymer gelation can occur through polymer-ionic molecule complexation in our model. For polymer-polymer cross-links through the ionic molecules, three types of solutions for nBI are obtained, depending...
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.; Massachusetts Inst. of Tech., Cambridge
1981-01-01
In collaboration with Shimon Levit and Zvi Paltiel, significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples will be summarized here. (orig./HSI)
Mean-field theory of anyons near Bose statistics
International Nuclear Information System (INIS)
McCabe, J.; MacKenzie, R.
1992-01-01
The validity of a mean-field approximation for a boson-based free anyon gas near Bose statistics is shown. The magnetic properties of the system is discussed in the approximation that the statistical magnetic field is uniform. It is proved that the anyon gas does not exhibit a Meissner effect in the domain of validity the approximation. (K.A.) 7 refs
Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report
International Nuclear Information System (INIS)
Wadia, Spenta R.
2009-01-01
We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)
International Nuclear Information System (INIS)
Kerres, U.; Mack, G.; Palma, G.
1994-12-01
We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two-step method. It combines i) dimensional reduction to a 3-dimensional lattice theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations. (orig.)
International Nuclear Information System (INIS)
Kerres, U.
1995-01-01
We propose the study of the phase transition in the scalar electroweak theory at finite temperature by a two-step method. It combines i) dimensional reduction to a 3-dimensional lattice theory via perturbative blockspin transformation, and ii) either further real space renormalization group transformations, or solution of gap equations, for the 3d lattice theory. A gap equation can be obtained by using the Peierls inequality to find the best quadratic approximation to the 3d action. This method avoids the lack of self consistency of the usual treatments which do not separate infrared and UV-problems by introduction of a lattice cutoff. The effective 3d lattice action could also be used in computer simulations. ((orig.))
Quark mean field theory and consistency with nuclear matter
International Nuclear Information System (INIS)
Dey, J.; Dey, M.; Frederico, T.; Tomio, L.
1990-09-01
1/N c expansion in QCD (with N c the number of colours) suggests using a potential from meson sector (e.g. Richardson) for baryons. For light quarks a σ field has to be introduced to ensure chiral symmetry breaking ( χ SB). It is found that nuclear matter properties can be used to pin down the χ SB-modelling. All masses, M N , m σ , m ω are found to scale with density. The equations are solved self consistently. (author). 29 refs, 2 tabs
Cheng, Shengfeng; Wen, Chengyuan; Egorov, Sergei
2015-03-01
Molecular dynamics simulations and self-consistent field theory calculations are employed to study the interactions between a nanoparticle and a polymer brush at various densities of chains grafted to a plane. Simulations with both implicit and explicit solvent are performed. In either case the nanoparticle is loaded to the brush at a constant velocity. Then a series of simulations are performed to compute the force exerted on the nanoparticle that is fixed at various distances from the grafting plane. The potential of mean force is calculated and compared to the prediction based on a self-consistent field theory. Our simulations show that the explicit solvent leads to effects that are not captured in simulations with implicit solvent, indicating the importance of including explicit solvent in molecular simulations of such systems. Our results also demonstrate an interesting correlation between the force on the nanoparticle and the density profile of the brush. We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Tesla K40 GPU used for this research.
Electron confinement in quantum nanostructures: Self-consistent Poisson-Schroedinger theory
International Nuclear Information System (INIS)
Luscombe, J.H.; Bouchard, A.M.; Luban, M.
1992-01-01
We compute the self-consistent electron states and confining potential, V(r,T), for laterally confined cylindrical quantum wires at a temperature T from a numerical solution of the coupled Poisson and Schroedinger (PS) equations. Finite-temperature effects are included in the electron density function, n(r,T), via the single-particle density matrix in the grand-canonical ensemble using the self-consistent bound states. We compare our results for a GaAs quantum wire with those obtained previously [J. H. Luscombe and M. Luban, Appl. Phys. Lett. 57, 61 (1990)] from a finite-temperature Thomas-Fermi (TF) approximation. We find that the TF results agree well with those of the more realistic, but also more computationally intensive PS theory, except for low temperatures or for cases where the quantum wire is almost, but not totally, depleted due to a combination of either small geometry, surface boundary conditions, or low doping concentrations. In the latter situations, the number of subbands that are populated is relatively small, and both n(r,T) and V(r,T) exhibit Friedel-type oscillations. Otherwise the TF theory, which is based on free-particle states, is remarkably accurate. We also present results for the partial electron density functions associated with the angular momentum quantum numbers, and discuss their role in populating the quantum wire
Justifying quasiparticle self-consistent schemes via gradient optimization in Baym-Kadanoff theory.
Ismail-Beigi, Sohrab
2017-09-27
The question of which non-interacting Green's function 'best' describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a realistic manner. Here, we study this question within the framework of Baym-Kadanoff theory, an approach where one locates the stationary point of a total energy functional of the one-particle Green's function in order to find the total ground-state energy as well as all one-particle properties such as the density matrix, chemical potential, or the quasiparticle energy spectrum and quasiparticle wave functions. For the case of the Klein functional, our basic finding is that minimizing the length of the gradient of the total energy functional over non-interacting Green's functions yields a set of self-consistent equations for quasiparticles that is identical to those of the quasiparticle self-consistent GW (QSGW) (van Schilfgaarde et al 2006 Phys. Rev. Lett. 96 226402-4) approach, thereby providing an a priori justification for such an approach to electronic structure calculations. In fact, this result is general, applies to any self-energy operator, and is not restricted to any particular approximation, e.g., the GW approximation for the self-energy. The approach also shows that, when working in the basis of quasiparticle states, solving the diagonal part of the self-consistent Dyson equation is of primary importance while the off-diagonals are of secondary importance, a common observation in the electronic structure literature of self-energy calculations. Finally, numerical tests and analytical arguments show that when the Dyson equation produces multiple quasiparticle solutions corresponding to a single non-interacting state, minimizing the length of the gradient translates into choosing the solution with largest quasiparticle weight.
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura
2016-07-12
A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.
Quantum correlated cluster mean-field theory applied to the transverse Ising model.
Zimmer, F M; Schmidt, M; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Multifractality and quantum diffusion from self-consistent theory of localization
Energy Technology Data Exchange (ETDEWEB)
Suslov, I. M., E-mail: suslov@kapitza.ras.ru [Kapitza Institute for Physical Problems (Russian Federation)
2015-11-15
Multifractal properties of wave functions in a disordered system can be derived from self-consistent theory of localization by Vollhardt and Wölfle. A diagrammatic interpretation of results allows to obtain all scaling relations used in numerical experiments. The arguments are given that the one-loop Wegner result for a space dimension d = 2 + ϵ is exact, so the multifractal spectrum is strictly parabolical. The σ-models are shown to be deficient at the four-loop level and the possible reasons of that are discussed. The extremely slow convergence to the thermodynamic limit is demonstrated. The open question on the relation between multifractality and a spatial dispersion of the diffusion coefficient D(ω, q) is resolved in the compromise manner due to ambiguity of the D(ω, q) definition. Comparison is made with the extensive numerical material.
Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density
Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.
1988-01-01
The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.
Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals
International Nuclear Information System (INIS)
Takeda, Hiroyuki; John, Sajeev
2011-01-01
We theoretically demonstrate the population switching of quantum dots (QD's), modeled as two-level atoms in idealized one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) by self-consistent solution of the Maxwell-Bloch equations. In our semiclassical theory, energy states of the electron are quantized, and electron dynamics is described by the atomic Bloch equation, while electromagnetic waves satisfy the classical Maxwell equations. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states (LDOS) and spontaneous emission rates exhibit abrupt changes with frequency, enabling large QD population inversion driven by both continuous and pulsed optical fields. We recapture and generalize this ultrafast population switching using the Maxwell-Bloch equations. Radiative emission from the QD is obtained directly from the surrounding PC geometry using finite-difference time-domain simulation of the electromagnetic field. The atomic Bloch equations provide a source term for the electromagnetic field. The total electromagnetic field, consisting of the external input and radiated field, drives the polarization components of the atomic Bloch vector. We also include a microscopic model for phonon dephasing of the atomic polarization and nonradiative decay caused by damped phonons. Our self-consistent theory captures stimulated emission and coherent feedback effects of the atomic Mollow sidebands, neglected in earlier treatments. This leads to remarkable high-contrast QD-population switching with relatively modest (factor of 10) jump discontinuities in the electromagnetic LDOS. Switching is demonstrated in three separate models of QD's placed (i) in the vicinity of a band edge of a 1D PC, (ii) near a cutoff frequency in a bimodal waveguide channel of a 2D PC, and (iii) in the vicinity of a localized defect mode side coupled to a single-mode waveguide channel in a 2D PC.
Mean field theory of dynamic phase transitions in ferromagnets
International Nuclear Information System (INIS)
Idigoras, O.; Vavassori, P.; Berger, A.
2012-01-01
We have studied the second order dynamic phase transition (DPT) of the two-dimensional kinetic Ising model by means of numerical calculations. While it is well established that the order parameter Q of the DPT is the average magnetization per external field oscillation cycle, the possible identity of the conjugate field has been addressed only recently. In this work, we demonstrate that our entire set of numerical data is fully consistent with the applied bias field H b being the conjugate field of order parameter Q. For this purpose, we have analyzed the Q(H b )-dependence and we have found that it follows the expected power law behavior with the same critical exponent as the mean field equilibrium case.
Haule, Kristjan
2018-04-01
The Dynamical Mean Field Theory (DMFT) in combination with the band structure methods has been able to address reach physics of correlated materials, such as the fluctuating local moments, spin and orbital fluctuations, atomic multiplet physics and band formation on equal footing. Recently it is getting increasingly recognized that more predictive ab-initio theory of correlated systems needs to also address the feedback effect of the correlated electronic structure on the ionic positions, as the metal-insulator transition is almost always accompanied with considerable structural distortions. We will review recently developed extension of merger between the Density Functional Theory (DFT) and DMFT method, dubbed DFT+ embedded DMFT (DFT+eDMFT), whichsuccessfully addresses this challenge. It is based on the stationary Luttinger-Ward functional to minimize the numerical error, it subtracts the exact double-counting of DFT and DMFT, and implements self-consistent forces on all atoms in the unit cell. In a few examples, we will also show how the method elucidated the important feedback effect of correlations on crystal structure in rare earth nickelates to explain the mechanism of the metal-insulator transition. The method showed that such feedback effect is also essential to understand the dynamic stability of the high-temperature body-centered cubic phase of elemental iron, and in particular it predicted strong enhancement of the electron-phonon coupling over DFT values in FeSe, which was very recently verified by pioneering time-domain experiment.
A self-consistent nonlinear theory of resistive-wall instability in a relativistic electron beam
International Nuclear Information System (INIS)
Uhm, H.S.
1994-01-01
A self-consistent nonlinear theory of resistive-wall instability is developed for a relativistic electron beam propagating through a grounded cylindrical resistive tube. The theory is based on the assumption that the frequency of the resistive-wall instability is lower than the cutoff frequency of the waveguide. The theory is concentrated on study of the beam current modulation directly related to the resistive-wall klystron, in which a relativistic electron beam is modulated at the first cavity and propagates downstream through the resistive wall. Because of the self-excitation of the space charge waves by the resistive-wall instability, a highly nonlinear current modulation of the electron beam is accomplished as the beam propagates downstream. A partial integrodifferential equation is obtained in terms of the initial energy modulation (ε), the self-field effects (h), and the resistive-wall effects (κ). Analytically investigating the partial integrodifferential equation, a scaling law of the propagation distance z m at which the maximum current modulation occurs is obtained. It is found in general that the self-field effects dominate over the resistive-wall effects at the beginning of the propagation. As the beam propagates farther downstream, the resistive-wall effects dominate. Because of a relatively large growth rate of the instability, the required tube length of the klystron is short for most applications
Exact mean-field theory of ionic solutions: non-Debye screening
International Nuclear Information System (INIS)
Varela, L.M.; Garcia, Manuel; Mosquera, Victor
2003-01-01
The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory
Generalized molecular orbital theory: a limited multiconfiguration self-consistent-field-theory
International Nuclear Information System (INIS)
Hall, M.B.
1981-01-01
The generalized molecular orbital (GMO) approach is a limited type of multiconfiguration self-consistent-field (MCSCF) calculation which divides the orbitals of a closed shell molecule into four shells: doubly occupied, strongly occupied, weakly occupied, and unoccupied. The orbitals within each shell have the same occupation number and are associated with the same Fock operator. Thus, the orbital optimization is ideally suited to solution via a coupling operator. The determination of the orbitals is followed by a configuration interaction (CI) calculation within the strongly and weakly occupied shells. Results for BH 3 show a striking similarity between the GMO's and the natural orbitals (NO's) from an all singles and doubles CI calculation. Although the GMO approach would not be accurate for an entire potential surface, results for spectroscopic constants of N 2 show that it is suitable near the equilibrium geometry. This paper describes the use of the GMO technique to determine the primary orbital space, but a potentially important application may be in the determination of a secondary orbital space following a more accurate MCSCF determination of the primary space
Higher order alchemical derivatives from coupled perturbed self-consistent field theory.
Lesiuk, Michał; Balawender, Robert; Zachara, Janusz
2012-01-21
We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics
Self-consistent theory of three-dimensional convection in the geomagnetic tail
International Nuclear Information System (INIS)
Birn, J.; Schindler, K.
1983-01-01
The self-consistent theory of time-dependent convection in the earth's magnetotail of Schindler and Birn (1982) is extended to three dimensions to include more realistic tail geometry and three-dimensional flow. We confirm that a steady state solution implies unrealistic tail geometry or large particle or energy losses that are unrealistic during quiet times and conclude therefore that as in the 2-dimensional case the magnetotail becomes time-dependent for typical convection electric fields. Explicit solutions are derived, even analytically, for the three-dimensional flow and the electric and magnetic field in a realistic tail geometry, and quantitative examples are presented. Consequences of time-dependent convection are demonstrated considering two idealized cases of magnetosphere response to solar wind changes: (1) uniform compression as the likely consequence of increasing (static, dynamic or magnetic) solar wind pressure; and (2) compression only in the z direction perpendicular to the plasma sheet as the probable consequence of a dawn to dusk external electric field (E/sub y/>0), corresponding to a southward interplanetary magnetic field component (B/sub z/ 0 with geomagnetic activity. Several other features, already present in the 2-dimensional theory, are confirmed
Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory
Aarts, G.; Smit, J.
2000-01-01
As a toy model for dynamics in nonequilibrium quantum field theory we consider the abelian Higgs model in 1+1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function
Self-Consistent Theory of Shot Noise Suppression in Ballistic Conductors
Bulashenko, O. M.; Rubí, J. M.; Kochelap, V. A.
Shot-noise measurements become a fundamental tool to probe carrier interactions in mesoscopic systems [1]. A matter of particular interest is the significance of Coulomb interaction which may keep nearby electrons more regularly spaced rather than strictly at random and lead to the noise reduction. That effect occurs in different physical situations. Among them are charge-limited ballistic transport, resonant tunneling, single-electron tunneling, etc. In this communication we address the problem of Coulomb correlations in ballistic conductors under the space-charge-limited transport conditions, and present for the first time a semiclassical self-consistent theory of shot noise in these conductors by solving analytically the kinetic equation coupled self-consistently with a Poisson equation. Basing upon this theory, exact results for current noise in a two-terminal ballistic conductor under the action of long-range Coulomb correlations has been derived. The noise reduction factor (in respect to the uncorrelated value) is obtained in a closed analytical form for a full range of biases ranging from thermal to shot-noise limits which describe perfectly the results of the Monte Carlo simulations for a nondegenerate electron gas [2]. The magnitude of the noise reduction exceeds 0.01, which is of interest from the point of view of possible applications. Using these analytical results one may estimate a relative contribution to the noise from different groups of carriers (in energy space and/or real space) and to investigate in great detail the correlations between different groups of carriers. This leads us to suggest an electron energy spectroscopy experiment to probe the Coulomb correlations in ballistic conductors. Indeed, while the injected carriers are uncorrelated, those in the volume of the conductor are strongly correlated, as follows from the derived formulas for the fluctuation of the distribution function. Those correlations may be observed experimentally by
Nourhani, Amir; Crespi, Vincent H.; Lammert, Paul E.
2015-06-01
We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected. We present a flexible approach to these processes using bias potential as a control parameter field and a locally-open-circuit reference state, carried through in detail for a spherical motor. While the phenomenological flavor makes meaningful contact with experiment easier, required inputs can also conceivably come from, e.g., Frumkin-Butler-Volmer kinetics. Previously obtained results are recovered in the weak-heterogeneity limit and improved small-basis approximations tailored to structural heterogeneity are presented. Under the assumption of weak inhomogeneity, a scaling form is deduced for motor speed as a function of fuel concentration and swimmer size. We argue that this form should be robust and demonstrate a good fit to experimental data.
A finite element approach to self-consistent field theory calculations of multiblock polymers
Energy Technology Data Exchange (ETDEWEB)
Ackerman, David M. [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States); Delaney, Kris; Fredrickson, Glenn H. [Materials Research Laboratory, University of California, Santa Barbara (United States); Ganapathysubramanian, Baskar, E-mail: baskarg@iastate.edu [Department of Mechanical Engineering, Iowa State University, Ames, IA 50011 (United States)
2017-02-15
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.
Self-consistent field theory for the interactions between keratin intermediate filaments
International Nuclear Information System (INIS)
Akinshina, Anna; Jambon-Puillet, Etienne; Warren, Patrick B; Noro, Massimo G
2013-01-01
Keratins are important structural proteins found in skin, hair and nails. Keratin Intermediate Filaments are major components of corneocytes, nonviable horny cells of the Stratum Corneum, the outermost layer of skin. It is considered that interactions between unstructured domains of Keratin Intermediate Filaments are the key factor in maintaining the elasticity of the skin. We have developed a model for the interactions between keratin intermediate filaments based on self-consistent field theory. The intermediate filaments are represented by charged surfaces, and the disordered terminal domains of the keratins are represented by charged heteropolymers grafted to these surfaces. We estimate the system is close to a charge compensation point where the heteropolymer grafting density is matched to the surface charge density. Using a protein model with amino acid resolution for the terminal domains, we find that the terminal chains can mediate a weak attraction between the keratin surfaces. The origin of the attraction is a combination of bridging and electrostatics. The attraction disappears when the system moves away from the charge compensation point, or when excess small ions and/or NMF-representing free amino acids are added. These results are in concordance with experimental observations, and support the idea that the interaction between keratin filaments, and ultimately in part the elastic properties of the keratin-containing tissue, is controlled by a combination of the physico-chemical properties of the disordered terminal domains and the composition of the medium in the inter-filament region
Self-consistent theory of a harmonic gyroklystron with a minimum Q cavity
International Nuclear Information System (INIS)
Tran, T.M.; Kreischer, K.E.; Temkin, R.J.
1986-01-01
In this paper, the energy extraction stage of the gyroklystron [in Advances in Electronics and Electron Physics, edited by C. Marton (Academic, New York, 1979), Vol. 1, pp. 1--54], with a minimum Q cavity is investigated by using a self-consistent radio-frequency (rf) field model. In the low-field, low-current limit, expressions for the self-consistent field and the resulting energy extraction efficiency are derived analytically for an arbitrary cyclotron harmonic number. To our knowledge, these are the first analytic results for the self-consistent field structure and efficiency of a gyrotron device. The large signal regime analysis is carried out by numerically integrating the coupled self-consistent equations. Several examples in this regime are presented
International Nuclear Information System (INIS)
Schlichting, H.
1985-01-01
We do a linearised mean field calculation in axial gauge for the four dimensional mixed fundamental adjoint SU(2) lattice gauge theory and extract the gluon condensate parameter from the expectation values of the plaquette and the action by subtracting mean field perturbation theory from Monte Carlo data. (orig.)
Martínez-Veracoechea, Francisco J.
2009-03-10
A combination of particle-based simulations and self-consistent field theory (SCFT) is used to study the stabilization of multiple ordered bicontinuous phases in blends of a diblock copolymer (DBC) and a homopolymer. The double-diamond phase (DD) and plumber\\'s nightmare phase (P) were spontaneously formed in the range of homopolymer volume fraction simulated via coarse-grained molecular dynamics. To the best of our knowledge, this is the first time that such phases have been obtained in continuum-space molecular simulations of DBC systems. Though tentative phase boundaries were delineated via free-energy calculations, macrophase separation could not be satisfactorily assessed within the framework of particle-based simulations. Therefore, SCFT was used to explore the DBC/homopolymer phase diagram in more detail, showing that although in many cases two-phase coexistence of a DBC-rich phase and a homopolymer-rich phase does precede the stability of complex bicontinuous phases the DD phase can be stable in a relatively wide region of the phase diagram. Whereas the P phase was always metastable with respect to macrophase separation under the thermodynamic conditions explored with SCFT, it was sometimes nearly stable, suggesting that full stability could be achieved in other unexplored regions of parameter space. Moreover, even the predicted DD- and P-phase metastability regions were located significantly far from the spinodal line, suggesting that these phases could be observed in experiments as "long-lived" metastable phases under those conditions. This conjecture is also consistent with large-system molecular dynamics simulations that showed that the time scale of mesophase formation is much faster than that of macrophase separation. © 2009 American Chemical Society.
Vibrational multiconfiguration self-consistent field theory: implementation and test calculations.
Heislbetz, Sandra; Rauhut, Guntram
2010-03-28
A state-specific vibrational multiconfiguration self-consistent field (VMCSCF) approach based on a multimode expansion of the potential energy surface is presented for the accurate calculation of anharmonic vibrational spectra. As a special case of this general approach vibrational complete active space self-consistent field calculations will be discussed. The latter method shows better convergence than the general VMCSCF approach and must be considered the preferred choice within the multiconfigurational framework. Benchmark calculations are provided for a small set of test molecules.
Self-consistent field theory of protein adsorption in a non-Gaussian polyelectrolyte brush
Biesheuvel, P.M.; Leermakers, F.A.M.; Stuart, M.A.C.
2006-01-01
To describe adsorption of globular protein molecules in a polyelectrolyte brush we use the strong-stretching approximation of the Edwards self-consistent field equation, combined with corrections for a non-Gaussian brush. To describe chemical potentials in this mixture of (globular) species of
Directory of Open Access Journals (Sweden)
L.S. Ferreira
2016-02-01
Full Text Available Proton radioactivity from deformed nuclei is described for the first time by a self-consistent calculation based on covariant relativistic density functionals derived from meson exchange and point coupling models. The calculation provides an important new test to these interactions at the limits of stability, since the mixing of different angular momenta in the single particle wave functions is probed.
Relativistic four-component multiconfigurational self-consistent-field theory for molecules
DEFF Research Database (Denmark)
Jensen, Hans Jørgen Aa; Dyall, Kenneth G.; Saue, Trond
1996-01-01
A formalism for relativistic four-component multiconfigurational self-consistent-field calculations on molecules is presented. The formalism parallels a direct second-order restricted-step algorithm developed for nonrelativistic molecular calculations. The presentation here focuses on the differe......A formalism for relativistic four-component multiconfigurational self-consistent-field calculations on molecules is presented. The formalism parallels a direct second-order restricted-step algorithm developed for nonrelativistic molecular calculations. The presentation here focuses...... the memory used by the largest nonrelativistic calculation in the equivalent basis, due to the complex arithmetic. The feasibility of the calculations is then determined more by the disk space for storage of integrals and N-particle expansion vectors....
Self-consistent field theory based molecular dynamics with linear system-size scaling
Energy Technology Data Exchange (ETDEWEB)
Richters, Dorothee [Institute of Mathematics and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 9, D-55128 Mainz (Germany); Kühne, Thomas D., E-mail: kuehne@uni-mainz.de [Institute of Physical Chemistry and Center for Computational Sciences, Johannes Gutenberg University Mainz, Staudinger Weg 7, D-55128 Mainz (Germany); Technical and Macromolecular Chemistry, University of Paderborn, Warburger Str. 100, D-33098 Paderborn (Germany)
2014-04-07
We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is circumvented by means of a properly modified Langevin equation. The predictive power of the present approach is illustrated using the example of liquid methane under extreme conditions.
Martinez-Veracoechea, Francisco J.; Escobedo, Fernando A.
2009-01-01
Using self-consistent field theory, the Plumber's Nightmare and the double diamond phases are predicted to be stable in a finite region of phase diagrams for blends of AB diblock copolymer (DBC) and A-component homopolymer. To the best of our
Feuz, L.; Leermakers, F.A.M.; Textor, M.; Borisov, O.V.
2008-01-01
The two-gradient version of the Scheutjens¿Fleer self-consistent field (SF-SCF) theory is employed to model the interaction between a molecular bottle brush with a polyelectrolyte backbone and neutral hydrophilic side chains and an oppositely charged surface. Our system mimics graft-copolymers with
Semiclassical approximations in a mean-field theory with collision terms
International Nuclear Information System (INIS)
Galetti, D.
1986-01-01
Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt
International Nuclear Information System (INIS)
Backes, Steffen
2017-04-01
The study of the electronic properties of correlated systems is a very diverse field and has lead to valuable insight into the physics of real materials. In these systems, the decisive factor that governs the physical properties is the ratio between the electronic kinetic energy, which promotes delocalization over the lattice, and the Coulomb interaction, which instead favours localized electronic states. Due to this competition, correlated electronic systems can show unique and interesting properties like the Metal-Insulator transition, diverse phase diagrams, strong temperature dependence and in general a high sensitivity to the environmental conditions. A theoretical description of these systems is not an easy task, since perturbative approaches that do not preserve the competition between the kinetic and interaction terms can only be applied in special limiting cases. One of the most famous approaches to obtain the electronic properties of a real material is the ab initio density functional theory (DFT) method. It allows one to obtain the ground state density of the system under investigation by mapping onto an effective non-interacting system that has to be found self-consistently. While being an exact theory, in practical implementations certain approximations have to be made to the exchange-correlation potential. The local density approximation (LDA), which approximates the exchange-correlation contribution to the total energy by that of a homogeneous electron gas with the corresponding density, has proven quite successful in many cases. Though, this approximation in general leads to an underestimation of electronic correlations and is not able to describe a metal-insulator transition due to electronic localization in the presence of strong Coulomb interaction. A different approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), which is non-perturbative in the kinetic and interaction term but neglects all non
Energy Technology Data Exchange (ETDEWEB)
Backes, Steffen
2017-04-15
The study of the electronic properties of correlated systems is a very diverse field and has lead to valuable insight into the physics of real materials. In these systems, the decisive factor that governs the physical properties is the ratio between the electronic kinetic energy, which promotes delocalization over the lattice, and the Coulomb interaction, which instead favours localized electronic states. Due to this competition, correlated electronic systems can show unique and interesting properties like the Metal-Insulator transition, diverse phase diagrams, strong temperature dependence and in general a high sensitivity to the environmental conditions. A theoretical description of these systems is not an easy task, since perturbative approaches that do not preserve the competition between the kinetic and interaction terms can only be applied in special limiting cases. One of the most famous approaches to obtain the electronic properties of a real material is the ab initio density functional theory (DFT) method. It allows one to obtain the ground state density of the system under investigation by mapping onto an effective non-interacting system that has to be found self-consistently. While being an exact theory, in practical implementations certain approximations have to be made to the exchange-correlation potential. The local density approximation (LDA), which approximates the exchange-correlation contribution to the total energy by that of a homogeneous electron gas with the corresponding density, has proven quite successful in many cases. Though, this approximation in general leads to an underestimation of electronic correlations and is not able to describe a metal-insulator transition due to electronic localization in the presence of strong Coulomb interaction. A different approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), which is non-perturbative in the kinetic and interaction term but neglects all non
Development of mean field theories in nuclear physics and in desordered media
International Nuclear Information System (INIS)
Orland, Henri.
1981-04-01
This work, in two parts, deals with the development of mean field theories in nuclear physics (nuclei in balance and collisions of heavy ions) as well as in disordered media. In the first part, two different ways of tackling the problem of developments around mean field theories are explained. Possessing an approach wave function for the system, the natural idea for including the correlations is to develop the exact wave function of the system around the mean field wave function. The first two chapters show two different ways of dealing with this problem: the perturbative approach - Hartree-Fock equations with two body collisions and functional methods. In the second part: mean field theory for spin glasses. The problem for spin glasses is to construct a physically acceptable mean field theory. The importance of this problem in statistical mechanics is linked to the fact that the mean field theory provides a qualitative description of the low temperature phase and is the starting point needed for using more sophisticated methods (renormalization group). Two approaches to this problem are presented, one based on the Sherrington-Kirkpatrick model and the other based on a model of spins with purely local disorder and competitive interaction between the spins [fr
Self-consistent theory of hadron-nucleus scattering. Application to pion physics
International Nuclear Information System (INIS)
Johnson, M.B.
1981-01-01
The first part of this set of two seminars will consist of a review of several of the important accomplishments made in the last few years in the field of pion-nucleus physics. Next I discuss some questions raised by these accomplishments and show that for some very natural reasons the commonly employed theoretical methods cannot be applied to answer these questions. This situation leads to the idea of self-consistency, which is first explained in a general context. The remainder of the seminars are devoted to illustrating the idea within a simple multiple-scattering model for the case of pion scattering. An evaluation of the effectiveness of the self-consistent requirment to produce a solution to the model is made, and a few of the questions raised by recent accomplishments in the field of pion physics are addressed in the model. Finally, the results of the model calculation are compared to experimental data and implications of the results discussed. (orig./HSI)
Self-consistent cluster theories for alloys with diagonal and off-diagonal disorder
International Nuclear Information System (INIS)
Gonis, A.; Garland, J.W.
1978-01-01
The molecular coherent-potential approximation (MCPA) and other, simpler cluster approximations for disordered alloys are studied both analytically and numerically for alloys with diagonal and off-diagonal disorder (ODD). First, the MCPA for alloys with only diagonal disorder is rederived within the interactor formalism of Blackman, Esterling, and Berk. This formalism, which simplifies the numerical implementation of the MCPA, is then used to generalize the MCPA so as to take account of ODD. It is shown that the analytic properties of the MCPA are preserved under this generalization. Also, two computationally simple cluster approximations, the self-consistent central-site approximation (SCCSA) and the self-consistent boundary-site approximation (SCBSA), are generalized to include the effects of ODD. It is shown that for one-dimensional systems with only nearest-neighbor hopping the SCBSA yields Green's functions which are identical to those given by the MCPA and thus are analytic, even in the presence of ODD. Finally, the results of numerical calculations are reported for one-dimensional systems with only nearest-neighbor hopping but with both diagonal and off-diagonal disorder. These calculations were performed using the single-site approximation of Blackman, Esterling, and Berk and three different cluster approximations: the multishell method previously proposed by the authors, the SCCSA, and the SCBSA. The results of these calculations are compared with exact results and with previous results obtained using the truncated t-matix approximation and the recent method of Kaplan and Gray. These comparisons suggest that the multishell method and the generalization of the SCBSA given in this paper are more efficient and accurate for the calculation of densities of states for systems with ODD. On the other hand, as expected, the SCCSA was found to yield severely nonanalytic results for the values of band parameters used
Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Birgenau, R. J.
1977-01-01
By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...... in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated...
Non-equilibrium mean-field theories on scale-free networks
International Nuclear Information System (INIS)
Caccioli, Fabio; Dall'Asta, Luca
2009-01-01
Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks
Martinez-Veracoechea, Francisco J.
2009-11-24
Using self-consistent field theory, the Plumber\\'s Nightmare and the double diamond phases are predicted to be stable in a finite region of phase diagrams for blends of AB diblock copolymer (DBC) and A-component homopolymer. To the best of our knowledge, this is the first time that the P phase has been predicted to be stable using self-consistent field theory. The stabilization is achieved by tuning the composition or conformational asymmetry of the DBC chain, and the architecture or length of the homopolymer. The basic features of the phase diagrams are the same in all cases studied, suggesting a general type of behavior for these systems. Finally, it is noted that the homopolymer length should be a convenient variable to stabilize bicontinuous phases in experiments. © 2009 American Chemical Society.
DEFF Research Database (Denmark)
Miyagi, Haruhide; Madsen, Lars Bojer
2013-01-01
We present the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory as a framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme...... well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high...
Mean field theories and dual variation mathematical structures of the mesoscopic model
Suzuki, Takashi
2015-01-01
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Self-consistent field theory simulations of polymers on arbitrary domains
Energy Technology Data Exchange (ETDEWEB)
Ouaknin, Gaddiel, E-mail: gaddielouaknin@umail.ucsb.edu [Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070 (United States); Laachi, Nabil; Delaney, Kris [Materials Research Laboratory, University of California, Santa Barbara, CA 93106-5080 (United States); Fredrickson, Glenn H. [Materials Research Laboratory, University of California, Santa Barbara, CA 93106-5080 (United States); Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080 (United States); Department of Materials, University of California, Santa Barbara, CA 93106-5050 (United States); Gibou, Frederic [Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070 (United States); Department of Computer Science, University of California, Santa Barbara, CA 93106-5110 (United States)
2016-12-15
We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refine the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.
Mean field theory of nuclei and shell model. Present status and future outlook
International Nuclear Information System (INIS)
Nakada, Hitoshi
2003-01-01
Many of the recent topics of the nuclear structure are concerned on the problems of unstable nuclei. It has been revealed experimentally that the nuclear halos and the neutron skins as well as the cluster structures or the molecule-like structures can be present in the unstable nuclei, and the magic numbers well established in the stable nuclei disappear occasionally while new ones appear. The shell model based on the mean field approximation has been successfully applied to stable nuclei to explain the nuclear structure as the finite many body system quantitatively and it is considered as the standard model at present. If the unstable nuclei will be understood on the same model basis or not is a matter related to fundamental principle of nuclear structure theories. In this lecture, the fundamental concept and the framework of the theory of nuclear structure based on the mean field theory and the shell model are presented to make clear the problems and to suggest directions for future researches. At first fundamental properties of nuclei are described under the subtitles: saturation and magic numbers, nuclear force and effective interactions, nuclear matter, and LS splitting. Then the mean field theory is presented under subtitles: the potential model, the mean field theory, Hartree-Fock approximation for nuclear matter, density dependent force, semiclassical mean field theory, mean field theory and symmetry, Skyrme interaction and density functional, density matrix expansion, finite range interactions, effective masses, and motion of center of mass. The subsequent section is devoted to the shell model with the subtitles: beyond the mean field approximation, core polarization, effective interaction of shell model, one-particle wave function, nuclear deformation and shell model, and shell model of cross shell. Finally structure of unstable nuclei is discussed with the subtitles: general remark on the study of unstable nuclear structure, asymptotic behavior of wave
Self-consistent theory of steady-state lamellar solidification in binary eutectic systems
International Nuclear Information System (INIS)
Nash, G.E.; Glicksman, M.E.
1976-01-01
The potential theoretic methods developed recently at NRL for solving the diffusion equation are applied to the free-boundary problem describing lamellar eutectic solidification. Using these techniques, the original boundary value problem is reduced to a set of coupled integro-differential equations for the shape of the solid/liquid interface and various quantities defined on the interface. The behavior of the solutions is discussed in a qualitative fashion, leading to some interesting inferences regarding the nature of the eutectic solidification process. Using the information obtained from the analysis referred to above, an approximate theory of the lamellar-rod transition is formulated. The predictions of the theory are shown to be in qualitative agreement with experimental observations of this transition. In addition, a simplified version of the general integro-differential equations is developed and is used to assess the effect of interface curvature on the interfacial solute concentrations, and to check the new theory for consistency with experiment
Mean-field theory of spin-glasses with finite coordination number
Kanter, I.; Sompolinsky, H.
1987-01-01
The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.
Self-consistent DFT +U method for real-space time-dependent density functional theory calculations
Tancogne-Dejean, Nicolas; Oliveira, Micael J. T.; Rubio, Angel
2017-12-01
We implemented various DFT+U schemes, including the Agapito, Curtarolo, and Buongiorno Nardelli functional (ACBN0) self-consistent density-functional version of the DFT +U method [Phys. Rev. X 5, 011006 (2015), 10.1103/PhysRevX.5.011006] within the massively parallel real-space time-dependent density functional theory (TDDFT) code octopus. We further extended the method to the case of the calculation of response functions with real-time TDDFT+U and to the description of noncollinear spin systems. The implementation is tested by investigating the ground-state and optical properties of various transition-metal oxides, bulk topological insulators, and molecules. Our results are found to be in good agreement with previously published results for both the electronic band structure and structural properties. The self-consistent calculated values of U and J are also in good agreement with the values commonly used in the literature. We found that the time-dependent extension of the self-consistent DFT+U method yields improved optical properties when compared to the empirical TDDFT+U scheme. This work thus opens a different theoretical framework to address the nonequilibrium properties of correlated systems.
International Nuclear Information System (INIS)
Bender, C.M.; Cooper, F.
1985-01-01
An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi
A simplified density matrix minimization for linear scaling self-consistent field theory
International Nuclear Information System (INIS)
Challacombe, M.
1999-01-01
A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics
Time-odd mean fields in covariant density functional theory: Rotating systems
International Nuclear Information System (INIS)
Afanasjev, A. V.; Abusara, H.
2010-01-01
Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration, and rotational frequency dependencies of their impact on the moments of inertia have been analyzed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean-field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid-body value. On the contrary, superdeformed and hyperdeformed nuclei have the moments of inertia which are close to rigid-body value. The structure of the currents in rotating frame, their microscopic origin, and the relations to the moments of inertia have been systematically analyzed. The phenomenon of signature separation in odd-odd nuclei, induced by time-odd mean fields, has been analyzed in detail.
DEFF Research Database (Denmark)
Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard
2011-01-01
Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled......-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using Møller-Plesset-type (MP......) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational...
A self-consistent formulation of quantum field theory on S4
International Nuclear Information System (INIS)
Harris, B.A.; Joshi, G.C.
1991-01-01
In this paper, a consistent formulation of field theory on a four-sphere was constructed and a method from which various amplitudes may be calculated is described. The standard results of quantum electrodynamics are derived, providing a valuable check on the validity of this approach, as well as allowing a direct comparison between this and previous work done in the area. It is believed that the matrix element approach offers a new way to deal with some of the more troublesome aspects of previous calculations. In particular one can easily handle the transverse part of the photon propagator which had made the (1 - α) gauge parts difficult to calculate. However the main advantage of this method is the ability to compute functions which involve the contraction of indices across different η integrals. This tends to happen when one has derivative couplings such as those in scalar electrodynamics. 12 refs., 3 figs
Energy Technology Data Exchange (ETDEWEB)
Haertle, Rainer [Institut fuer Theoretische Physik, Georg-August-Universitaet Goettingen, Goettingen (Germany); Millis, Andrew J. [Department of Physics, Columbia University, New York (United States)
2016-07-01
We present a new impurity solver for real-time and nonequilibrium dynamical mean field theory applications, based on the recently developed hierarchical quantum master equation approach. Our method employs a hybridization expansion of the time evolution operator, including an advanced, systematic truncation scheme. Convergence to exact results for not too low temperatures has been demonstrated by a direct comparison to quantum Monte Carlo simulations. The approach is time-local, which gives us access to slow dynamics such as, e.g., in the presence of magnetic fields or exchange interactions and to nonequilibrium steady states. Here, we present first results of this new scheme for the description of strongly correlated materials in the framework of dynamical mean field theory, including benchmark and new results for the Hubbard and periodic Anderson model.
Covariant density functional theory beyond mean field and applications for nuclei far from stability
International Nuclear Information System (INIS)
Ring, P
2010-01-01
Density functional theory provides a very powerful tool for a unified microscopic description of nuclei all over the periodic table. It is not only successful in reproducing bulk properties of nuclear ground states such as binding energies, radii, or deformation parameters, but it also allows the investigation of collective phenomena, such as giant resonances and rotational excitations. However, it is based on the mean field concept and therefore it has its limits. We discuss here two methods based based on covariant density functional theory going beyond the mean field concept, (i) models with an energy dependent self energy allowing the coupling to complex configurations and a quantitative description of the width of giant resonances and (ii) methods of configuration mixing between Slater determinants with different deformation and orientation providing are very successful description of transitional nuclei and quantum phase transitions.
Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel
2013-07-19
We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale T(FL). Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale T(sat). We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above T(FL), in particular the linear-in-T resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements.
Double giant resonances in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Ring, P.; Podobnik, B.
1996-01-01
Collective vibrations in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory (RMFT). Isoscalar quadrupole and isovector dipole oscillations that correspond to giant resonances are studied, and possible excitations of higher modes are investigated. We find evidence for modes which can be interpreted as double resonances. In a quantized RMFT they correspond to two-phonon states. (orig.)
Nonlinear many-body reaction theories from nuclear mean field approximations
International Nuclear Information System (INIS)
Griffin, J.J.
1983-01-01
Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)
Energy Technology Data Exchange (ETDEWEB)
Hahn, Y.K., E-mail: ykhahn22@verizon.net
2014-12-15
The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the
DEFF Research Database (Denmark)
Pedersen, T.G.; Johansen, P.M.
1997-01-01
. The theory provides an explanation for the high long-term stability of the photoinduced anisotropy as well as a theoretical prediction of the temporal behavior of photoinduced birefringence. The theoretical results agree favorably with measurements in the entire range of writing intensities used......A novel mean-field theory of photoinduced reorientation and optical anisotropy in liquid crystalline side-chain polymers is presented and compared with experiments, The reorientation mechanism is based on photoinduced trans cis isomerization and a multidomain model of the material is introduced...
Advances in dynamic and mean field games theory, applications, and numerical methods
Viscolani, Bruno
2017-01-01
This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinar...
Neutron stars in relativistic mean field theory with isovector scalar meson
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M.; Stachniewicz, S. [H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)
1998-03-01
We study the equation of state (EOS) of {beta}-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson (a{sub 0}(980)). A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s}{approx}30 MeV. We find that the quantity most sensitive to the {delta}-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the {delta}-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger {delta}-meson coupling. (author) 8 refs, 6 figs, 2 tabs
Nuclear matter in relativistic mean field theory with isovector scalar meson.
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M. [Institute of Nuclear Physics, Cracow (Poland)
1996-12-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)] is studied. While the {delta}-meson field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to {delta}-field to the nuclear symmetry energy is negative. To fit the empirical value, E{sub s}{approx}30 MeV, a stronger {rho}-meson coupling is required than in absence of the {delta}-field. The energy per particle of neutron star matter is than larger at high densities than the one with no {delta}-field included. Also, the proton fraction of {beta}-stable matter increases. Splitting of proton and neutron effective masses due to the {delta}-field can affect transport properties of neutron star matter. (author). 4 refs, 6 figs.
Neutron stars in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.; Stachniewicz, S.
1996-12-01
We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)]. A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼ 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the δ-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing δmeson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab
Neutron stars in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.; Stachniewicz, S.
1998-01-01
We study the equation of state (EOS) of β-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson (a 0 (980)). A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼30 MeV. We find that the quantity most sensitive to the δ-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the δ-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger δ-meson coupling. (author)
Neutron stars in relativistic mean field theory with isovector scalar meson
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M.; Stachniewicz, S. [Institute of Nuclear Physics, Cracow (Poland)
1996-12-01
We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)]. A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s} {approx} 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the {delta}-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing {delta}meson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab.
Nuclear matter in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.
1996-12-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)] is studied. While the δ-meson field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to δ-field to the nuclear symmetry energy is negative. To fit the empirical value, E s ∼30 MeV, a stronger ρ-meson coupling is required than in absence of the δ-field. The energy per particle of neutron star matter is than larger at high densities than the one with no δ-field included. Also, the proton fraction of β-stable matter increases. Splitting of proton and neutron effective masses due to the δ-field can affect transport properties of neutron star matter. (author). 4 refs, 6 figs
Short-range correlations in an extended time-dependent mean-field theory
International Nuclear Information System (INIS)
Madler, P.
1982-01-01
A generalization is performed of the time-dependent mean-field theory by an explicit inclusion of strong short-range correlations on a level of microscopic reversibility relating them to realistic nucleon-nucleon forces. Invoking a least action principle for correlated trial wave functions, equations of motion for the correlation functions and the single-particle model wave function are derived in lowest order of the FAHT cluster expansion. Higher order effects as well as long-range correlations are consider only to the extent to which they contribute to the mean field via a readjusted phenomenological effective two-body interaction. The corresponding correlated stationary problem is investigated and appropriate initial conditions to describe a heavy ion reaction are proposed. The singleparticle density matrix is evaluated
Jang, Seung Woo; Kotani, Takao; Kino, Hiori; Kuroki, Kazuhiko; Han, Myung Joon
2015-07-24
Despite decades of progress, an understanding of unconventional superconductivity still remains elusive. An important open question is about the material dependence of the superconducting properties. Using the quasiparticle self-consistent GW method, we re-examine the electronic structure of copper oxide high-Tc materials. We show that QSGW captures several important features, distinctive from the conventional LDA results. The energy level splitting between d(x(2)-y(2)) and d(3z(2)-r(2)) is significantly enlarged and the van Hove singularity point is lowered. The calculated results compare better than LDA with recent experimental results from resonant inelastic xray scattering and angle resolved photoemission experiments. This agreement with the experiments supports the previously suggested two-band theory for the material dependence of the superconducting transition temperature, Tc.
Simple Theory for the Dynamics of Mean-Field-Like Models of Glass-Forming Fluids
Szamel, Grzegorz
2017-10-01
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The theory predicts an ergodicity-breaking transition that is identical to the so-called dynamic transition predicted within the replica approach. Thus, it can provide the missing dynamic component of the random first order transition framework. In the large-dimensional limit the theory reproduces the result of a recent exact calculation of Maimbourg et al. [Phys. Rev. Lett. 116, 015902 (2016), 10.1103/PhysRevLett.116.015902]. Our approach provides an alternative, physically motivated derivation of this result.
Conserving gapless mean-field theory for weakly interacting Bose gases
International Nuclear Information System (INIS)
Kita, Takafumi
2006-01-01
This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function Ψ and the Nambu Green's function G for the quasiparticle field. Imposing its stationarity respect to Ψ and G yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: 'conserving' and 'gapless'. The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length a and particle mass m to clarify its basic thermodynamic properties under two complementary conditions of constant density n and constant pressure p. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near T c inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature T c shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case T c increases from the ideal gas value T 0 as T c /T 0 =1+2.33an 1/3 , whereas it decreases in the latter as T c /T 0 =1-3.84a(mp/2πℎ 2 ) 1/5 . Temperature dependences of basic thermodynamic quantities are clarified explicitly. (author)
Reiner, A; Høye, J S
2005-12-01
The hierarchical reference theory and the self-consistent Ornstein-Zernike approximation are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase coexistence and the equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. As a first step towards this goal, we consider the problem of combining the lowest order gamma expansion result for the incorporation of a Fourier component of the interaction with the requirement of consistency between internal and free energies, leaving aside the compressibility relation. For simplicity, we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models. It turns out that the analytically tractable mean spherical approximation is a solution to this problem, as are several of its generalizations. Analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions that any closure to the Ornstein-Zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution. These criteria are expected to remain valid for more general discrete and continuous systems, even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations.
Naturalness of Nonlinear Scalar Self-Couplings in a Relativistic Mean Field Theory for Neutron Stars
International Nuclear Information System (INIS)
Maekawa, Claudio; Razeira, Moises; Vasconcellos, Cesar A. Z.; Dillig, Manfred; Bodmann, Bardo E. J.
2004-01-01
We investigate the role of naturalness in effective field theory. We focus on dense hadronic matter using a generalized relativistic multi-baryon lagrangian density mean field approach which contains nonlinear self-couplings of the σ, δ meson fields and the fundamental baryon octet. We adjust the model parameters to describe bulk static properties of ordinary nuclear matter. Then, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars
One-pion exchange current corrections for nuclear magnetic moments in relativistic mean field theory
International Nuclear Information System (INIS)
Li Jian; Yao, J.M.; Meng Jie; Arima, Akito
2011-01-01
The one-pion exchange current corrections to isoscalar and isovector magnetic moments of double-closed shell nuclei plus and minus one nucleon with A = 15, 17, 39 and 41 have been studied in the relativistic mean field (RMF) theory and compared with previous relativistic and non-relativistic results. It has been found that the one-pion exchange current gives a negligible contribution to the isoscalar magnetic moments but a significant correction to the isovector ones. However, the one-pion exchange current enhances the isovector magnetic moments further and does not improve the corresponding description for the concerned nuclei in the present work. (author)
Pionic atoms, the relativistic mean-field theory and the pion-nucleon scattering lenghts
International Nuclear Information System (INIS)
Goudsmit, P.F.A.; Leisi, H.J.; Matsinos, E.
1991-01-01
Analysing pionic-atom data of isoscalar nuclei within the relativistic mean-field (RMF) theory, we determine the pseudoscalar πNN mixing parameter x=0.24±0.06 (syst.) and the strength of the nuclear scalar meson field for pions, S π =-34±14 (syst.) MeV. We show that these values are compatible with the elementary π-N interaction. Our RMF model provides a solution to the long-standing problem of the s-wave repulsion. (orig.)
Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut
2017-07-01
The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.
Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms
International Nuclear Information System (INIS)
Sugahara, Y.; Toki, H.
1994-01-01
We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))
Mean-field theory of differential rotation in density stratified turbulent convection
Rogachevskii, I.
2018-04-01
A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.
A systematic study of even-even nuclei in the nuclear chart by the relativistic mean field theory
Energy Technology Data Exchange (ETDEWEB)
Sumiyoshi, K.; Hirata, D.; Tanihata, I.; Sugahara, Y.; Toki, H. [Institute of Physical and Chemical Research, Wako, Saitama (Japan)
1997-03-01
We study systematically the properties of nuclei in the whole mass range up to the drip lines by the relativistic mean field (RMF) theory with deformations as a microscopic framework to provide the data of nuclear structure in the nuclear chart. The RMF theory is a phenomenological many-body framework, in which the self-consistent equations for nucleons and mesons are solved with arbitrary deformation, and has a potential ability to provide all the essential information of nuclear structure such as masses, radii and deformations together with single particle states and wave functions from the effective lagrangian containing nuclear interaction. As a first step toward the whole project, we study the ground state properties of even-even nuclei ranging from Z=8 to Z=120 up to the proton and neutron drip lines in the RMF theory. We adopt the parameter set TMA, which has been determined by the experimental masses and charge radii in a wide mass range, for the effective lagrangian of the RMF theory. We take into account the axially symmetric deformation using the constrained method on the quadrupole moment. We provide the properties of all even-even nuclei with all the possible ground state deformations extracted from the deformation energy curves by the constrained calculations. By studying the calculated ground state properties systematically, we aim to explore the general trend of masses, radii and deformations in the whole region of the nuclear chart. We discuss the agreement with experimental data and the predictions such as magicness and triaxial deformations beyond the experimental frontier. (author)
Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.
Chou, Yen-Liang; Ihle, Thomas
2015-02-01
Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.
Orbital effect of the magnetic field in dynamical mean-field theory
Acheche, S.; Arsenault, L.-F.; Tremblay, A.-M. S.
2017-12-01
The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate, and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.
Directory of Open Access Journals (Sweden)
Ying Jiang
2017-02-01
Full Text Available This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials.
Watanabe, Shinji; Miyake, Kazumasa
2018-03-01
The thermal expansion coefficient α and the Grüneisen parameter Γ near the magnetic quantum critical point (QCP) are derived on the basis of the self-consistent renormalization (SCR) theory of spin fluctuations. From the SCR entropy, the specific heat CV, α, and Γ are shown to be expressed in a simple form as CV = Ca - Cb, α = αa + αb, and Γ = Γa + Γb, respectively, where Ci, αi, and Γi (i = a, b) are related with each other. As the temperature T decreases, Ca, αb, and Γb become dominant in CV, α, and Γ, respectively. The inverse susceptibility of spin fluctuation coupled to the volume V in Γb is found to give rise to the divergence of Γ at the QCP for each class of ferromagnetism and antiferromagnetism (AFM) in spatial dimensions d = 3 and 2. This V-dependent inverse susceptibility in αb and Γb contributes to the T dependences of α and Γ, and even affects their criticality in the case of the AFM QCP in d = 2. Γa is expressed as Γ a(T = 0) = - V/T0( {partial T0}/{partial V} )T = 0 with T0 being the characteristic temperature of spin fluctuation, which has an enhanced value in heavy electron systems.
Liang, Yufeng; Vinson, John; Pemmaraju, Sri; Drisdell, Walter S; Shirley, Eric L; Prendergast, David
2017-03-03
Constrained-occupancy delta-self-consistent-field (ΔSCF) methods and many-body perturbation theories (MBPT) are two strategies for obtaining electronic excitations from first principles. Using the two distinct approaches, we study the O 1s core excitations that have become increasingly important for characterizing transition-metal oxides and understanding strong electronic correlation. The ΔSCF approach, in its current single-particle form, systematically underestimates the pre-edge intensity for chosen oxides, despite its success in weakly correlated systems. By contrast, the Bethe-Salpeter equation within MBPT predicts much better line shapes. This motivates one to reexamine the many-electron dynamics of x-ray excitations. We find that the single-particle ΔSCF approach can be rectified by explicitly calculating many-electron transition amplitudes, producing x-ray spectra in excellent agreement with experiments. This study paves the way to accurately predict x-ray near-edge spectral fingerprints for physics and materials science beyond the Bethe-Salpether equation.
DEFF Research Database (Denmark)
Miyagi, Haruhide; Madsen, Lars Bojer
We have developed a new theoretical framework for time-dependent many-electron problems named time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory. The theory generalizes the multicongurational time-dependent Hartree-Fock (MCTDHF) theory by truncating the expansion...
Atomically flat superconducting nanofilms: multiband properties and mean-field theory
Shanenko, A. A.; Aguiar, J. Albino; Vagov, A.; Croitoru, M. D.; Milošević, M. V.
2015-05-01
Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.
Atomically flat superconducting nanofilms: multiband properties and mean-field theory
International Nuclear Information System (INIS)
Shanenko, A A; Aguiar, J Albino; Vagov, A; Croitoru, M D; Milošević, M V
2015-01-01
Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D–2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin–Wagner–Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri–Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg–Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields. (paper)
Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
International Nuclear Information System (INIS)
Yang Xuhua; Sun Bao; Wang Bo; Sun Youxian
2010-01-01
Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper. (general)
Transport in simple liquids and dense gases: kinetic mean-field theory and the KAC limit
International Nuclear Information System (INIS)
Karkheck, J.; Stell, G.; Martina, E.
1982-01-01
Maximization of entropy is used in conjunction with the BBGKY hierarchy to obtain a closed one-particle kinetic equation. For an interparticle potential of hard-sphere core plus smooth attractive tail, this equation contains a hard-core collision integral, identical to that of the revised Enskog theory, plus a mean-field term which is linear in the tail strength. The thermodynamics contained therein leads directly to the now-standard statistical-mechanical methods to construct a state-dependent effective hard-core potential in relation to a more realistic potential. These methods induce an extension of the transport coefficients to the Lennard-Jones potential. Predictions of the resulting transport theory compare very favorably with thermal conductivity and shear viscosity experimental results for real simple liquids and dense gases, and also with molecular dynamics simulation results. Poor agreement between theory and experiment is found for moderately dense and dilute gases. The kinetic theory also contains an entropy functional and an H-theorem is proven. Extension to mixtures is straightforward and the Kac-limit is discussed in detail
Mean field theory of EM algorithm for Bayesian grey scale image restoration
International Nuclear Information System (INIS)
Inoue, Jun-ichi; Tanaka, Kazuyuki
2003-01-01
The EM algorithm for the Bayesian grey scale image restoration is investigated in the framework of the mean field theory. Our model system is identical to the infinite range random field Q-Ising model. The maximum marginal likelihood method is applied to the determination of hyper-parameters. We calculate both the data-averaged mean square error between the original image and its maximizer of posterior marginal estimate, and the data-averaged marginal likelihood function exactly. After evaluating the hyper-parameter dependence of the data-averaged marginal likelihood function, we derive the EM algorithm which updates the hyper-parameters to obtain the maximum likelihood estimate analytically. The time evolutions of the hyper-parameters and so-called Q function are obtained. The relation between the speed of convergence of the hyper-parameters and the shape of the Q function is explained from the viewpoint of dynamics
The mean field theory in EM procedures for blind Markov random field image restoration.
Zhang, J
1993-01-01
A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.
On the binding energy of double Λ hypernuclei in the relativistic mean field theory
International Nuclear Information System (INIS)
Marcos, S.; Lombard, R.J.
1997-01-01
The binding energy of two Λ hyperons bound to a nuclear core is calculated within the relativistic mean field theory. The starting point is a two body relativistic equation of the Breit type suggested by the RMFT, and corrected for the two-particle interaction. The 2 Λ correlation energy is evaluated and the contribution of the δ and φ mesons, acting solely between hyperons, to the bond energy σB ΛΛ of ( ΛΛ ) 6 He, ( ΛΛ ) 10 Be and ( ΛΛ ) 13 B is calculated. Predictions of the ΔB ΛΛ A dependence are made for heavier Λ-hypernuclei. (K.A.)
A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes
International Nuclear Information System (INIS)
Han, Yining; Huang, Shanghui; Yan, Tianying
2014-01-01
The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (C d ). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007J. Phys. Chem. B 111 5545–57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter ξ for the anion/cation volume ratio, besides the ionic compressibility γ in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon ξ = 1, and further reduces to Gouy–Chapman theory in the γ → 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric C d , with the higher peak in C d occurring at positive polarization for the smaller anionic size. At high potential, C d decays asymptotically toward KKBA MFT characterized by γ for the negative polarization, and characterized by ξγ for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher C d , which exceeds that of Gouy–Chapman theory. (paper)
A mean-field theory on the differential capacitance of asymmetric ionic liquid electrolytes.
Han, Yining; Huang, Shanghui; Yan, Tianying
2014-07-16
The size of ions significantly influences the electric double layer structure of room temperature ionic liquid (IL) electrolytes and their differential capacitance (Cd). In this study, we extended the mean-field theory (MFT) developed independently by Kornyshev (2007J. Phys. Chem. B 111 5545-57) and Kilic, Bazant, and Ajdari (2007 Phys. Rev. E 75 021502) (the KKBA MFT) to take into account the asymmetric 1:1 IL electrolytes by introducing an additional parameter ξ for the anion/cation volume ratio, besides the ionic compressibility γ in the KKBA MFT. The MFT of asymmetric ions becomes KKBA MFT upon ξ = 1, and further reduces to Gouy-Chapman theory in the γ → 0 limit. The result of the extended MFT demonstrates that the asymmetric ILs give rise to an asymmetric Cd, with the higher peak in Cd occurring at positive polarization for the smaller anionic size. At high potential, Cd decays asymptotically toward KKBA MFT characterized by γ for the negative polarization, and characterized by ξγ for the positive polarization, with inverse-square-root behavior. At low potential, around the potential of zero charge, the asymmetric ions cause a higher Cd, which exceeds that of Gouy-Chapman theory.
Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials.
Edison, J R; Monson, P A
2013-11-12
We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes.
Dimension of ring polymers in bulk studied by Monte-Carlo simulation and self-consistent theory.
Suzuki, Jiro; Takano, Atsushi; Deguchi, Tetsuo; Matsushita, Yushu
2009-10-14
We studied equilibrium conformations of ring polymers in melt over the wide range of segment number N of up to 4096 with Monte-Carlo simulation and obtained N dependence of radius of gyration of chains R(g). The simulation model used is bond fluctuation model (BFM), where polymer segments bear excluded volume; however, the excluded volume effect vanishes at N-->infinity, and linear polymer can be regarded as an ideal chain. Simulation for ring polymers in melt was performed, and the nu value in the relationship R(g) proportional to N(nu) is decreased gradually with increasing N, and finally it reaches the limiting value, 1/3, in the range of N>or=1536, i.e., R(g) proportional to N(1/3). We confirmed that the simulation result is consistent with that of the self-consistent theory including the topological effect and the osmotic pressure of ring polymers. Moreover, the averaged chain conformation of ring polymers in equilibrium state was given in the BFM. In small N region, the segment density of each molecule near the center of mass of the molecule is decreased with increasing N. In large N region the decrease is suppressed, and the density is found to be kept constant without showing N dependence. This means that ring polymer molecules do not segregate from the other molecules even if ring polymers in melt have the relationship nu=1/3. Considerably smaller dimensions of ring polymers at high molecular weight are due to their inherent nature of having no chain ends, and hence they have less-entangled conformations.
Self-consistent many-body perturbation theory in range-separated density-functional theory
DEFF Research Database (Denmark)
Fromager, Emmanuel; Jensen, Hans Jørgen Aagaard
2008-01-01
effects adequately which, on the other hand, can be described by many-body perturbation theory MBPT. It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short...
Coagulation kinetics beyond mean field theory using an optimised Poisson representation
Energy Technology Data Exchange (ETDEWEB)
Burnett, James [Department of Mathematics, UCL, Gower Street, London WC1E 6BT (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT (United Kingdom)
2015-05-21
Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.
The time-dependent relativistic mean-field theory and the random phase approximation
International Nuclear Information System (INIS)
Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang
2001-01-01
The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained
Relationship between Feshbach's and Green's function theories of the nucleon-nucleus mean field
International Nuclear Information System (INIS)
Capuzzi, F.; Mahaux, C.
1995-01-01
We clarify the relationship and difference between theories of the optical-model potential which had previously been developed in the framework of Feshbach's projection operator approach to nuclear reactions and of Green's function theory, respectively. For definiteness, we consider the nucleon-nucleus system but all results can readily be adapted to the atomic case. The effects of antisymmetrization are properly taken into account. It is shown that one can develop along closely parallel lines the theories of open-quotes holeclose quotes and open-quotes particleclose quotes mean fields. The open-quotes holeclose quotes one-body Hamiltonians describe the single-particle properties of the system formed when one nucleon is taken away from the target ground state, for instance in knockout of pickup processes. The particle one-body Hamiltonians are associated with the system formed when one nucleon is elastically scattered from the ground state, or is added to it by means of stripping reactions. An infinite number of particle, as well as of hole, Hamiltonians are constructed which all yield exactly the same single-particle wave functions. Many open-quotes equivalentclose quotes one-body Hamiltonians can coexist because these operators have a complicated structure: they are nonlocal, complex, and energy-dependent. They do not have the same analytic properties in the complex energy plane. Their real and imaginary parts fulfill dispersion relations which may be different. It is shown that hole and particle Hamiltonians can also be constructed by decomposing any vector of the Hilbert space into two parts which are not orthogonal to one another, in contrast to Feshbach's original theory; one interest of this procedure is that the construction and properties of the corresponding hole Hamiltonian can be justified in a mathematically rigorous way. We exhibit the relationship between the hole and particle Hamiltonians and the open-quotes mass operator.close quotes
International Nuclear Information System (INIS)
Singh, BirBikram; Patra, S. K.; Gupta, Raj K.
2010-01-01
We have studied the (ground-state) cluster radioactive decays within the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta, in Proceedings of the 5th International Conference on Nuclear Reaction Mechanisms, Varenna, edited by E. Gadioli (Ricerca Scientifica ed Educazione Permanente, Milano, 1988), p. 416; S. S. Malik and R. K. Gupta, Phys. Rev. C 39, 1992 (1989)]. The relativistic mean-field (RMF) theory is used to obtain the nuclear matter densities for the double folding procedure used to construct the cluster-daughter potential with M3Y nucleon-nucleon interaction including exchange effects. Following the PCM approach, we have deduced empirically the preformation probability P 0 emp from the experimental data on both the α- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic 208 Pb or its neighboring nuclei as daughters. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the α and heavier clusters in radioactive nuclei. P 0 α(emp) for α decays is almost constant (∼10 -2 -10 -3 ) for all the parent nuclei considered here, and P 0 c(emp) for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for P 0 c(emp) are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.
Nuclear sub-structure in 112–122Ba nuclei within relativistic mean field theory
International Nuclear Information System (INIS)
Bhuyan, M.; Patra, S.K.; Arumugam, P.; Gupta, Raj K.
2011-01-01
Working within the framework of relativistic mean field theory, we study for the first time the clustering structure (nuclear sub-structure) of 112–122 Ba nuclei in an axially deformed cylindrical coordinate. We calculate the individual neutrons and protons density distributions for Ba-isotopes. From the analysis of the clustering configurations in total (neutrons-plus-protons) density distributions for various shapes of both the ground and excited states, we find different sub-structures inside the Ba nuclei considered here. The important step, carried out here for the first time, is the counting of number of protons and neutrons present in the clustering region(s). 12 C is shown to constitute the cluster configuration in prolate-deformed ground-states of 112–116 Ba and oblate-deformed first excited states of 118–122 Ba nuclei. Presence of other lighter clusters such as 2 H, 3 H and nuclei in the neighborhood of N = Z, 14 N, 34–36 Cl, 36 Ar and 42 Ca are also indicated in the ground and excited states of these nuclei. Cases with no cluster configuration are shown for 112–116 Ba in their first and second excited states. All these results are of interest for the observed intermediate-mass-fragments and fusion–fission processes, and the so far unobserved evaporation residues from the decaying Ba* compound nuclei formed in heavy ion reactions. (author)
Energy Technology Data Exchange (ETDEWEB)
Heilmann, D.B.
2007-02-15
The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)
International Nuclear Information System (INIS)
Heilmann, D.B.
2007-02-01
The two-plane HUBBARD model, which is a model for some electronic properties of undoped YBCO superconductors as well as displays a MOTT metal-to-insulator transition and a metal-to-band insulator transition, is studied within Dynamical Mean-Field Theory using HIRSCH-FYE Monte Carlo. In order to find the different transitions and distinguish the types of insulator, we calculate the single-particle spectral densities, the self-energies and the optical conductivities. We conclude that there is a continuous transition from MOTT to band insulator. In the second part, ground state properties of a diagonally disordered HUBBARD model is studied using a generalisation of Path Integral Renormalisation Group, a variational method which can also determine low-lying excitations. In particular, the distribution of antiferromagnetic properties is investigated. We conclude that antiferromagnetism breaks down in a percolation-type transition at a critical disorder, which is not changed appreciably by the inclusion of correlation effects, when compared to earlier studies. Electronic and excitation properties at the system sizes considered turn out to primarily depend on the geometry. (orig.)
Higgs-Yukawa model with higher dimension operators via extended mean field theory
Akerlund, Oscar
2016-01-01
Using Extended Mean Field Theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the Standard Model Higgs sector, and the effect of higher dimension operators. We note that the discussion of vacuum stability is completely modified in the presence of a $\\phi^6$ term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass $M_h=125$ GeV. By taking a $\\phi^6$ interaction in the Higgs potential as a proxy for a UV completion of the Standard Model, the transition becomes stronger and turns first order if the scale of new physics, i.e. the mass of the lightest mediator particle, is around $1.5$ TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.
DEFF Research Database (Denmark)
Bak, Keld L.; Jørgensen, Poul; Jensen, H.J.A.
1992-01-01
A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response of a ref......A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response...... to the full configuration interaction limit. Comparisons are made with state-averaged MCSCF results for MgH2 and finite-difference configuration interaction by perturbation with multiconfigurational zeroth-order wave function reflected by interactive process (CIPSI) results for BH....
Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence
Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen
2018-04-01
The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.
Heald, C.R.; Stolnik, S.; Matteis, De C.; Garnett, M.C.; Illum, L.; Davis, S.S.; Leermakers, F.A.M.
2003-01-01
Self-consistent field (SCF) modelling studies can be used to predict the properties of poly(lactic acid):poly(ethyleneoxide) (PLA:PEG) nanoparticles using the theory developed by Scheutjens and Fleer. Good agreement in the results between experimental and modelled data has been observed previously
Mean-field theory of active electrolytes: Dynamic adsorption and overscreening
Frydel, Derek; Podgornik, Rudolf
2018-05-01
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.
Magnetic moments in present relativistic nuclear theories: a mean-field problem
International Nuclear Information System (INIS)
Desplanques, B.
1986-07-01
We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description. 18 refs
General model of phospholipid bilayers in fluid phase within the single chain mean field theory
Energy Technology Data Exchange (ETDEWEB)
Guo, Yachong; Baulin, Vladimir A. [Departament d’Enginyeria Química, Universitat Rovira i Virgili, Av. dels Paisos Catalans 26, 43007 Tarragona (Spain); Pogodin, Sergey [Institute of Chemical Research of Catalonia, ICIQ, Av. Paisos Catalans 16, 43007 Tarragona (Spain)
2014-05-07
Coarse-grained model for saturated phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsaturated phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equilibrium and mechanical properties of a range of saturated lipid molecules that differ only in length of their hydrophobic tails and unsaturated (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as saturated lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equilibrium area per lipid correspond to experimentally measured values for each lipid, changing linearly with the length of the tail. The model for unsaturated phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estimation of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable estimates for free energies. The proposed model may further be used for studies of mixtures of lipids, small molecule inclusions, interactions of bilayers with embedded proteins.
International Nuclear Information System (INIS)
Naik, S.
1990-01-01
We have developed a mean field theory technique to study the confinement-deconfinement phase transition and chiral symmetry restoring phase transition with dynamical fermions and with finite chemical potential and finite temperature. The approximation scheme concerns the saddle point scenario and large space dimension. The static quark-antiquark potentials are identified from the Wilson loop correlation functions in both the fundamental and the adjoint representation of the gauge group with different temperatures. The difference between the responses of the chemical potential to the fermion number with singlet and non-singlet isospin configuration is found. We compare our results with recent Monte Carlo data. (orig.)
An effective correlated mean-field theory applied in the spin-1/2 Ising ferromagnetic model
Energy Technology Data Exchange (ETDEWEB)
Roberto Viana, J.; Salmon, Octávio R. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); Ricardo de Sousa, J. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil); National Institute of Science and Technology for Complex Systems, Universidade Federal do Amazonas, 3000, Japiim, 69077-000 Manaus, AM (Brazil); Neto, Minos A.; Padilha, Igor T. [Universidade Federal do Amazonas – UFAM, Manaus 69077-000, AM (Brazil)
2014-11-15
We developed a new treatment for mean-field theory applied in spins systems, denominated effective correlated mean-field (ECMF). We apply this theory to study the spin-1/2 Ising ferromagnetic model with nearest-neighbor interactions on a square lattice. We use clusters of finite sizes and study the criticality of the ferromagnetic system, where we obtain a convergence of critical temperature for the value k{sub B}T{sub c}/J≃2.27905±0.00141. Also the behavior of magnetic and thermodynamic properties, using the condition of minimum energy of the physical system is obtained. - Highlights: • We developed spin models to study real magnetic systems. • We study the thermodynamic and magnetic properties of the ferromagnetism. • We enhanced a mean-field theory applied in spins models.
Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.
1999-01-01
We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an
Generator coordinate representation of the time independent mean field theory of collisions
International Nuclear Information System (INIS)
Giraud, B.G.; Lemm, J.; Weiguny, A.; Wierling, A.
1991-01-01
We show how matrix elements of the T-matrix can be easily estimated on a basis of Slater determinants, with a mean field approximation. Linear superpositions of these Slater determinants then generate plane waves, or distorted (Coulomb) waves. This provides physical matrix elements of T
Energy Technology Data Exchange (ETDEWEB)
Lin, Lin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
2013-10-28
We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied by the total potential. They can be viewed as preconditioners for a fixed point iteration. We point out different requirements for constructing preconditioners for insulating and metallic systems respectively, and discuss how to construct preconditioners to keep the convergence rate of the fixed point iteration independent of the size of the atomistic system. We propose a new preconditioner that can treat insulating and metallic system in a unified way. The new preconditioner, which we call an elliptic preconditioner, is constructed by solving an elliptic partial differential equation. The elliptic preconditioner is shown to be more effective in accelerating the convergence of a fixed point iteration than the existing approaches for large inhomogeneous systems at low temperature.
Kinetic mean field theories: Results of energy constraint in maximizing entropy
Stell, G.; Karkheck, J.; Beijeren, H. van
1983-01-01
Structure of liquids and solids; crystallography Classical, semiclassical, and quantum theories of liquid structure Statistical theories of liquid structure - Kinetic and transport theory of fluids; physical properties of gases Kinetic and transport theory
An RVB state with fermionic charges and bosonic spins: Mean field theory
International Nuclear Information System (INIS)
Flensberg, K.; Hedegard, P.; Brix Pedersen, M.
1989-01-01
We consider a representation of the Hubbard model, in which the charge carriers are fermions and the spin carriers are bosons. We show that there exist a mean-field solution with a condensate of spin-singlets and we characterize the low temperature behavior of the quasiparticles. Finally we calculate the tunneling spectrum for a normal metal-RVB state tunnel junction and suggest the tunneling experiment as a probe of the statistics of the RVB quasiparticles. (orig.)
A mean field theory for the cold quark gluon plasma applied to stellar structure
Energy Technology Data Exchange (ETDEWEB)
Fogaca, D. A.; Navarra, F. S.; Franzon, B. [Instituto de Fisica, Universidade de Sao Paulo Rua do Matao, Travessa R, 187, 05508-090 Sao Paulo, SP (Brazil); Horvath, J. E. [Instituto de Astronomia, Geofisica e Ciencias Atmosfericas, Universidade de Sao Paulo, Rua do Matao, 1226, 05508-090, Sao Paulo, SP (Brazil)
2013-03-25
An equation of state based on a mean-field approximation of QCD is used to describe the cold quark gluon plasma and also to study the structure of compact stars. We obtain stellar masses compatible with the pulsar PSR J1614-2230 that was determined to have a mass of (1.97 {+-} 0.04 M{sub Circled-Dot-Operator }), and the corresponding radius around 10-11 km.
Statistical thermodynamics and mean-field theory for the alloy under irradiation model
International Nuclear Information System (INIS)
Kamyshendo, V.
1993-01-01
A generalization of statistical thermodynamics to the open systems case, is discussed, using as an example the alloy-under-irradiation model. The statistical properties of stationary states are described with the use of generalized thermodynamic potentials and 'quasi-interactions' determined from the master equation for micro-configuration probabilities. Methods for resolving this equation are illustrated by the mean-field type calculations of correlators, thermodynamic potentials and phase diagrams for disordered alloys
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Czech Academy of Sciences Publication Activity Database
Anisimov, V.I.; Korotin, D. M.; Korotin, M. A.; Kozhevnikov, A, V.; Kuneš, Jan; Shorikov, A.O.; Skornyakov, S.L.; Streltsov, S. V.
2009-01-01
Roč. 21, č. 7 (2009), 075602/1-075602/7 ISSN 0953-8984 Institutional research plan: CEZ:AV0Z10100521 Keywords : iron pnictide * electronic correlations * dynamical mean-field theory Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.964, year: 2009
Energy Technology Data Exchange (ETDEWEB)
Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Czech Academy of Sciences Publication Activity Database
Kolorenč, Jindřich; Shick, Alexander; Lichtenstein, A.I.
2015-01-01
Roč. 92, č. 8 (2015), "085125-1"-"085125-10" ISSN 1098-0121 R&D Projects: GA ČR GC15-05872J Institutional support: RVO:68378271 Keywords : electronic-structure calculations * dynamical mean-field theory * Mott insulators * actinides * oxides * photoemission Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.736, year: 2014
Kurashige, Yuki; Yanai, Takeshi
2011-09-07
We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics
Suo, Tongchuan; Whitmore, Mark D
2014-11-28
We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a "mushroom" regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ(1/3) scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ(1/3). In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ(1/3). We also compare the results for two different solvents with each other, and with earlier Θ solvent results.
International Nuclear Information System (INIS)
Suo, Tongchuan; Whitmore, Mark D.
2014-01-01
We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a “mushroom” regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ 1/3 scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ 1/3 . In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ 1/3 . We also compare the results for two different solvents with each other, and with earlier Θ solvent results
Fission barriers and asymmetric ground states in the relativistic mean-field theory
International Nuclear Information System (INIS)
Rutz, K.; Reinhard, P.G.; Greiner, W.
1995-01-01
The symmetric and asymmetric fission path for 240 Pu, 232 Th and 226 Ra is investigated within the relativistic mean-field model. Standard parametrizations which are well fitted to nuclear ground-state properties are found to deliver reasonable qualitative and quantitative features of fission, comparable to similar nonrelativistic calculations. Furthermore, stable octupole deformations in the ground states of radium isotopes are investigated. They are found in a series of isotopes, qualitatively in agreement with nonrelativistic models. But the quantitative details differ amongst the models and between the various relativistic parametrizations. (orig.)
Mean-field theory of photoinduced formation of surface reliefs in side-chain azobenzene polymers
DEFF Research Database (Denmark)
Pedersen, Thomas Garm; Johansen, Per Michael; Holme, N.C.R.
1998-01-01
A mean-field model of photoinduced surface reliefs in dye containing side-chain polymers is presented. It is demonstrated that photoinduced ordering of dye molecules subject to anisotropic intermolecular interactions leads to mass transport even when the intensity of the incident light is spatially...... uniform. Theoretical profiles are obtained using a simple variational method and excellent agreement with experimental surface reliefs recorded under various polarization configurations is found. The polarization dependence of both period and shape of the profiles is correctly reproduced by the model....
Energy Technology Data Exchange (ETDEWEB)
Xiao, Xiazi [State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871 (China); CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, BIC-ESAT, Peking University, Beijing 100871 (China); Terentyev, Dmitry [Structural Material Group, Institute of Nuclear Materials Science, SCK CEN, Mol (Belgium); Yu, Long [State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871 (China); Bakaev, A. [Structural Material Group, Institute of Nuclear Materials Science, SCK CEN, Mol (Belgium); Jin, Zhaohui [School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China); Duan, Huiling, E-mail: hlduan@pku.edu.cn [State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871 (China); CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, BIC-ESAT, Peking University, Beijing 100871 (China)
2016-08-15
The thermo-mechanical behavior of non-irradiated (at 223 K, 302 K and 573 K) and neutron irradiated (at 573 K) Fe-2.5Cr, Fe-5Cr and Fe-9Cr alloys is studied by a self-consistent plasticity theory, which consists of constitutive equations describing the contribution of radiation defects at grain level, and the elastic-viscoplastic self-consistent method to obtain polycrystalline behaviors. Attention is paid to two types of radiation-induced defects: interstitial dislocation loops and solute rich clusters, which are believed to be the main sources of hardening in Fe-Cr alloys at medium irradiation doses. Both the hardening mechanism and microstructural evolution are investigated by using available experimental data on microstructures, and implementing hardening rules derived from atomistic data. Good agreement with experimental data is achieved for both the yield stress and strain hardening of non-irradiated and irradiated Fe-Cr alloys by treating dislocation loops as strong thermally activated obstacles and solute rich clusters as weak shearable ones. - Highlights: • A self-consistent plasticity theory is proposed for irradiated Fe-Cr alloys. • Both the irradiation-induced hardening and plastic flow evolution are studied. • Dislocation loops and solute rich clusters are considered as the main defects. • Numerical results of the proposed model match with corresponding experimental data.
International Nuclear Information System (INIS)
Edegger, B.
2007-01-01
We consider the theory of high temperature superconductivity from the viewpoint of a strongly correlated electron system. In particular, we discuss Gutzwiller projected wave functions, which incorporate strong correlations by prohibiting double occupancy in orbitals with strong on-site repulsion. After a general overview on high temperature superconductivity, we discuss Anderson's resonating valence bond (RVB) picture and its implementation by renormalized mean field theory (RMFT) and variational Monte Carlo (VMC) techniques. In the following, we present a detailed review on RMFT and VMC results with emphasis on our recent contributions. Especially, we are interested in spectral features of Gutzwiller-Bogolyubov quasiparticles obtained by extending VMC and RMFT techniques to excited states. We explicitly illustrate this method to determine the quasiparticle weight and provide a comparison with angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). We conclude by summarizing recent successes and by discussing open questions, which must be solved for a thorough understanding of high temperature superconductivity by Gutzwiller projected wave functions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Edegger, B.
2007-08-10
We consider the theory of high temperature superconductivity from the viewpoint of a strongly correlated electron system. In particular, we discuss Gutzwiller projected wave functions, which incorporate strong correlations by prohibiting double occupancy in orbitals with strong on-site repulsion. After a general overview on high temperature superconductivity, we discuss Anderson's resonating valence bond (RVB) picture and its implementation by renormalized mean field theory (RMFT) and variational Monte Carlo (VMC) techniques. In the following, we present a detailed review on RMFT and VMC results with emphasis on our recent contributions. Especially, we are interested in spectral features of Gutzwiller-Bogolyubov quasiparticles obtained by extending VMC and RMFT techniques to excited states. We explicitly illustrate this method to determine the quasiparticle weight and provide a comparison with angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). We conclude by summarizing recent successes and by discussing open questions, which must be solved for a thorough understanding of high temperature superconductivity by Gutzwiller projected wave functions. (orig.)
Finite nucleus Dirac mean field theory and random phase approximation using finite B splines
International Nuclear Information System (INIS)
McNeil, J.A.; Furnstahl, R.J.; Rost, E.; Shepard, J.R.; Department of Physics, University of Maryland, College Park, Maryland 20742; Department of Physics, University of Colorado, Boulder, Colorado 80309)
1989-01-01
We calculate the finite nucleus Dirac mean field spectrum in a Galerkin approach using finite basis splines. We review the method and present results for the relativistic σ-ω model for the closed-shell nuclei 16 O and 40 Ca. We study the convergence of the method as a function of the size of the basis and the closure properties of the spectrum using an energy-weighted dipole sum rule. We apply the method to the Dirac random-phase-approximation response and present results for the isoscalar 1/sup -/ and 3/sup -/ longitudinal form factors of 16 O and 40 Ca. We also use a B-spline spectral representation of the positive-energy projector to evaluate partial energy-weighted sum rules and compare with nonrelativistic sum rule results
Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2001-01-01
We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge...... of the distribution of couplings between the random variables is required, our method adapts to the concrete set of couplings. We show the significance of the approach in two ways: Our approach reproduces replica symmetric results for a wide class of toy models (assuming a nonglassy phase) with given disorder...... distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches....
Parity doubling structure of nucleon at non-zero density in the holographic mean field theory
Directory of Open Access Journals (Sweden)
He Bing-Ran
2014-06-01
Full Text Available We summarize our recent work in which we develope the holographic mean field approach to study the dense baryonic matter in a bottom-up holographic QCD model including baryons and scalar mesons in addition to vector mesons. We first show that, at zero density, the rate of the chiral invariant mass of nucleon is controlled by the ratio of the infrared boundary values of two baryon fields included in the model. Then, at non-zero density, we find that the chiral condensate decreases with the increasing density indicating the partial restoration of the chiral symmetry. Our result shows that the more amount of the proton mass comes from the chiral symmetry breaking, the faster the effective nucleon mass decrease with density.
Mean field theory of epidemic spreading with effective contacts on networks
International Nuclear Information System (INIS)
Wu, Qingchu; Chen, Shufang
2015-01-01
We present a general approach to the analysis of the susceptible-infected-susceptible model with effective contacts on networks, where each susceptible node will be infected with a certain probability only for effective contacts. In the network, each node has a given effective contact number. By using the one-vertex heterogenous mean-field (HMF) approximation and the pair HMF approximation, we obtain conditions for epidemic outbreak on degree-uncorrelated networks. Our results suggest that the epidemic threshold is closely related to the effective contact and its distribution. However, when the effective contact is only dependent of node degree, the epidemic threshold can be established by the degree distribution of networks.
Ogawa, Shun; Yamaguchi, Yoshiyuki Y
2015-06-01
An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two nonclassical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends the universality class of the nonclassical exponents to spatially periodic one-dimensional systems and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.
Borisov, O.V.; Zhulina, E.B.; Leermakers, F.A.M.; Muller, A.H.E.
2011-01-01
We present an overview of statistical thermodynamic theories that describe the self-assembly of amphiphilic ionic/hydrophobic diblock copolymers in dilute solution. Block copolymers with both strongly and weakly dissociating (pH-sensitive) ionic blocks are considered. We focus mostly on structural
Jain, Shekhar; Ginzburg, Valeriy V; Jog, Prasanna; Weinhold, Jeffrey; Srivastava, Rakesh; Chapman, Walter G
2009-07-28
The interaction between two polymer grafted surfaces is important in many applications, such as nanocomposites, colloid stabilization, and polymer alloys. In our previous work [Jain et al., J. Chem. Phys. 128, 154910 (2008)], we showed that interfacial statistical associating fluid density theory (iSAFT) successfully calculates the structure of grafted polymer chains in the absence/presence of a free polymer. In the current work, we have applied this density functional theory to calculate the force of interaction between two such grafted monolayers in implicit good solvent conditions. In particular, we have considered the case where the segment sizes of the free (sigma(f)) and grafted (sigma(g)) polymers are different. The interactions between the two monolayers in the absence of the free polymer are always repulsive. However, in the presence of the free polymer, the force either can be purely repulsive or can have an attractive minimum depending upon the relative chain lengths of the free (N(f)) and grafted polymers (N(g)). The attractive minimum is observed only when the ratio alpha = N(f)/N(g) is greater than a critical value. We find that these critical values of alpha satisfy the following scaling relation: rho(g) square root(N(g)) beta(3) proportional to alpha(-lambda), where beta = sigma(f)/sigma(g) and lambda is the scaling exponent. For beta = 1 or the same segment sizes of the free and grafted polymers, this scaling relation is in agreement with those from previous theoretical studies using self-consistent field theory (SCFT). Detailed comparisons between iSAFT and SCFT are made for the structures of the monolayers and their forces of interaction. These comparisons lead to interesting implications for the modeling of nanocomposite thermodynamics.
DEFF Research Database (Denmark)
Svane, Axel; Christensen, Niels Egede; Gorczyca, I.
2010-01-01
on the basis of the local approximation to density functional theory, although generally overestimated by 0.2–0.3 eV in comparison with experimental gap values. Details of the electronic energies and the effective masses including their pressure dependence are compared with available experimental information....... The band gap of InGaN2 is considerably smaller than what would be expected by linear interpolation implying a significant band gap bowing in InGaN alloys....
International Nuclear Information System (INIS)
Hesse, M.; Birn, J.; Schindler, K.
1990-01-01
A self-consistent two-fluid theory that includes the magnetic field and shear patterns therein is developed to model stationary electrostatic structures with field-aligned potential drops. Shear flow is also included in the theory since this seems to be a prominent feature of the structures of interest. In addition, Ohmic dissipation, a Hall term and pressure gradients in a generalized Ohm's law, modified for cases without quasi-neutrality are included. In the analytic theory, the electrostatic force is balanced by field-aligned pressure gradients, i.e., thermal effects in the direction of the magnetic field, and by pressure gradients and magnetic stresses in the perpendicular direction. Within this theory simple examples of applications are presented to demonstrate the kind of solutions resulting from the model. The results show how the effects of charge separation and shear in the magnetic field and the velocity can be combined to form self-consistent structures such as are found to exist above the aurora, suggested also in association with solar flares
Energy Technology Data Exchange (ETDEWEB)
Bertrand, Thierry [Inst. de Physique Nucleaire, Lyon-1 Univ., 69 - Villeurbanne (France)
1998-12-11
The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum 40 refs., 33 figs., 14 tabs.
Temperature dependence of magnetic anisotropy and magnetostriction: Beyond the mean-field theory
International Nuclear Information System (INIS)
Millev, Y.; Faehnle, M.
1994-05-01
The first nonvanishing magnetic anisotropy coefficient is calculated as a function of temperature for any spin quantum number and all temperatures below the Curie temperature for the case of face-centred cubic symmetry within the random-phase approximation (RPA). A detailed and instructive comparison between the mean-field and the RPA predictions is carried out. The RPA magnetization curves are also given for the first time for spins S>1/2. Most of the theoretical considerations are quite general as regard lattice type and even decoupling scheme and can thus be applied straightforwardly to other cases of interest. The progress reported here has been attained with the help of a new simplified and improved parametric approach and of a recent calculation of the average occupation number of magnons within the RPA. In particular, the new approach makes unnecessary the solving of integral equations so that the proposed procedure is especially simple and practically versatile in applications to any particular anisotropic material. (author). Refs, 6 figs
Effective interactions and mean field theory: from nuclear matter to nuclei
International Nuclear Information System (INIS)
Cochet, B.
2005-07-01
The Skyrme force is a zero-range force that allows the construction of the mean field inside the nucleus in a simple way. Skyrme forces are reasonably predictive but some features of the infinite nuclear matter or the mass of heavy nuclei are not well computed. The aim of this work is to propose an expanded parametrization of the Skyrme force in order to improve its predictive power. The first part is dedicated to the construction of the expansion of the parametrization. We recall how the effective forces are linked to the nucleon-nucleon interaction then we show the limits of the standard Skyrme forces and we propose a relatively natural improvements based on the integration of spin and isospin instabilities. The second part deals with the validation of the model, first by describing infinite nuclear matter then by studying β-balanced nuclear matter which has enabled us to reproduce some features of neutron stars like mass and radius. The computation of properties of nuclei like binding energy, mass, radii depends strongly on the adjustment procedure. (A.C.)
International Nuclear Information System (INIS)
Umar, A.S.; Klein, A.
1986-01-01
A recent formulation of the theory of large amplitude collective motion in the adiabatic limit is applied to a generalized monopole shell model. Numerical calculations are carried out for the three-level model, approximately equivalent to a classical system with two degrees of freedom. Our results go somewhat beyond previous treatments of this system and provide substantiation for the validity of the method, in suitable parameter ranges, as a way of recognizing and decoupling the collective and the non-collective degrees of freedom. (orig.)
International Nuclear Information System (INIS)
Zhang, H.; Rizwan-uddin; Dorning, J.J.
1995-01-01
A diffusion equation-based systematic homogenization theory and a self-consistent dehomogenization theory for fuel assemblies have been developed for use with coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is based on a multiple-scales asymptotic expansion carried out through second order in a small parameter, the ratio of the average diffusion length to the reactor characteristic dimension. By starting from the neutron diffusion equation for a three-dimensional heterogeneous medium and introducing two spatial scales, the development systematically yields an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections and assembly-surface-flux discontinuity factors. The rector eigenvalue 1/k eff is shown to be obtained to the second order in the small parameter, and the heterogeneous diffusion theory flux is shown to be obtained to leading order in that parameter. The latter of these two results provides a natural procedure for the reconstruction of the local fluxes and the determination of pin powers, even though homogenized assemblies are used in the global nodal diffusion calculation
Quasiparticle method in relativistic mean-field theories of nuclear structure
International Nuclear Information System (INIS)
Ai, H.
1988-01-01
In recent years, in order to understand the success of Dirac phenomenology, relativistic Brueckner-Hartree-Fock (RBHF) theory has been developed. This theory is a relativistic many-body theory of nuclear structure. Based upon the RBHF theory, which is characterized as having no free parameters other than those introduced in fitting free-space nucleon-nucleon scattering data, we construct an effective interaction. This interaction, when treated in a relativistic Hartree-Fock approximation, reproduces, rather accurately, the nucleon self-energy in nuclear matter, Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations, and the saturation curves calculated with the full relativistic Brueckner-Hartree-Fock theory. This effective interaction is constructed by adding a number of pseudoparticles to the mesons used to construct one-boson-exchange (OBE) models of the nuclear force. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange, while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation
Linear response in stochastic mean-field theories and the onset of instabilities
International Nuclear Information System (INIS)
Colonna, M.; Chomaz, Ph.
1993-01-01
The small amplitude response of stochastic one-body theories, such as the Boltzmann-Langevin approach is studied. Whereas the two-time correlation function only describes the propagation of fluctuations initially present, the equal-time correlation function is related to the source of stochasticity. For stable systems it yields the Einstein relation, while for unstable systems it determines the growth of the instabilities. These features are illustrated for unstable nuclear matter in two dimensions. (author) 14 refs.; 5 figs
Transport processes in macroscopically disordered media from mean field theory to percolation
Snarskii, Andrei A; Sevryukov, Vladimir A; Morozovskiy, Alexander; Malinsky, Joseph
2016-01-01
This book reflects on recent advances in the understanding of percolation systems to present a wide range of transport phenomena in inhomogeneous disordered systems. Further developments in the theory of macroscopically inhomogeneous media are also addressed. These developments include galvano-electric, thermoelectric, elastic properties, 1/f noise and higher current momenta, Anderson localization, and harmonic generation in composites in the vicinity of the percolation threshold. The book describes how one can find effective characteristics, such as conductivity, dielectric permittivity, magnetic permeability, with knowledge of the distribution of different components constituting an inhomogeneous medium. Considered are a wide range of recent studies dedicated to the elucidation of physical properties of macroscopically disordered systems. Aimed at researchers and advanced students, it contains a straightforward set of useful tools which will allow the reader to derive the basic physical properties of compli...
International Nuclear Information System (INIS)
Lalazissis, G.A.; Ring, P.
1996-01-01
A systematic study of the ground-state properties of even-even rare earth nuclei has been performed in the framework of the Relativistic Mean-Field (RMF) theory using the parameter set NL-SH. Nuclear radii, isotope shifts and deformation properties of the heavier rare-earth nuclei have been obtained, which encompass atomic numbers ranging from Z=60 to Z=70 and include a large range of isospin. It is shown that RMF theory is able to provide a good and comprehensive description of the empirical binding energies of the isotopic chains. At the same time the quadrupole deformations β 2 obtained in the RMF theory are found to be in good agreement with the available empirical values. The theory predicts a shape transition from prolate to oblate for nuclei at neutron number N=78 in all the chains. A further addition of neutrons up to the magic number 82 brings about the spherical shape. For nuclei above N=82, the RMF theory predicts the well-known onset of prolate deformation at about N=88, which saturates at about N=102. The deformation properties display an identical behaviour for all the nuclear chains. A good description of the above deformation transitions in the RMF theory in all the isotopic chains leads to a successful reproduction of the anomalous behaviour of the empirical isotopic shifts of the rare-earth nuclei. The RMF theory exhibits a remarkable success in providing a unified and microscopic description of various empirical data. (orig.)
Kovalenko, Andriy; Gusarov, Sergey
2018-01-31
In this work, we will address different aspects of self-consistent field coupling of computational chemistry methods at different time and length scales in modern materials and biomolecular science. Multiscale methods framework yields dramatically improved accuracy, efficiency, and applicability by coupling models and methods on different scales. This field benefits many areas of research and applications by providing fundamental understanding and predictions. It could also play a particular role in commercialization by guiding new developments and by allowing quick evaluation of prospective research projects. We employ molecular theory of solvation which allows us to accurately introduce the effect of the environment on complex nano-, macro-, and biomolecular systems. The uniqueness of this method is that it can be naturally coupled with the whole range of computational chemistry approaches, including QM, MM, and coarse graining.
Superfluid and insulating phases in an interacting-boson model: mean-field theory and the RPA
International Nuclear Information System (INIS)
Sheshadri, K.; Pandit, R.; Krishnamurthy, H.R.; Ramakrishnan, T.V.
1993-01-01
The bosonic Hubbard model is studied via a simple mean-field theory. At zero temperature, in addition to yielding a phase diagram that is qualitatively correct, namely a superfluid phase for non-integer fillings and a Mott transition from a superfluid to an insulating phase for integer fillings, this theory gives results that are in good agreement with Monte Carlo simulations. In particular, the superfluid fraction obtained as a function of the interaction strength U for both integer and non-integer fillings is close to the simulation results. In all phases the excitation spectra are obtained by using the random phase approximation (RPA): the spectrum has a gap in the insulating phase and is gapless (and linear at small wave vectors) in the superfluid phase. Analytic results are presented in the limits of large U and small superfluid density. Finite-temperature phase diagrams and the Mott-insulator-normal-phase crossover are also described. (orig.)
Ground-state properties of exotic nuclei near Z=40 in the relativistic mean-field theory
International Nuclear Information System (INIS)
Lalazissis, G.A.
1995-01-01
Study of the ground-state properties of Kr, Sr and Zr isotopes has been performed in the framework of the relativistic mean-field (RMF) theory using the recently proposed relativistic parameter set NL-SH. It is shown that the RMF theory provides an unified and excellent description of the binding energies, isotope shifts and deformation properties of nuclei over a large range of isospin in the Z=40 region. It is observed that the RMF theory with the force NL-SH is able to describe the anomalous kinks in isotope shifts in Kr and Sr nuclei, the problem which has hitherto remained unresolved. This is in contrast with the density-dependent Skyrme-Hartree-Fock approach which does not reproduce the behaviour of the isotope shifts about shell closure. On the Zr chain we predict that the isotope shifts exhibit a trend similar to that of the Kr and Sr nuclei. The RMF theory also predicts shape coexistence in heavy Sr isotopes. Several dramatic shape transitions in the isotopic chains are shown to be a general feature of nuclei in this region. A comparison of the properties with the available mass models shows that the results of the RMF theory are generally in accord with the predictions of the finite-range droplet model. ((orig.))
International Nuclear Information System (INIS)
Nishiyama, Seiya; Providencia, Joao da; Komatsu, Takao
2007-01-01
To go beyond perturbative method in terms of variables of collective motion, using infinite-dimensional fermions, we have aimed to construct the self-consistent-field (SCF) theory, i.e., time dependent Hartree-Fock theory on associative affine Kac-Moody algebras along the soliton theory. In this paper, toward such an ultimate goal we will reconstruct a theoretical frame for a υ (external parameter)-dependent SCF method to describe more precisely the dynamics on the infinite-dimensional fermion Fock space. An infinite-dimensional fermion operator is introduced through Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent and a Υ-periodic potential. As an illustration, we derive explicit expressions for the Laurent coefficients of soliton solutions for sl n and for su n on infinite-dimensional Grassmannian. The associative affine Kac-Moody algebras play a crucial role to determine the dynamics on the infinite-dimensional fermion Fock space
International Nuclear Information System (INIS)
Ciofini, Ilaria; Adamo, Carlo; Chermette, Henry
2005-01-01
Corrections to the self-interaction error which is rooted in all standard exchange-correlation functionals in the density functional theory (DFT) have become the object of an increasing interest. After an introduction reminding the origin of the self-interaction error in the DFT formalism, and a brief review of the self-interaction free approximations, we present a simple, yet effective, self-consistent method to correct this error. The model is based on an average density self-interaction correction (ADSIC), where both exchange and Coulomb contributions are screened by a fraction of the electron density. The ansatz on which the method is built makes it particularly appealing, due to its simplicity and its favorable scaling with the size of the system. We have tested the ADSIC approach on one of the classical pathological problem for density functional theory: the direct estimation of the ionization potential from orbital eigenvalues. A large set of different chemical systems, ranging from simple atoms to large fullerenes, has been considered as test cases. Our results show that the ADSIC approach provides good numerical values for all the molecular systems, the agreement with the experimental values increasing, due to its average ansatz, with the size (conjugation) of the systems
Energy Technology Data Exchange (ETDEWEB)
Typel, S; Wolter, H H [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D
2001-07-01
In this work, we introduce a method to reduce the microscopic mean-field theory to a classical macroscopic dynamics at the initial stage of fusion reaction. We show that TDHF (Time-dependent Hartree-Fock) could be a useful tool to infer information on the fusion barrier as well as on one-body dissipation effect. We apply the reduction of information to the case of head-on reaction between a {sup 16}O and {sup 16,22,24,28}O in order to quantify the effect of neutron skin on fusion. We show that the precise determination of fusion barrier requires, in addition to the relative distance between center of mass, the introduction of an additional collective coordinate that explicitly breaks the neutron-proton symmetry. With this additional collective variable, we obtain a rather precise determination of the barrier position, height and diffuseness as well as one-body friction. (author)
Kleeorin, N.
2018-06-01
We discuss a mean-field theory of the generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale non-uniform flow is produced due to either a combined action of a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known as a vorticity dynamo) due to a combined effect of the large-scale shear and Reynolds stress-induced generation of the mean vorticity. The latter is due to the effect of large-scale shear on the Reynolds stress. A fast rotation suppresses this large-scale instability.
Directory of Open Access Journals (Sweden)
Seiya Nishiyama
2009-01-01
Full Text Available The maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a collective submanifold in which a canonicity condition makes the collective variables to be an orthogonal coordinate-system. For this aim we adopt a concept of curvature unfamiliar in the conventional time-dependent (TD self-consistent field (SCF theory. Our basic idea lies in the introduction of a sort of Lagrange manner familiar to fluid dynamics to describe a collective coordinate-system. This manner enables us to take a one-form which is linearly composed of a TD SCF Hamiltonian and infinitesimal generators induced by collective variable differentials of a canonical transformation on a group. The integrability condition of the system read the curvature C = 0. Our method is constructed manifesting itself the structure of the group under consideration. To go beyond the maximaly-decoupled method, we have aimed to construct an SCF theory, i.e., υ (external parameter-dependent Hartree-Fock (HF theory. Toward such an ultimate goal, the υ-HF theory has been reconstructed on an affine Kac-Moody algebra along the soliton theory, using infinite-dimensional fermion. An infinite-dimensional fermion operator is introduced through a Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent potential with a Υ-periodicity. A bilinear equation for the υ-HF theory has been transcribed onto the corresponding τ-function using the regular representation for the group and the Schur-polynomials. The υ-HF SCF theory on an infinite-dimensional Fock space F∞ leads to a dynamics on an infinite-dimensional Grassmannian Gr∞ and may describe more precisely such a dynamics on the group manifold. A finite-dimensional Grassmannian is identified with a Gr
International Nuclear Information System (INIS)
Fradera, J.; Cuesta-López, S.
2013-01-01
Highlights: • The work presented in this manuscript provides a reliable computational tool to quantify the He complex phenomena in a HCLL. • A model based on the self-consistent nucleation theory (SCT) is exposed. It includes radiation induced nucleation modelling and surface tension corrections. • Results informed reinforce the necessity of conducting experiments to determine nucleation conditions and bubble transport parameters in LM breeders. • Our findings and model provide a good qualitative insight into the helium nucleation phenomenon in LM systems for fusion technology and can be used to identify key system parameters. -- Abstract: Helium (He) nucleation in liquid metal breeding blankets of a DT fusion reactor may have a significant impact regarding system design, safety and operation. Large He production rates are expected due to tritium (T) fuel self-sufficiency requirement, as both, He and T, are produced at the same rate. Low He solubility, local high concentrations, radiation damage and fluid discontinuities, among other phenomena, may yield the necessary conditions for He nucleation. Hence, He nucleation may have a significant impact on T inventory and may lower the T breeding ratio. A model based on the self-consistent nucleation theory (SCT) with a surface tension curvature correction model has been implemented in OpenFOAM ® CFD code. A modification through a single parameter of the necessary nucleation condition is proposed in order to take into account all the nucleation triggering phenomena, specially radiation induced nucleation. Moreover, the kinetic growth model has been adapted so as to allow for the transition from a critical cluster to a macroscopic bubble with a diffusion growth process. Limitations and capabilities of the models are shown by means of zero-dimensional simulations and sensitivity analyses to key parameters under HCLL breeding unit conditions. Results provide a good qualitative insight into the helium nucleation
Energy Technology Data Exchange (ETDEWEB)
Fradera, J., E-mail: jfradera@ubu.es; Cuesta-López, S., E-mail: scuesta@ubu.es
2013-12-15
Highlights: • The work presented in this manuscript provides a reliable computational tool to quantify the He complex phenomena in a HCLL. • A model based on the self-consistent nucleation theory (SCT) is exposed. It includes radiation induced nucleation modelling and surface tension corrections. • Results informed reinforce the necessity of conducting experiments to determine nucleation conditions and bubble transport parameters in LM breeders. • Our findings and model provide a good qualitative insight into the helium nucleation phenomenon in LM systems for fusion technology and can be used to identify key system parameters. -- Abstract: Helium (He) nucleation in liquid metal breeding blankets of a DT fusion reactor may have a significant impact regarding system design, safety and operation. Large He production rates are expected due to tritium (T) fuel self-sufficiency requirement, as both, He and T, are produced at the same rate. Low He solubility, local high concentrations, radiation damage and fluid discontinuities, among other phenomena, may yield the necessary conditions for He nucleation. Hence, He nucleation may have a significant impact on T inventory and may lower the T breeding ratio. A model based on the self-consistent nucleation theory (SCT) with a surface tension curvature correction model has been implemented in OpenFOAM{sup ®} CFD code. A modification through a single parameter of the necessary nucleation condition is proposed in order to take into account all the nucleation triggering phenomena, specially radiation induced nucleation. Moreover, the kinetic growth model has been adapted so as to allow for the transition from a critical cluster to a macroscopic bubble with a diffusion growth process. Limitations and capabilities of the models are shown by means of zero-dimensional simulations and sensitivity analyses to key parameters under HCLL breeding unit conditions. Results provide a good qualitative insight into the helium
International Nuclear Information System (INIS)
Niez, Jean-Jacques
2010-01-01
This work aims to obtain the effective dielectric constant tensor of a warm plasma in the spirit of the derivation of a mixing law. The medium is made of non point-like ions immersed in an electron gas with usual conditions relating the various lengths which define the problem. In this paper the ion dielectric constants are taken from their RPA responses as developed in a previous paper [1]. Furthermore the treatment of the screening effects is made through a mathematical redefinition of the initial problem as proposed in Ref. [1]. Here the complete calculation of the T-matrix describing the scattering of an electromagnetic wave on an isolated ion immersed in an 'effective medium' is given. It is used for building , in the spirit of a mixing law, a self-consistent effective medium theory for the plasma dielectric tensor. We then extend the results obtained in Ref. [1] to higher orders in ion or dielectric inclusion densities. The techniques presented are generic and can be used in areas such as elasticity, thermoelasticity, and piezoelectricity.
Surface incompressibility from semiclassical relativistic mean field calculations
International Nuclear Information System (INIS)
Patra, S.K.; Centelles, M.; Vinas, X.; Estal, M. del
2002-01-01
By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility K A has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of K A for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made
Self-consistent areas law in QCD
International Nuclear Information System (INIS)
Makeenko, Yu.M.; Migdal, A.A.
1980-01-01
The problem of obtaining the self-consistent areas law in quantum chromodynamics (QCD) is considered from the point of view of the quark confinement. The exact equation for the loop average in multicolor QCD is reduced to a bootstrap form. Its iterations yield new manifestly gauge invariant perturbation theory in the loop space, reproducing asymptotic freedom. For large loops, the areas law apprears to be a self-consistent solution
Cai, Chunhua; Zhang, Liangshun; Lin, Jiaping; Wang, Liquan
2008-10-09
We investigated, both experimentally and theoretically, the self-assembly behaviors of pH- and thermosensitive poly(L-glutamic acid)- b-poly(propylene oxide)-b-poly(L-glutamic acid) (PLGA-b-PPO-b-PLGA) triblock copolymers in aqueous solution by means of transmission electron microscopy (TEM), scanning electron microscopy (SEM), dynamic light scattering (DLS), circular dichroism (CD), and self-consistent field theory (SCFT) simulations. Vesicles were observed when the hydrophilic PLGA block length is shorter or the pH value of solution is lower. The vesicles were found to transform to spherical micelles when the PLGA block length increases or its conformation changes from helix to coil with increasing the pH value. In addition, increasing temperature gives rise to a decrease in the size of aggregates, which is related to the dehydration of the PPO segments at higher temperatures. The SCFT simulation results show that the vesicles transform to the spherical micelles with increasing the fraction or statistical length of A block in model ABA triblock copolymer, which corresponds to the increase in the PLGA length or its conformation change from helix to coil in experiments, respectively. The SCFT calculations also provide chain distribution information in the aggregates. On the basis of both experimental and SCFT results, the mechanism of the structure change of the PLGA- b-PPO- b-PLGA aggregates was proposed.
Delange, Pascal; Backes, Steffen; van Roekeghem, Ambroise; Pourovskii, Leonid; Jiang, Hong; Biermann, Silke
2018-04-01
The most intriguing properties of emergent materials are typically consequences of highly correlated quantum states of their electronic degrees of freedom. Describing those materials from first principles remains a challenge for modern condensed matter theory. Here, we review, apply and discuss novel approaches to spectral properties of correlated electron materials, assessing current day predictive capabilities of electronic structure calculations. In particular, we focus on the recent Screened Exchange Dynamical Mean-Field Theory scheme and its relation to generalized Kohn-Sham Theory. These concepts are illustrated on the transition metal pnictide BaCo2As2 and elemental zinc and cadmium.
International Nuclear Information System (INIS)
Hasegawa, Hideo
2003-01-01
A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E 67, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of N-unit neurons, each of which is expressed by coupled K-dimensional differential equations (DEs), are assumed to be subject to spatially correlated white noises. The original KN-dimensional stochastic DEs have been replaced by K(K+2)-dimensional deterministic DEs expressed in terms of means and the second-order moments of local and global variables: the fourth-order contributions are taken into account by the Gaussian decoupling approximation. Our DMA has been applied to an ensemble of Hodgkin-Huxley (HH) neurons (K=4), for which effects of the noise, the coupling strength, and the ensemble size on the response to a single-spike input have been investigated. Numerical results calculated by the DMA theory are in good agreement with those obtained by direct simulations, although the former computation is about a thousand times faster than the latter for a typical HH neuron ensemble with N=100
Schoen, Martin; Haslam, Andrew J; Jackson, George
2017-10-24
The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.
International Nuclear Information System (INIS)
Rafelski, J.
1979-01-01
After an introductory overview of the bag model the author uses the self-consistent solution of the coupled Dirac-meson fields to represent a bound state of strongly ineteracting fermions. In this framework he discusses the vivial approach to classical field equations. After a short description of the used numerical methods the properties of bound states of scalar self-consistent Fields and the solutions of a self-coupled Dirac field are considered. (HSI) [de
Kwadrin, A.; Koenderink, A.F.
2014-01-01
Metasurfaces and metamaterials promise arbitrary rerouting of light using two-dimensional (2D) planar arrangements of electric and magnetic scatterers, respectively, 3D stacks built out of such 2D planes. An important problem is how to self-consistently model the response of these systems in a
Grabska-Barwińska, Agnieszka; Latham, Peter E
2014-06-01
We use mean field techniques to compute the distribution of excitatory and inhibitory firing rates in large networks of randomly connected spiking quadratic integrate and fire neurons. These techniques are based on the assumption that activity is asynchronous and Poisson. For most parameter settings these assumptions are strongly violated; nevertheless, so long as the networks are not too synchronous, we find good agreement between mean field prediction and network simulations. Thus, much of the intuition developed for randomly connected networks in the asynchronous regime applies to mildly synchronous networks.
van Roekeghem, Ambroise; Richard, Pierre; Shi, Xun; Wu, Shangfei; Zeng, Lingkun; Saparov, Bayrammurad; Ohtsubo, Yoshiyuki; Qian, Tian; Sefat, Athena S.; Biermann, Silke; Ding, Hong
2016-06-01
We present a study of the tetragonal to collapsed-tetragonal transition of CaFe2As2 using angle-resolved photoemission spectroscopy and dynamical mean field theory-based electronic structure calculations. We observe that the collapsed-tetragonal phase exhibits reduced correlations and a higher coherence temperature due to the stronger Fe-As hybridization. Furthermore, a comparison of measured photoemission spectra and theoretical spectral functions shows that momentum-dependent corrections to the density functional band structure are essential for the description of low-energy quasiparticle dispersions. We introduce those using the recently proposed combined "screened exchange + dynamical mean field theory" scheme.
Energy Technology Data Exchange (ETDEWEB)
Matsuzaki, M. [Fukuoka Univ. of Education, Dept. of Physics, Munakata, Fukuoka (Japan); Tanigawa, T.
1999-08-01
We propose a simple method to reproduce the {sup 1}S{sub 0} pairing properties of nuclear matter, which are obtained by a sophisticated model, by introducing a density-independent cutoff into the relativistic mean field model. This applies well to the physically relevant density range. (author)
International Nuclear Information System (INIS)
Saperstein, E.E.
1992-01-01
The influence of the detailed behavior of the nuclear densities on the Glauber-theory description of hadron-nucleus scattering is discussed in connection with the problem of determination of elementary hadron-nucleon amplitudes from such analysis. Arguments are given in favor of using the self-consistent FFS nuclear densities for this purpose. 20 refs., 6 figs
Mean-field theory for the Tsub(c2)-minimum in the phase diagram of Ersub(1-x)Hosub(x)Rh4B4
International Nuclear Information System (INIS)
Schuh, B.; Grewe, N.
1981-01-01
The experimentally observed shape of the phase boundary between the superconducting and the ferromagnetically ordered state in the reentrant ferromagnetic superconductor compound Ersub(1-x)Hosub(x)Rh 4 B 4 is explained within a simple Ginsburg-Landau mean field theory as resulting from a competition of two order parameters corresponding to the magnetic Ho- and Er-moments respectively. (author)
International Nuclear Information System (INIS)
Hazeltine, R.D.
1988-12-01
The boundary layer arising in the radial vicinity of a tokamak limiter is examined, with special reference to the TEXT tokamak. It is shown that sheath structure depends upon the self-consistent effects of ion guiding-center orbit modification, as well as the radial variation of E /times/ B-induced toroidal rotation. Reasonable agreement with experiment is obtained from an idealized model which, however simplified, preserves such self-consistent effects. It is argued that the radial sheath, which occurs whenever confining magnetic field-lines lie in the plasma boundary surface, is an object of some intrinsic interest. It differs from the more familiar axial sheath because magnetized charges respond very differently to parallel and perpendicular electric fields. 11 refs., 1 fig
Athreya, C. N.; Mukilventhan, A.; Suwas, Satyam; Vedantam, Srikanth; Subramanya Sarma, V.
2018-04-01
The influence of the mode of deformation on recrystallisation behaviour of Ti was studied by experiments and modelling. Ti samples were deformed through torsion and rolling to the same equivalent strain of 0.5. The deformed samples were annealed at different temperatures for different time durations and the recrystallisation kinetics were compared. Recrystallisation is found to be faster in the rolled samples compared to the torsion deformed samples. This is attributed to the differences in stored energy and number of nuclei per unit area in the two modes of deformation. Considering decay in stored energy during recrystallisation, the grain boundary mobility was estimated through a mean field model. The activation energy for recrystallisation obtained from experiments matched with the activation energy for grain boundary migration obtained from mobility calculation. A multi-phase field model (with mobility estimated from the mean field model as a constitutive input) was used to simulate the kinetics, microstructure and texture evolution. The recrystallisation kinetics and grain size distributions obtained from experiments matched reasonably well with the phase field simulations. The recrystallisation texture predicted through phase field simulations compares well with experiments though few additional texture components are present in simulations. This is attributed to the anisotropy in grain boundary mobility, which is not accounted for in the present study.
Self-consistency in Capital Markets
Benbrahim, Hamid
2013-03-01
Capital Markets are considered, at least in theory, information engines whereby traders contribute to price formation with their diverse perspectives. Regardless whether one believes in efficient market theory on not, actions by individual traders influence prices of securities, which in turn influence actions by other traders. This influence is exerted through a number of mechanisms including portfolio balancing, margin maintenance, trend following, and sentiment. As a result market behaviors emerge from a number of mechanisms ranging from self-consistency due to wisdom of the crowds and self-fulfilling prophecies, to more chaotic behavior resulting from dynamics similar to the three body system, namely the interplay between equities, options, and futures. This talk will address questions and findings regarding the search for self-consistency in capital markets.
International Nuclear Information System (INIS)
Perez-Moreno, Javier; Hung, Sheng-Ting; Kuzyk, Mark G.; Zhou, Juefei; Ramini, Shiva K.; Clays, Koen
2011-01-01
We show that a combination of linear absorption spectroscopy, hyper-Rayleigh scattering, and a theoretical analysis using sum rules to reduce the size of the parameter space leads to a prediction of the imaginary part of the second hyperpolarizability of the dye AF-455 that agrees with the experimental data gathered through two-photon absorption spectroscopy. Our procedure, which demands self-consistency between several measurement techniques and does not use adjustable parameters, provides a means for determining transition moments between the dominant excited states based strictly on experimental characterization. This is made possible by our new approach that uses sum rules and molecular symmetry to rigorously reduce the number of required physical quantities.
Energy Technology Data Exchange (ETDEWEB)
Speck, Thomas [Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz (Germany); Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut [Institut für Theoretische Physik II, Heinrich-Heine-Universität, D-40225 Düsseldorf (Germany)
2015-06-14
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
The emission of heavy clusters described in the mean-field HFB theory: the case of 242Cm
International Nuclear Information System (INIS)
Robledo, L.M.; Warda, M.
2008-01-01
The emission of a nucleus of 34 Si by the parent 96 242 Cm is a process in the diffuse borderline between cluster emission and standard mass asymmetric fission. In this paper we analyze in a microscopic framework such process using the standard mean field techniques used to describe cluster emission. They include Hartree-Fock-Bogoliubov constrained calculations with the Gogny D1S interaction and the octupole moment operator as the collective coordinate to describe the process. Collective masses and all kind of zero point energy corrections are considered which allows for a parameter free estimation of the process' half-life. The agreement with experiment is quite satisfactory. (author)
Configuration mixing of mean-field states
International Nuclear Information System (INIS)
Bender, M; Heenen, P-H
2005-01-01
Starting from self-consistent mean-field models, we discuss how to include correlations from fluctuations in collective degrees of freedom through symmetry restoration and configuration mixing, which give access to ground-state correlations and collective excitations. As an example for the method, we discuss the spectroscopy of neutron-deficient Pb isotopes
Gomes, Diogo A.
2014-01-06
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Gomes, Diogo A.
2014-01-01
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
International Nuclear Information System (INIS)
Ertaş, Mehmet; Keskin, Mustafa
2012-01-01
The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.
Energy Technology Data Exchange (ETDEWEB)
Ertaş, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2012-07-23
The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.
International Nuclear Information System (INIS)
Marumori, T.; Sakata, F.; Maskawa, T.; Une, T.; Hashimoto, Y.
1983-01-01
The main purpose of this paper is to develop a full quantum theory, which is capable by itself of determining a ''maximally-decoupled'' collective motion. The paper is divided into two parts. In the first part, the motivation and basic idea of the theory are explained, and the ''maximal-decoupling condition'' on the collective motion is formulated within the framework of the time-dependent Hartree-Fock theory, in a general form called the invariance principle of the (time-dependent) Schrodinger equation. In the second part, it is shown that when the author positively utilize the invariance principle, we can construct a full quantum theory of the ''maximally-decoupled'' collective motion. This quantum theory is shown to be a generalization of the kinematical boson-mapping theories so far developed, in such a way that the dynamical ''maximal-decoupling condition'' on the collective motion is automatically satisfied
International Nuclear Information System (INIS)
Goodwin, Zachary A.H.; Feng, Guang; Kornyshev, Alexei A.
2017-01-01
We develop the theory of the electrical double layer in ionic liquids as proposed earlier by Kornyshev (2007). In the free energy function we keep the so called ‘short-range correlation terms’ which were omitted there. With some simplifying assumptions, we arrive at a modified expression for differential capacitance, which makes differential capacitance curves less sharply depending on electrode potential and having smaller values at extrema than in the previous theory. This brings the results closer to typical experimental observations, and makes it appealing to use this formalism for treatment of experimental data. Implications on Debye length and the extent of ion paring in ionic liquids are then briefly discussed.
Ziaei, Vafa; Bredow, Thomas
2018-05-01
An accurate theoretical prediction of ionization potential (IP) and electron affinity (EA) is key in understanding complex photochemical processes in aqueous environments. There have been numerous efforts in literature to accurately predict IP and EA of liquid water, however with often conflicting results depending on the level of theory and the underlying water structures. In a recent study based on hybrid-non-self-consistent many-body perturbation theory (MBPT) Gaiduk et al (2018 Nat. Commun. 9 247) predicted an IP of 10.2 eV and EA of 0.2 eV, resulting in an electronic band gap (i.e. electronic gap (IP-EA) as measured by photoelectron spectroscopy) of about 10 eV, redefining the widely cited experimental gap of 8.7 eV in literature. In the present work, we show that GW self-consistency and an implicit vertex correction in MBPT considerably affect recently reported EA values by Gaiduk et al (2018 Nat. Commun. 9 247) by about 1 eV. Furthermore, the choice of pseudo-potential is critical for an accurate determination of the absolute band positions. Consequently, the self-consistent GW approach with an implicit vertex correction based on projector augmented wave (PAW) method on top of quantum water structures predicts an IP of 10.2, an EA of 1.1, a fundamental gap of 9.1 eV and an exciton binding (Eb) energy of 0.9 eV for the first absorption band of liquid water via the Bethe–Salpeter equation (BSE). Only within such a self-consistent approach a simultanously accurate prediction of IP, EA, Eg, Eb is possible.
Energy Technology Data Exchange (ETDEWEB)
Burrola-Gándara, L. A., E-mail: andres.burrola@gmail.com; Santillan-Rodriguez, C. R.; Rivera-Gomez, F. J.; Saenz-Hernandez, R. J.; Botello-Zubiate, M. E.; Matutes-Aquino, J. A. [Departamento de Física de Materiales, Centro de Investigación en Materiales Avanzados, S.C., Miguel de Cervantes 120, Complejo Industrial Chihuahua, Chihuahua 31109 (Mexico)
2015-05-07
Magnetocaloric materials with second order phase transition near the Curie temperature can be described by critical phenomena theory. In this theory, scaling, universality, and renormalization are key concepts from which several phase transition order criteria are derived. In this work, the rescaled universal curve, Banerjee and mean field theory criteria were used to make a comparison for several magnetocaloric materials including pure Gd, SmCo{sub 1.8}Fe{sub 0.2}, MnFeP{sub 0.46}As{sub 0.54}, and La{sub 0.7}Ca{sub 0.15}Sr{sub 0.15}MnO{sub 3}. Pure Gd, SmCo{sub 1.8}Fe{sub 0.2}, and La{sub 0.7}Ca{sub 0.15}Sr{sub 0.15}MnO{sub 3} present a collapse of the rescaled magnetic entropy change curves into a universal curve, which indicates a second order phase transition; applying Banerjee criterion to H/σ vs σ{sup 2} Arrot plots and the mean field theory relation |ΔS{sub M}| ∝ (μ{sub 0}H/T{sub c}){sup 2/3} for the same materials also determines a second order phase transition. However, in the MnFeP{sub 0.46}As{sub 0.54} sample, the Banerjee criterion applied to the H/σ vs σ{sup 2} Arrot plot indicates a first order magnetic phase transition, while the mean field theory prediction for a second order phase transition, |ΔS{sub M}| ∝ (μ{sub 0}H/T{sub c}){sup 2/3}, describes a second order behavior. Also, a mixture of first and second order behavior was indicated by the rescaled universal curve criterion. The diverse results obtained for each criterion in MnFeP{sub 0.46}As{sub 0.54} are apparently related to the magnetoelastic effect and to the simultaneous presence of weak and strong magnetism in Fe (3f) and Mn (3g) alternate atomic layers, respectively. The simultaneous application of the universal curve, the Banerjee and the mean field theory criteria has allowed a better understanding about the nature of the order of the phase transitions in different magnetocaloric materials.
International Nuclear Information System (INIS)
Quinn, C.M.; Schwartz, M.E.
1981-01-01
The chemistry of large systems such as clusters may be readily investigated by valence-electron theories based on model potentials, but such an approach does not allow for the examination of core-electron binding energies which are commonly measured experimentally for such systems. Here we merge our previously developed Gaussian based valence-electron model potential theory with all-electron ab initio theory to allow for the calculation of core orbital binding energies when desired. For the atoms whose cores are to be examined, we use the real nuclear changes, all of the electrons, and the appropriate many-electron basis sets. For the rest of the system we use reduced nuclear charges, the Gaussian based model potentials, only the valence electrons, and appropriate valence-electron basis sets. Detailed results for neutral Al 2 are presented for the cases of all-electron, mixed real--model, and model--model SCF--MO calculations. Several different all-electron and valence electron calculations have been done to test the use of the model potential per se, as well as the effect of basis set choice. The results are in all cases in excellent agreement with one another. Based on these studies, a set of ''double-zeta'' valence and all-electron basis functions have been used for further SCF--MO studies on Al 3 , Al 4 , AlNO, and OAl 3 . For a variety of difference combinations of real and model atoms we find excellent agreement for relative total energies, orbital energies (both core and valence), and Mulliken atomic populations. Finally, direct core-hole-state ionic calculations are reported in detail for Al 2 and AlNO, and noted for Al 3 and Al 4 . Results for corresponding frozen-orbital energy differences, relaxed SCF--MO energy differences, and relaxation energies are in all cases in excellent agreement (never differing by more than 0.07 eV, usually by somewhat less). The study clearly demonstrates the accuracy of the mixed real--model theory
Biroli, G.; Kotliar, G.
2004-01-01
We reply to the comment by K. Aryanpour, Th. Maier and M. Jarrell (cond-mat/0301460) on our paper (Phys. Rev. B {\\bf 65} 155112 (2002)). We demonstrate using general arguments and explicit examples that whenever the correlation length is finite, local observables converge exponentially fast in the cluster size, $L_{c}$, within Cellular Dynamical Mean Field Theory (CDMFT). This is a faster rate of convergence than the $1/L_{c}^{2}$ behavior of the Dynamical Cluster approximation (DCA) thus ref...
Energy Technology Data Exchange (ETDEWEB)
Yokogawa, D., E-mail: d.yokogawa@chem.nagoya-u.ac.jp [Department of Chemistry, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602 (Japan); Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Chikusa, Nagoya 464-8602 (Japan)
2016-09-07
Theoretical approach to design bright bio-imaging molecules is one of the most progressing ones. However, because of the system size and computational accuracy, the number of theoretical studies is limited to our knowledge. To overcome the difficulties, we developed a new method based on reference interaction site model self-consistent field explicitly including spatial electron density distribution and time-dependent density functional theory. We applied it to the calculation of indole and 5-cyanoindole at ground and excited states in gas and solution phases. The changes in the optimized geometries were clearly explained with resonance structures and the Stokes shift was correctly reproduced.
International Nuclear Information System (INIS)
Kita, Takafumi
2009-01-01
Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure to construct such approximations systematically by using either an exact relation for the interaction energy or the Hugenholtz-Pines relation to express the thermodynamic potential in a Luttinger-Ward form. Inspection of the self-consistent perturbation expansion up to the third order with respect to the interaction shows that the two relations yield a unique identical result at each order, reproducing the conserving-gapless mean-field theory [T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005)] as the lowest-order approximation. The uniqueness implies that the series becomes exact when infinite terms are retained. We also derive useful expressions for the entropy and superfluid density in terms of Green's function and a set of real-time dynamical equations to describe thermalization of the condensate.
Quasiparticle self-consistent GW method for the spectral properties of complex materials.
Bruneval, Fabien; Gatti, Matteo
2014-01-01
The GW approximation to the formally exact many-body perturbation theory has been applied successfully to materials for several decades. Since the practical calculations are extremely cumbersome, the GW self-energy is most commonly evaluated using a first-order perturbative approach: This is the so-called G 0 W 0 scheme. However, the G 0 W 0 approximation depends heavily on the mean-field theory that is employed as a basis for the perturbation theory. Recently, a procedure to reach a kind of self-consistency within the GW framework has been proposed. The quasiparticle self-consistent GW (QSGW) approximation retains some positive aspects of a self-consistent approach, but circumvents the intricacies of the complete GW theory, which is inconveniently based on a non-Hermitian and dynamical self-energy. This new scheme allows one to surmount most of the flaws of the usual G 0 W 0 at a moderate calculation cost and at a reasonable implementation burden. In particular, the issues of small band gap semiconductors, of large band gap insulators, and of some transition metal oxides are then cured. The QSGW method broadens the range of materials for which the spectral properties can be predicted with confidence.
Edison, John R; Monson, Peter A
2013-06-21
This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)]. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Bauso, Dario
2014-01-06
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Mean-field approach to unconventional superconductivity
International Nuclear Information System (INIS)
Sacks, William; Mauger, Alain; Noat, Yves
2014-01-01
Highlights: • A model Hamiltonian for unconventional superconductivity (SC) is proposed. • The pseudogap (PG) state is described in terms of pair fluctuations. • SC coherence is restored by a new pair–pair interaction, which counteracts fluctuations. • Given the temperature dependence of the parameters, the SC to PG transition is examined. • The theory fits the ‘peak–dip–hump’ features of cuprate and pnictide excitation spectra. - Abstract: We propose a model that connects the quasiparticle spectral function of high-T c superconductors to the condensation energy. Given the evidence for pair correlations above T c , we consider a coarse-grain Hamiltonian of fluctuating pairs describing the incoherent pseudogap (PG) state, together with a novel pair–pair interaction term that restores long-range superconducting (SC) coherence below T c . A mean-field solution then leads to a self-consistent gap equation containing the new pair–pair coupling. The corresponding spectral function A(k,E) reveals the characteristic peak–dip–hump features of cuprates, now observed on iron pnictides (LiFeAs). The continuous transition from SC to PG states is discussed
Self-consistent model of confinement
International Nuclear Information System (INIS)
Swift, A.R.
1988-01-01
A model of the large-spatial-distance, zero--three-momentum, limit of QCD is developed from the hypothesis that there is an infrared singularity. Single quarks and gluons do not propagate because they have infinite energy after renormalization. The Hamiltonian formulation of the path integral is used to quantize QCD with physical, nonpropagating fields. Perturbation theory in the infrared limit is simplified by the absence of self-energy insertions and by the suppression of large classes of diagrams due to vanishing propagators. Remaining terms in the perturbation series are resummed to produce a set of nonlinear, renormalizable integral equations which fix both the confining interaction and the physical propagators. Solutions demonstrate the self-consistency of the concepts of an infrared singularity and nonpropagating fields. The Wilson loop is calculated to provide a general proof of confinement. Bethe-Salpeter equations for quark-antiquark pairs and for two gluons have finite-energy solutions in the color-singlet channel. The choice of gauge is addressed in detail. Large classes of corrections to the model are discussed and shown to support self-consistency
Quasi-Particle Self-Consistent GW for Molecules.
Kaplan, F; Harding, M E; Seiler, C; Weigend, F; Evers, F; van Setten, M J
2016-06-14
We present the formalism and implementation of quasi-particle self-consistent GW (qsGW) and eigenvalue only quasi-particle self-consistent GW (evGW) adapted to standard quantum chemistry packages. Our implementation is benchmarked against high-level quantum chemistry computations (coupled-cluster theory) and experimental results using a representative set of molecules. Furthermore, we compare the qsGW approach for five molecules relevant for organic photovoltaics to self-consistent GW results (scGW) and analyze the effects of the self-consistency on the ground state density by comparing calculated dipole moments to their experimental values. We show that qsGW makes a significant improvement over conventional G0W0 and that partially self-consistent flavors (in particular evGW) can be excellent alternatives.
Cattes, Stefanie M.; Gubbins, Keith E.; Schoen, Martin
2016-05-01
In this work, we employ classical density functional theory (DFT) to investigate for the first time equilibrium properties of a Heisenberg fluid confined to nanoscopic slit pores of variable width. Within DFT pair correlations are treated at modified mean-field level. We consider three types of walls: hard ones, where the fluid-wall potential becomes infinite upon molecular contact but vanishes otherwise, and hard walls with superimposed short-range attraction with and without explicit orientation dependence. To model the distance dependence of the attractions, we employ a Yukawa potential. The orientation dependence is realized through anchoring of molecules at the substrates, i.e., an energetic discrimination of specific molecular orientations. If the walls are hard or attractive without specific anchoring, the results are "quasi-bulk"-like in that they can be linked to a confinement-induced reduction of the bulk mean field. In these cases, the precise nature of the walls is completely irrelevant at coexistence. Only for specific anchoring nontrivial features arise, because then the fluid-wall interaction potential affects the orientation distribution function in a nontrivial way and thus appears explicitly in the Euler-Lagrange equations to be solved for minima of the grand potential of coexisting phases.
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, BP. 63, 46000 Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Mounkachi, O.; El Moussaoui, H. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco)
2014-06-01
Self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the MnSe lattice. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn lattices. Magnetic moments considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The zero-field high temperature static susceptibility series of the spin −4.28 nearest-neighbor Ising model on face centered cubic (fcc) and lattices is thoroughly analyzed by means of a power series coherent anomaly method (CAM). The exchange interaction between the magnetic atoms and the Néel temperature are deduced using the mean filed and HTSEs theories. - Highlights: • Ab initio calculations are used to investigate both electronic and magnetic properties of the MnSe alloys. • Obtained data from ab initio calculations are used as input for the HTSEs. • The Néel temperature is obtained for MnSe alloys.
Knolle, Johannes; Bhattacharjee, Subhro; Moessner, Roderich
2018-04-01
We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the K -J -Γ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material α -RuCl3 in the light of the results from this extended parton theory.
Quantum mean-field approximations for nuclear bound states and tunneling
International Nuclear Information System (INIS)
Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge
1979-01-01
A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems
Harrison, R. G.
2015-07-01
A mean-field positive-feedback (PFB) theory of ferromagnetism is used to explain the origin of Barkhausen noise (BN) and to show why it is most pronounced in the irreversible regions of the hysteresis loop. By incorporating the ABBM-Sablik model of BN into the PFB theory, we obtain analytical solutions that simultaneously describe both the major hysteresis loop and, by calculating separate expressions for the differential susceptibility in the irreversible and reversible regions, the BN power response at all points of the loop. The PFB theory depends on summing components of the applied field, in particular, the non-monotonic field-magnetization relationship characterizing hysteresis, associated with physical processes occurring in the material. The resulting physical model is then validated by detailed comparisons with measured single-peak BN data in three different steels. It also agrees with the well-known influence of a demagnetizing field on the position and shape of these peaks. The results could form the basis of a physics-based method for modeling and understanding the significance of the observed single-peak (and in multi-constituent materials, multi-peak) BN envelope responses seen in contemporary applications of BN, such as quality control in manufacturing, non-destructive testing, and monitoring the microstructural state of ferromagnetic materials.
Bradas, James C.; Fennelly, Alphonsus J.; Smalley, Larry L.
1987-01-01
It is shown that a generalized (or 'power law') inflationary phase arises naturally and inevitably in a simple (Bianchi type-I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved stress-energy-momentum tensor with the spin density of Ray and Smalley (1982, 1983). This is made explicit by an analytical solution of the field equations of motion of the fluid variables. The inflation is caused by the angular kinetic energy density due to spin. The model further elucidates the relationship between fluid vorticity, the angular velocity of the inertially dragged tetrads, and the precession of the principal axes of the shear ellipsoid. Shear is not effective in damping the inflation.
International Nuclear Information System (INIS)
Kimura, M.; Kawabe, H.; Nishikawa, K.; Aono, S.
1986-01-01
Ordered phases such as CDW, SDW, and the singlet superconductivity(SSC) are predicted by means of a mean field theory. The electronic Hamiltonian is linearized by introducing order parameters which are expected to arise, and these order parameters are determined self-consistently. The behaviors of gap, transition temperature, and condensation energy are greatly different from those of BCS theory. The coexistence of the various phases is discussed. Aside from a very special case the single phase is most stable
International Nuclear Information System (INIS)
Bissbort, Ulf; Hofstetter, Walter; Thomale, Ronny
2010-01-01
We discuss the stochastic mean-field theory (SMFT) method, which is a new approach for describing disordered Bose systems in the thermodynamic limit including localization and dimensional effects. We explicate the method in detail and apply it to the disordered Bose-Hubbard model at finite temperature, with on-site box disorder, as well as experimentally relevant unbounded speckle disorder. We find that disorder-induced condensation and re-entrant behavior at constant filling are only possible at low temperatures, beyond the reach of current experiments [M. Pasienski, D. McKay, M. White, and B. DeMarco, e-print arXiv:0908.1182]. Including off-diagonal hopping disorder as well, we investigate its effect on the phase diagram in addition to pure on-site disorder. To make connection to present experiments on a quantitative level, we also combine SMFT with an LDA approach and obtain the condensate fraction in the presence of an external trapping potential.
Mean-field approximation minimizes relative entropy
International Nuclear Information System (INIS)
Bilbro, G.L.; Snyder, W.E.; Mann, R.C.
1991-01-01
The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach
Yang, Yang; Yu, Haibo; York, Darrin; Cui, Qiang; Elstner, Marcus
2007-10-25
The standard self-consistent-charge density-functional-tight-binding (SCC-DFTB) method (Phys. Rev. B 1998, 58, 7260) is derived by a second-order expansion of the density functional theory total energy expression, followed by an approximation of the charge density fluctuations by charge monopoles and an effective damped Coulomb interaction between the atomic net charges. The central assumptions behind this effective charge-charge interaction are the inverse relation of atomic size and chemical hardness and the use of a fixed chemical hardness parameter independent of the atomic charge state. While these approximations seem to be unproblematic for many covalently bound systems, they are quantitatively insufficient for hydrogen-bonding interactions and (anionic) molecules with localized net charges. Here, we present an extension of the SCC-DFTB method to incorporate third-order terms in the charge density fluctuations, leading to chemical hardness parameters that are dependent on the atomic charge state and a modification of the Coulomb scaling to improve the electrostatic treatment within the second-order terms. These modifications lead to a significant improvement in the description of hydrogen-bonding interactions and proton affinities of biologically relevant molecules.
Maurer, Reinhard J; Reuter, Karsten
2013-07-07
Accurate and efficient simulation of excited state properties is an important and much aspired cornerstone in the study of adsorbate dynamics on metal surfaces. To this end, the recently proposed linear expansion Δ-self-consistent field method by Gavnholt et al. [Phys. Rev. B 78, 075441 (2008)] presents an efficient alternative to time consuming quasi-particle calculations. In this method, the standard Kohn-Sham equations of density-functional theory are solved with the constraint of a non-equilibrium occupation in a region of Hilbert-space resembling gas-phase orbitals of the adsorbate. In this work, we discuss the applicability of this method for the excited-state dynamics of metal-surface mounted organic adsorbates, specifically in the context of molecular switching. We present necessary advancements to allow for a consistent quality description of excited-state potential-energy surfaces (PESs), and illustrate the concept with the application to Azobenzene adsorbed on Ag(111) and Au(111) surfaces. We find that the explicit inclusion of substrate electronic states modifies the topologies of intra-molecular excited-state PESs of the molecule due to image charge and hybridization effects. While the molecule in gas phase shows a clear energetic separation of resonances that induce isomerization and backreaction, the surface-adsorbed molecule does not. The concomitant possibly simultaneous induction of both processes would lead to a significantly reduced switching efficiency of such a mechanism.
Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi
2015-07-01
In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl- + CH3Cl → ClCH3 + Cl-) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.
International Nuclear Information System (INIS)
Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi
2015-01-01
In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein–Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple S N 2 reaction (Cl − + CH 3 Cl → ClCH 3 + Cl − ) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF
Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi
2015-07-07
In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.
Self-consistent electrodynamic scattering in the symmetric Bragg case
International Nuclear Information System (INIS)
Campos, H.S.
1988-01-01
We have analyzed the symmetric Bragg case, introducing a model of self consistent scattering for two elliptically polarized beams. The crystal is taken as a set of mathematical planes, each of them defined by a surface density of dipoles. We have considered the mesofield and the epifield differently from that of the Ewald's theory and, we assumed a plane of dipoles and the associated fields as a self consistent scattering unit. The exact analytical treatment when applied to any two neighbouring planes, results in a general and self consistent Bragg's equation, in terms of the amplitude and phase variations. The generalized solution for the set of N planes was obtained after introducing an absorption factor in the incident radiation, in two ways: (i) the analytical one, through a rule of field similarity, which says that the incidence occurs in both faces of the all crystal planes and also, through a matricial development with the Chebyshev polynomials; (ii) using the numerical solution we calculated, iteratively, the reflectivity, the reflection phase, the transmissivity, the transmission phase and the energy. The results are showed through reflection and transmission curves, which are characteristics as from kinematical as dynamical theories. The conservation of the energy results from the Ewald's self consistency principle is used. In the absorption case, the results show that it is not the only cause for the asymmetric form in the reflection curves. The model contains basic elements for a unified, microscope, self consistent, vectorial and exact formulation for interpretating the X ray diffraction in perfect crystals. (author)
Self-consistent asset pricing models
Malevergne, Y.; Sornette, D.
2007-08-01
We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alphas and betas of the factor model are unobservable. Self-consistency leads to renormalized betas with zero effective alphas, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value αi at the origin between an asset i's return and the proxy's return. Self-consistency also introduces “orthogonality” and “normality” conditions linking the betas, alphas (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from January 1990 to February 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the self-consistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the
Ma, Manman; Xu, Zhenli
2014-12-28
Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.
Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media
Energy Technology Data Exchange (ETDEWEB)
Ma, Manman, E-mail: mmm@sjtu.edu.cn; Xu, Zhenli, E-mail: xuzl@sjtu.edu.cn [Department of Mathematics, Institute of Natural Sciences, and MoE Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240 (China)
2014-12-28
Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.
Energy Technology Data Exchange (ETDEWEB)
Liu, Zhaosen, E-mail: liuzhsnj@yahoo.com [Nanjing University of Information Science and Technology, Department of Applied Physics (China); Ian, Hou, E-mail: houian@umac.mo [University of Macau, Institute of Applied Physics and Materials Engineering, FST (China)
2016-01-15
We give a theoretical study on the magnetic properties of monolayer nanodisks with both Heisenberg exchange and Dzyaloshinsky–Moriya (DM) interactions. In particular, we survey the magnetic effects caused by anisotropy, external magnetic field, and disk size when DM interaction is present by means of a new quantum simulation method facilitated by a self-consistent algorithm based on mean field theory. This computational approach finds that uniaxial anisotropy and transversal magnetic field enhance the net magnetization as well as increase the transition temperature of the vortical phase while preserving the chiralities of the swirly magnetic structures, whereas when the strength of DM interaction is sufficiently strong for a given disk size, magnetic domains appear within the circularly bounded region, which vanish and give in to a single vortex when a transversal magnetic field is applied. The latter confirms the magnetic skyrmions induced by the magnetic field as observed in the experiments.
Self-consistent one-gluon exchange in soliton bag models
International Nuclear Information System (INIS)
Dodd, L.R.; Adelaide Univ.; Williams, A.G.
1988-01-01
The treatment of soliton bag models as two-point boundary value problems is extended to include self-consistent one-gluon exchange interactions. The colour-magnetic contribution to the nucleon-delta mass splitting is calculated self-consistently in the mean-field, one-gluon-exchange approximation for the Friedberg-Lee and Nielsen-Patkos models. Small glueball mass parameters (m GB ∝ 500 MeV) are favoured. Comparisons with previous calculations are made. (orig.)
Kutepov, A L
2015-08-12
Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ1 from the first-order perturbation theory, and the exact vertex Γ(E)). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. The results obtained with the exact vertex are directly related to the present open question-which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on perturbation theory (PT) systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric
Mean Field Type Control with Congestion
Energy Technology Data Exchange (ETDEWEB)
Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France)
2016-06-15
We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.
Self-consistent gravitational self-force
International Nuclear Information System (INIS)
Pound, Adam
2010-01-01
I review the problem of motion for small bodies in general relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed. I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body's past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long time scales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.
Mean-field models and superheavy elements
International Nuclear Information System (INIS)
Reinhard, P.G.; Bender, M.; Maruhn, J.A.; Frankfurt Univ.
2001-03-01
We discuss the performance of two widely used nuclear mean-field models, the relativistic mean-field theory (RMF) and the non-relativistic Skyrme-Hartree-Fock approach (SHF), with particular emphasis on the description of superheavy elements (SHE). We provide a short introduction to the SHF and RMF, the relations between these two approaches and the relations to other nuclear structure models, briefly review the basic properties with respect to normal nuclear observables, and finally present and discuss recent results on the binding properties of SHE computed with a broad selection of SHF and RMF parametrisations. (orig.)
Mean Field Games with a Dominating Player
Energy Technology Data Exchange (ETDEWEB)
Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)
2016-08-15
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.
Mean field games for cognitive radio networks
Tembine, Hamidou
2012-06-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.
Correlations and self-consistency in pion scattering. II
International Nuclear Information System (INIS)
Johnson, M.B.; Keister, B.D.
1978-01-01
In an attempt to overcome certain difficulties of summing higher order processes in pion multiple scattering theories, a new, systematic expansion for the interaction of a pion in nuclear matter is derived within the context of the Foldy-Walecka theory, incorporating nucleon-nucleon correlations and an idea of self-consistency. The first two orders in the expansion are evaluated as a function of the nonlocality range; the expansion appears to be rapidly converging, in contrast to expansion schemes previously examined. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Mukherji, Debashish; Stuehn, Torsten; Kremer, Kurt [Max-Planck Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz (Germany); Marques, Carlos M. [Max-Planck Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz (Germany); Institut Charles Sadron, Université de Strasbourg, CNRS, Strasbourg (France)
2015-03-21
Smart polymers are a modern class of polymeric materials that often exhibit unpredictable behavior in mixtures of solvents. One such phenomenon is co-non-solvency. Co-non-solvency occurs when two (perfectly) miscible and competing good solvents, for a given polymer, are mixed together. As a result, the same polymer collapses into a compact globule within intermediate mixing ratios. More interestingly, polymer collapses when the solvent quality remains good and even gets increasingly better by the addition of the better cosolvent. This is a puzzling phenomenon that is driven by strong local concentration fluctuations. Because of the discrete particle based nature of the interactions, Flory-Huggins type mean field arguments become unsuitable. In this work, we extend the analysis of the co-non-solvency effect presented earlier [D. Mukherji et al., Nat. Commun. 5, 4882 (2014)]. We explain why co-non-solvency is a generic phenomenon, which can only be understood by the thermodynamic treatment of the competitive displacement of (co)solvent components. This competition can result in a polymer collapse upon improvement of the solvent quality. Specific chemical details are not required to understand these complex conformational transitions. Therefore, a broad range of polymers are expected to exhibit similar reentrant coil-globule-coil transitions in competing good solvents.
International Nuclear Information System (INIS)
Mukherji, Debashish; Stuehn, Torsten; Kremer, Kurt; Marques, Carlos M.
2015-01-01
Smart polymers are a modern class of polymeric materials that often exhibit unpredictable behavior in mixtures of solvents. One such phenomenon is co-non-solvency. Co-non-solvency occurs when two (perfectly) miscible and competing good solvents, for a given polymer, are mixed together. As a result, the same polymer collapses into a compact globule within intermediate mixing ratios. More interestingly, polymer collapses when the solvent quality remains good and even gets increasingly better by the addition of the better cosolvent. This is a puzzling phenomenon that is driven by strong local concentration fluctuations. Because of the discrete particle based nature of the interactions, Flory-Huggins type mean field arguments become unsuitable. In this work, we extend the analysis of the co-non-solvency effect presented earlier [D. Mukherji et al., Nat. Commun. 5, 4882 (2014)]. We explain why co-non-solvency is a generic phenomenon, which can only be understood by the thermodynamic treatment of the competitive displacement of (co)solvent components. This competition can result in a polymer collapse upon improvement of the solvent quality. Specific chemical details are not required to understand these complex conformational transitions. Therefore, a broad range of polymers are expected to exhibit similar reentrant coil-globule-coil transitions in competing good solvents
Self-consistent modelling of ICRH
International Nuclear Information System (INIS)
Hellsten, T.; Hedin, J.; Johnson, T.; Laxaaback, M.; Tennfors, E.
2001-01-01
The performance of ICRH is often sensitive to the shape of the high energy part of the distribution functions of the resonating species. This requires self-consistent calculations of the distribution functions and the wave-field. In addition to the wave-particle interactions and Coulomb collisions the effects of the finite orbit width and the RF-induced spatial transport are found to be important. The inward drift dominates in general even for a symmetric toroidal wave spectrum in the centre of the plasma. An inward drift does not necessarily produce a more peaked heating profile. On the contrary, for low concentrations of hydrogen minority in deuterium plasmas it can even give rise to broader profiles. (author)
Non linear self consistency of microtearing modes
International Nuclear Information System (INIS)
Garbet, X.; Mourgues, F.; Samain, A.
1987-01-01
The self consistency of a microtearing turbulence is studied in non linear regimes where the ergodicity of the flux lines determines the electron response. The current which sustains the magnetic perturbation via the Ampere law results from the combines action of the radial electric field in the frame where the island chains are static and of the thermal electron diamagnetism. Numerical calculations show that at usual values of β pol in Tokamaks the turbulence can create a diffusion coefficient of order ν th p 2 i where p i is the ion larmor radius and ν th the electron ion collision frequency. On the other hand, collisionless regimes involving special profiles of each mode near the resonant surface seem possible
Self-consistent velocity dependent effective interactions
International Nuclear Information System (INIS)
Kubo, Takayuki; Sakamoto, Hideo; Kammuri, Tetsuo; Kishimoto, Teruo.
1993-09-01
The field coupling method is extended to a system with a velocity dependent mean potential. By means of this method, we can derive the effective interactions which are consistent with the mean potential. The self-consistent velocity dependent effective interactions are applied to the microscopic analysis of the structures of giant dipole resonances (GDR) of 148,154 Sm, of the first excited 2 + states of Sn isotopes and of the first excited 3 - states of Mo isotopes. It is clarified that the interactions play crucial roles in describing the splitting of the resonant structure of GDR peaks, in restoring the energy weighted sum rule values, and in reducing B (Eλ) values. (author)
International Nuclear Information System (INIS)
Lino, A.T.; Takahashi, E.K.; Leite, J.R.; Ferraz, A.C.
1988-01-01
The band structure of metallic sodium is calculated, using for the first time the self-consistent field variational cellular method. In order to implement the self-consistency in the variational cellular theory, the crystal electronic charge density was calculated within the muffin-tin approximation. The comparison between our results and those derived from other calculations leads to the conclusion that the proposed self-consistent version of the variational cellular method is fast and accurate. (author) [pt
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Shapes and dynamics from the time-dependent mean field
International Nuclear Information System (INIS)
Stevenson, P.D.; Goddard, P.M.; Rios, A.
2015-01-01
Explaining observed properties in terms of underlying shape degrees of freedom is a well-established prism with which to understand atomic nuclei. Self-consistent mean-field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time-dependent extension of the mean-field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of 28 Si in the first case, and 240 Pu in the latter case
Aizawa, Hirohito; Kuroki, Kazuhiko
2018-03-01
We present a first-principles band calculation for the quasi-one-dimensional (Q1D) organic superconductor (TMTSF) 2ClO4 . An effective tight-binding model with the TMTSF molecule to be regarded as the site is derived from a calculation based on maximally localized Wannier orbitals. We apply a two-particle self-consistent (TPSC) analysis by using a four-site Hubbard model, which is composed of the tight-binding model and an onsite (intramolecular) repulsive interaction, which serves as a variable parameter. We assume that the pairing mechanism is mediated by the spin fluctuation, and the sign of the superconducting gap changes between the inner and outer Fermi surfaces, which correspond to a d -wave gap function in a simplified Q1D model. With the parameters we adopt, the critical temperature for superconductivity estimated by the TPSC approach is approximately 1 K, which is consistent with experiment.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.
Self-consistent nuclear energy systems
International Nuclear Information System (INIS)
Shimizu, A.; Fujiie, Y.
1995-01-01
A concept of self-consistent energy systems (SCNES) has been proposed as an ultimate goal of the nuclear energy system in the coming centuries. SCNES should realize a stable and unlimited energy supply without endangering the human race and the global environment. It is defined as a system that realizes at least the following four objectives simultaneously: (a) energy generation -attain high efficiency in the utilization of fission energy; (b) fuel production - secure inexhaustible energy source: breeding of fissile material with the breeding ratio greater than one and complete burning of transuranium through recycling; (c) burning of radionuclides - zero release of radionuclides from the system: complete burning of transuranium and elimination of radioactive fission products by neutron capture reactions through recycling; (d) system safety - achieve system safety both for the public and experts: eliminate criticality-related safety issues by using natural laws and simple logic. This paper describes the concept of SCNES and discusses the feasibility of the system. Both ''neutron balance'' and ''energbalance'' of the system are introduced as the necessary conditions to be satisfied at least by SCNES. Evaluations made so far indicate that both the neutron balance and the energy balance can be realized by fast reactors but not by thermal reactors. Concerning the system safety, two safety concepts: ''self controllability'' and ''self-terminability'' are introduced to eliminate the criticality-related safety issues in fast reactors. (author)
International Nuclear Information System (INIS)
Guerra, E.M. de
2001-01-01
In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)
The self-consistent dynamic pole tide in global oceans
Dickman, S. R.
1985-01-01
The dynamic pole tide is characterized in a self-consistent manner by means of introducing a single nondifferential matrix equation compatible with the Liouville equation, modelling the ocean as global and of uniform depth. The deviations of the theory from the realistic ocean, associated with the nonglobality of the latter, are also given consideration, with an inference that in realistic oceans long-period modes of resonances would be increasingly likely to exist. The analysis of the nature of the pole tide and its effects on the Chandler wobble indicate that departures of the pole tide from the equilibrium may indeed be minimal.
Two-particle self-consistent approach to unconventional superconductivity
Energy Technology Data Exchange (ETDEWEB)
Otsuki, Junya [Department of Physics, Tohoku University, Sendai (Japan); Theoretische Physik III, Zentrum fuer Elektronische Korrelationen und Magnetismus, Universitaet Augsburg (Germany)
2013-07-01
A non-perturbative approach to unconventional superconductivity is developed based on the idea of the two-particle self-consistent (TPSC) theory. An exact sum-rule which the momentum-dependent pairing susceptibility satisfies is derived. Effective pairing interactions between quasiparticles are determined so that an approximate susceptibility should fulfill this sum-rule, in which fluctuations belonging to different symmetries mix at finite momentum. The mixing leads to a suppression of the d{sub x{sup 2}-y{sup 2}} pairing close to the half-filling, resulting in a maximum of T{sub c} away from half-filling.
Self-consistent electronic-structure calculations for interface geometries
International Nuclear Information System (INIS)
Sowa, E.C.; Gonis, A.; MacLaren, J.M.; Zhang, X.G.
1992-01-01
This paper describes a technique for computing self-consistent electronic structures and total energies of planar defects, such as interfaces, which are embedded in an otherwise perfect crystal. As in the Layer Korringa-Kohn-Rostoker approach, the solid is treated as a set of coupled layers of atoms, using Bloch's theorem to take advantage of the two-dimensional periodicity of the individual layers. The layers are coupled using the techniques of the Real-Space Multiple-Scattering Theory, avoiding artificial slab or supercell boundary conditions. A total-energy calculation on a Cu crystal, which has been split apart at a (111) plane, is used to illustrate the method
Lauw, Y; Leermakers, F A M; Cohen Stuart, M A; Pinheiro, J P; Custers, J P A; van den Broeke, L J P; Keurentjes, J T F
2006-12-19
We perform differential potentiometric titration measurements for the binding of Ca2+ ions to micelles composed of the carboxylic acid end-standing Pluronic P85 block copolymer (i.e., CAE-85 (COOH-(EO)26-(PO)39-(EO)26-COOH)). Two different ion-selective electrodes (ISEs) are used to detect the free calcium concentration; the first ISE is an indicator electrode, and the second is a reference electrode. The titration is done by adding the block copolymers to a known solution of Ca2+ at neutral pH and high enough temperature (above the critical micellization temperature CMT) and various amount of added monovalent salt. By measuring the difference in the electromotive force between the two ISEs, the amount of Ca2+ that is bound by the micelles is calculated. This is then used to determine the binding constant of Ca2+ with the micelles, which is a missing parameter needed to perform molecular realistic self-consistent-field (SCF) calculations. It turns out that the micelles from block copolymer CAE-85 bind Ca2+ ions both electrostatically and specifically. The specific binding between Ca2+ and carboxylic groups in the corona of the micelles is modeled through the reaction equilibrium -COOCa+ -COO- + Ca2+ with pKCa = 1.7 +/- 0.06.
Roberto Viana, J.; Rodriguez Salmon, Octavio D.; Neto, Minos A.; Carvalho, Diego C.
2018-02-01
A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume-Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.
Mean field interaction in biochemical reaction networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2011-01-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits
Lee, Hoyoung; Kim, Dae Hwan; Witte, Kevin N; Ohn, Kimberly; Choi, Je; Akgun, Bulent; Satija, Sushil; Won, You-Yeon
2012-06-21
By use of a combined experimental and theoretical approach, a model poly(ethylene oxide) (PEO) brush system, prepared by spreading a poly(ethylene oxide)-poly(n-butyl acrylate) (PEO-PnBA) amphiphilic diblock copolymer onto an air-water interface, was investigated. The polymer segment density profiles of the PEO brush in the direction normal to the air-water interface under various grafting density conditions were determined by using the neutron reflectivity (NR) measurement technique. To achieve a theoretically sound analysis of the reflectivity data, we used a data analysis method that utilizes the self-consistent field (SCF) theoretical modeling as a tool for predicting expected reflectivity results for comparison with the experimental data. Using this data analysis technique, we discovered that the effective Flory-Huggins interaction parameter of the PEO brush chains is significantly greater than that corresponding to the θ condition in Flory-Huggins solutions (i.e., χ(PEO-water)(brush chains)/χ(PEO-water)(θ condition) ≈ 1.2), suggesting that contrary to what is more commonly observed for PEO in normal situations (χ(PEO-water)(free chains)/χ(PEO-water)(θ condition) ≈ 0.92), the PEO chains are actually not "hydrophilic" when they exist as polymer brush chains, because of the many body interactions that are forced to be effective in the brush situation. This result is further supported by the fact that the surface pressures of the PEO brush calculated on the basis of the measured χ(PEO-water) value are in close agreement with the experimental surface pressure-area isotherm data. The SCF theoretical analysis of the surface pressure behavior of the PEO brush also suggests that even though the grafted PEO chains experience a poor solvent environment, the PEO brush layer exhibits positive surface pressures, because the hydrophobicity of the PEO brush chains (which favors compression) is insufficient to overcome the opposing effect of the chain
Self-consistent phonons in disordered systems
International Nuclear Information System (INIS)
Das, M.P.
1990-01-01
The time is now ripe for the development of a microscopic theory of the disordered systems in the context of phonons. The adiabatic approximation has helped to separate the electronic motion from that of the ions. In the microscopic dielectric formulation we have been able to obtain the interatomic forces for ordered systems by incorporating the effect of the electronic motion. The nature of the electronic states in disordered systems is now better understood with realistic coherent potential approximation calculations. Therefore, it will not be too ambitious to construct an average dielectric function for a disordered system. Then we can obtain a properly screened pair potential in terms of this dielectric function. In view of the availability of super fast computers, the development of the microscopic theories are expected to get a new direction. (author). 36 refs
Bubble nuclei in relativistic mean field theory
International Nuclear Information System (INIS)
Shukla, A.; Aberg, S.; Patra, S.K.
2011-01-01
Bubble nuclei are characterized by a depletion of their central density, i.e. the formation of the proton or neutron void and subsequently forming proton or neutron bubble nuclei. Possibility of the formation of bubble nuclei has been explored through different nuclear models and in different mass regions. Advancements in experimental nuclear physics has led our experimental access to many new shapes and structures, which were inaccessible hitherto. In the present paper, the possibility of observing nuclear bubble in oxygen isotopes, particularly for 22 O has been studied
Nuclear structure using relativistic mean field theory
International Nuclear Information System (INIS)
Maharana, J.P.; Warrier, L.S.; Gambhir, Y.K.
1995-01-01
The ground state binding energies of the studied Kr isotopes are well in agreement with the experiment and the variations of the nucleon single particle energies and occupancies are found to be as expected. (author). 10 refs., 12 figs
Mean field methods for cortical network dynamics
DEFF Research Database (Denmark)
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Self-consistent expansion for the molecular beam epitaxy equation.
Katzav, Eytan
2002-03-01
Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(r-r('),t-t('))=2D(0)[r-->-r(')](2rho-d)delta(t-t(')). I find a lower critical dimension d(c)(rho)=4+2rho, above which the linear MBE solution appears. Below the lower critical dimension a rho-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.
Fully self-consistent GW calculations for molecules
DEFF Research Database (Denmark)
Rostgaard, Carsten; Jacobsen, Karsten Wedel; Thygesen, Kristian Sommer
2010-01-01
We calculate single-particle excitation energies for a series of 34 molecules using fully self-consistent GW, one-shot G0W0, Hartree-Fock (HF), and hybrid density-functional theory (DFT). All calculations are performed within the projector-augmented wave method using a basis set of Wannier...... functions augmented by numerical atomic orbitals. The GW self-energy is calculated on the real frequency axis including its full frequency dependence and off-diagonal matrix elements. The mean absolute error of the ionization potential (IP) with respect to experiment is found to be 4.4, 2.6, 0.8, 0.4, and 0...
International Nuclear Information System (INIS)
Hees, Hendrik van; Knoll, Joern
2002-01-01
The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-01-01
The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)
Relativistic deformed mean-field calculation of binding energy differences of mirror nuclei
International Nuclear Information System (INIS)
Koepf, W.; Barreiro, L.A.
1996-01-01
Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existence of the Okamoto-Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is significantly smaller than the one obtained within state-of-the-art nonrelativistic calculations. (author). 35 refs
Modeling self-consistent multi-class dynamic traffic flow
Cho, Hsun-Jung; Lo, Shih-Ching
2002-09-01
In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.
Heavy-ion interactions in relativistic mean-field models
International Nuclear Information System (INIS)
Rashdan, M.
1996-01-01
The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model. (orig.)
Mean field interaction in biochemical reaction networks
Tembine, Hamidou
2011-09-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits and illustrate them with numerical examples. © 2011 IEEE.
Self-consistent calculation of atomic structure for mixture
International Nuclear Information System (INIS)
Meng Xujun; Bai Yun; Sun Yongsheng; Zhang Jinglin; Zong Xiaoping
2000-01-01
Based on relativistic Hartree-Fock-Slater self-consistent average atomic model, atomic structure for mixture is studied by summing up component volumes in mixture. Algorithmic procedure for solving both the group of Thomas-Fermi equations and the self-consistent atomic structure is presented in detail, and, some numerical results are discussed
Superheavy nuclei: a relativistic mean field outlook
International Nuclear Information System (INIS)
Afanasjev, A.V.
2006-01-01
The analysis of quasi-particle spectra in the heaviest A∼250 nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggests that only the parametrizations which predict Z = 120 and N = 172 as shell closures are reliable for superheavy nuclei within the relativistic mean field theory. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. A large central depression produces large shell gaps at Z = 120 and N = 172. The shell gaps at Z = 126 and N = 184 are favoured by a flat density distribution in the central part of the nucleus. It is shown that approximate particle number projection (PNP) by means of the Lipkin-Nogami (LN) method removes pairing collapse seen at these gaps in the calculations without PNP
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Self-consistent hybrid functionals for solids: a fully-automated implementation
Erba, A.
2017-08-01
A fully-automated algorithm for the determination of the system-specific optimal fraction of exact exchange in self-consistent hybrid functionals of the density-functional-theory is illustrated, as implemented into the public Crystal program. The exchange fraction of this new class of functionals is self-consistently updated proportionally to the inverse of the dielectric response of the system within an iterative procedure (Skone et al 2014 Phys. Rev. B 89, 195112). Each iteration of the present scheme, in turn, implies convergence of a self-consistent-field (SCF) and a coupled-perturbed-Hartree-Fock/Kohn-Sham (CPHF/KS) procedure. The present implementation, beside improving the user-friendliness of self-consistent hybrids, exploits the unperturbed and electric-field perturbed density matrices from previous iterations as guesses for subsequent SCF and CPHF/KS iterations, which is documented to reduce the overall computational cost of the whole process by a factor of 2.
Vibrational self-consistent field theory using optimized curvilinear coordinates.
Bulik, Ireneusz W; Frisch, Michael J; Vaccaro, Patrick H
2017-07-28
A vibrational SCF model is presented in which the functions forming the single-mode functions in the product wavefunction are expressed in terms of internal coordinates and the coordinates used for each mode are optimized variationally. This model involves no approximations to the kinetic energy operator and does not require a Taylor-series expansion of the potential. The non-linear optimization of coordinates is found to give much better product wavefunctions than the limited variations considered in most previous applications of SCF methods to vibrational problems. The approach is tested using published potential energy surfaces for water, ammonia, and formaldehyde. Variational flexibility allowed in the current ansätze results in excellent zero-point energies expressed through single-product states and accurate fundamental transition frequencies realized by short configuration-interaction expansions. Fully variational optimization of single-product states for excited vibrational levels also is discussed. The highlighted methodology constitutes an excellent starting point for more sophisticated treatments, as the bulk characteristics of many-mode coupling are accounted for efficiently in terms of compact wavefunctions (as evident from the accurate prediction of transition frequencies).
Empiricism or self-consistent theory in chemical kinetics?
International Nuclear Information System (INIS)
Gutman, E.M.
2007-01-01
To give theoretical background for mechanochemical kinetics, we need first of all to find a possibility to predict the kinetic parameters for real chemical processes by determining rate constants and reaction orders without developing strictly specialized and, to a great extent, artificial models, i.e. to derive the kinetic law of mass action from 'first principles'. However, the kinetic law of mass action has had only an empirical basis from the first experiments of Gulberg and Waage until now, in contrast to the classical law of mass action for chemical equilibrium rigorously derived in chemical thermodynamics from equilibrium condition. Nevertheless, in this paper, an attempt to derive the kinetic law of mass action from 'first principles' is made in macroscopic formulation. It has turned out to be possible owing to the methods of thermodynamics of irreversible processes that were unknown in Gulberg and Waage's time
International Nuclear Information System (INIS)
Grasso, M.
2009-10-01
This document is a summary of the author's research activities whose common topic is the N-body problem. The first chapter introduces the N-body issue through models based on the mean-field theory and on the Hartree-Fock-Bogoliubov equations. The second chapter presents the understanding of exotic nuclei features within the mean-field approach. Exotic phenomena like nuclear bubble structure, pairing correlations and pairing violations, giant neutron halos, non-standard terms in the Skyrme interactions are reviewed. The chapter 3 is dedicated to some extensions of the RPA (random phase approximation). For instance the computation of the shell structure far from the stability valley requires a more accurate assessment of the energy of the individual states through the introduction of a particle-vibration coupling. Different RPA extensions are described: first the self-consistent extension enlarged beyond particle-hole configurations, then the boson-mapping-based extension in a 3-level Lipkin model and also the second random-phase approximation. The chapter 4 gathers some studies concerning ultra-cold gases of trapped atoms. These systems are the only structures that allow the study of the correlations associated to superfluidity in terms of interaction intensity, temperature or system size. The mean-field approach is adequate for these studies. The last chapter draws a perspective for the mean-field-based models, their limits are assessed and ways of improvement are proposed. (A.C.)
Quasiparticle self-consistent GW method: a short summary
International Nuclear Information System (INIS)
Kotani, Takao; Schilfgaarde, Mark van; Faleev, Sergey V; Chantis, Athanasios
2007-01-01
We have developed a quasiparticle self-consistent GW method (QSGW), which is a new self-consistent method to calculate the electronic structure within the GW approximation. The method is formulated based on the idea of a self-consistent perturbation; the non-interacting Green function G 0 , which is the starting point for GWA to obtain G, is determined self-consistently so as to minimize the perturbative correction generated by GWA. After self-consistency is attained, we have G 0 , W (the screened Coulomb interaction) and G self-consistently. This G 0 can be interpreted as the optimum non-interacting propagator for the quasiparticles. We will summarize some theoretical discussions to justify QSGW. Then we will survey results which have been obtained up to now: e.g., band gaps for normal semiconductors are predicted to a precision of 0.1-0.3 eV; the self-consistency including the off-diagonal part is required for NiO and MnO; and so on. There are still some remaining disagreements with experiments; however, they are very systematic, and can be explained from the neglect of excitonic effects
Nonlinear and self-consistent treatment of ECRH
Energy Technology Data Exchange (ETDEWEB)
Tsironis, C.; Vlahos, L.
2005-07-01
A self-consistent formulation for the nonlinear interaction of electromagnetic waves with relativistic magnetized electrons is applied for the description of the ECRH. In general, electron-cyclotron absorption is the result of resonances between the cyclotron harmonics and the Doppler-shifted waver frequency. The resonant interaction results to an intense wave-particle energy exchange and an electron acceleration, and for that reason it is widely applied in fusion experiments for plasma heating and current drive. The linear theory, for the wave absorption, as well as the quasilinear theory for the electron distribution function, are the most frequently-used tools for the study of wave-particle interactions. However, in many cases the validity of these theories is violated, namely cases where nonlinear effects, like, e. g. particle trapping in the wave field, are dominant in the particle phase-space. Our model consists of electrons streaming and gyrating in a tokamak plasma slab, which is finite in the directions perpendicular to the main magnetic field. The particles interact with an electromagnetic electron-cyclotron wave of the ordinary (O-) or the extraordinary (X-) mode. A set of nonlinear and relativistic equations is derived, which take into account the effects of the charged particle motions on the wave. These consist of the equations of motion for the plasma electrons in the slab, as well as the wave equation in terms of the vector potential. The effect of the electron motions on the temporal evolution of the wave is reflected in the current density source term. (Author)
Nonlinear and self-consistent treatment of ECRH
International Nuclear Information System (INIS)
Tsironis, C.; Vlahos, L.
2005-01-01
A self-consistent formulation for the nonlinear interaction of electromagnetic waves with relativistic magnetized electrons is applied for the description of the ECRH. In general, electron-cyclotron absorption is the result of resonances between the cyclotron harmonics and the Doppler-shifted waver frequency. The resonant interaction results to an intense wave-particle energy exchange and an electron acceleration, and for that reason it is widely applied in fusion experiments for plasma heating and current drive. The linear theory, for the wave absorption, as well as the quasilinear theory for the electron distribution function, are the most frequently-used tools for the study of wave-particle interactions. However, in many cases the validity of these theories is violated, namely cases where nonlinear effects, like, e. g. particle trapping in the wave field, are dominant in the particle phase-space. Our model consists of electrons streaming and gyrating in a tokamak plasma slab, which is finite in the directions perpendicular to the main magnetic field. The particles interact with an electromagnetic electron-cyclotron wave of the ordinary (O-) or the extraordinary (X-) mode. A set of nonlinear and relativistic equations is derived, which take into account the effects of the charged particle motions on the wave. These consist of the equations of motion for the plasma electrons in the slab, as well as the wave equation in terms of the vector potential. The effect of the electron motions on the temporal evolution of the wave is reflected in the current density source term. (Author)
First principles molecular dynamics without self-consistent field optimization
International Nuclear Information System (INIS)
Souvatzis, Petros; Niklasson, Anders M. N.
2014-01-01
We present a first principles molecular dynamics approach that is based on time-reversible extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The optimization-free dynamics keeps the computational cost to a minimum and typically provides molecular trajectories that closely follow the exact Born-Oppenheimer potential energy surface. Only one single diagonalization and Hamiltonian (or Fockian) construction are required in each integration time step. The proposed dynamics is derived for a general free-energy potential surface valid at finite electronic temperatures within hybrid density functional theory. Even in the event of irregular functional behavior that may cause a dynamical instability, the optimization-free limit represents a natural starting guess for force calculations that may require a more elaborate iterative electronic ground state optimization. Our optimization-free dynamics thus represents a flexible theoretical framework for a broad and general class of ab initio molecular dynamics simulations
A new mixed self-consistent field procedure
Alvarez-Ibarra, A.; Köster, A. M.
2015-10-01
A new approach for the calculation of three-centre electronic repulsion integrals (ERIs) is developed, implemented and benchmarked in the framework of auxiliary density functional theory (ADFT). The so-called mixed self-consistent field (mixed SCF) divides the computationally costly ERIs in two sets: far-field and near-field. Far-field ERIs are calculated using the newly developed double asymptotic expansion as in the direct SCF scheme. Near-field ERIs are calculated only once prior to the SCF procedure and stored in memory, as in the conventional SCF scheme. Hence the name, mixed SCF. The implementation is particularly powerful when used in parallel architectures, since all RAM available are used for near-field ERI storage. In addition, the efficient distribution algorithm performs minimal intercommunication operations between processors, avoiding a potential bottleneck. One-, two- and three-dimensional systems are used for benchmarking, showing substantial time reduction in the ERI calculation for all of them. A Born-Oppenheimer molecular dynamics calculation for the Na+55 cluster is also shown in order to demonstrate the speed-up for small systems achievable with the mixed SCF. Dedicated to Sourav Pal on the occasion of his 60th birthday.
Self-Consistent Study of Conjugated Aromatic Molecular Transistors
International Nuclear Information System (INIS)
Jing, Wang; Yun-Ye, Liang; Hao, Chen; Peng, Wang; Note, R.; Mizuseki, H.; Kawazoe, Y.
2010-01-01
We study the current through conjugated aromatic molecular transistors modulated by a transverse field. The self-consistent calculation is realized with density function theory through the standard quantum chemistry software Gaussian03 and the non-equilibrium Green's function formalism. The calculated I – V curves controlled by the transverse field present the characteristics of different organic molecular transistors, the transverse field effect of which is improved by the substitutions of nitrogen atoms or fluorine atoms. On the other hand, the asymmetry of molecular configurations to the axis connecting two sulfur atoms is in favor of realizing the transverse field modulation. Suitably designed conjugated aromatic molecular transistors possess different I – V characteristics, some of them are similar to those of metal-oxide-semiconductor field-effect transistors (MOSFET). Some of the calculated molecular devices may work as elements in graphene electronics. Our results present the richness and flexibility of molecular transistors, which describe the colorful prospect of next generation devices. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Wasilewski, Bartosz; Marciniak, Wojciech; Werwiński, Mirosław
2018-05-01
Cubic Laves phases including , , , and are considered as promising candidates for application in hydrogen storage and magnetic refrigeration. While and are ferromagnets, alloying with Co decreases magnetic moments and Curie temperatures (T C) of pseudobinary and systems, leading to the paramagnetic states of and . The following study focuses on the investigation of Curie temperature of the and system from first principles. To do it, Monte Carlo (MC) simulations and the mean field theory (MFT) based on the disordered local moments (DLM) calculations are used. The DLM-MFT results agree qualitatively with the experimental data from the literature and preserve the characteristic features of dependencies for both and . However, we have encountered complications in the Co-rich regions due to failure of the local density approximation (LDA) in describing the Co magnetic moment in the DLM state. The analysis of Fe–Fe exchange couplings for and phases indicates that the nearest-neighbor interactions play the main role in the formation of .
Continuous time finite state mean field games
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigã o
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Risk-sensitive mean-field games
Tembine, Hamidou
2014-04-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Risk-sensitive mean-field games
Tembine, Hamidou; Zhu, Quanyan; Başar, Tamer
2014-01-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Continuous Time Finite State Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Gomes, Diogo A., E-mail: dgomes@math.ist.utl.pt [Instituto Superior Tecnico, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matematica (Portugal); Mohr, Joana, E-mail: joana.mohr@ufrgs.br; Souza, Rafael Rigao, E-mail: rafars@mat.ufrgs.br [UFRGS, Instituto de Matematica (Brazil)
2013-08-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
Continuous Time Finite State Mean Field Games
International Nuclear Information System (INIS)
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games
Extended Deterministic Mean-Field Games
Gomes, Diogo A.
2016-04-21
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Extended Deterministic Mean-Field Games
Gomes, Diogo A.; Voskanyan, Vardan K.
2016-01-01
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Self-consistency corrections in effective-interaction calculations
International Nuclear Information System (INIS)
Starkand, Y.; Kirson, M.W.
1975-01-01
Large-matrix extended-shell-model calculations are used to compute self-consistency corrections to the effective interaction and to the linked-cluster effective interaction. The corrections are found to be numerically significant and to affect the rate of convergence of the corresponding perturbation series. The influence of various partial corrections is tested. It is concluded that self-consistency is an important effect in determining the effective interaction and improving the rate of convergence. (author)
Nuclear charge-exchange excitations in a self-consistent covariant approach
International Nuclear Information System (INIS)
Liang, Haozhao
2010-01-01
-isospin resonances via the exchange terms, which leads to a profound effect in the nuclear isovector properties, e.g., the density dependence of the symmetry energy in nuclear matter. In the investigation of the isospin symmetry-breaking corrections for the superallowed β decays, it is found that the corrections δ c are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections δ c , the nucleus-independent Ft values are obtained in combination with the experimental ft values in the most recent survey and the improved radiative corrections. The values of Cabibbo-Kobayashi-Maskawa matrix element |V ud | thus obtained well agree with those obtained in neutron decay, pion decay, and nuclear mirror transitions, while the sum of squared top-row elements somehow deviates from the unitarity condition. Expressing the weak lepton-hadron interaction in the standard current-current form, the relevant transitions from the nuclear ground state to the excited states are calculated with RHF+RPA approach. In this way, the semileptonic weak interaction processes, e.g., neutrino reactions, charged lepton capture, β-decays, can be investigated microscopically and self-consistently. First illustrative calculations of the inclusive neutrino-nucleus cross section are performed for the 16 O(ν e ,e - ) 16 F reaction, and a good agreement with the previous theoretical studies is obtained. The main effort is dedicated to discussing the substantial influence of different recipes for the axial vector coupling strength and the theoretical low-lying excited states of the daughter nucleus. (author)
Mean-field models and exotic nuclei
Energy Technology Data Exchange (ETDEWEB)
Bender, M; Buervenich, T; Maruhn, J A; Greiner, W [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); [Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P G [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Mean-field models and exotic nuclei
International Nuclear Information System (INIS)
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W.; Rutz, K.; Reinhard, P.G.
1998-01-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody; Tembine, Hamidou; Tempone, Raul
2016-01-01
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Dresselhaus, Thomas; Neugebauer, Johannes; Knecht, Stefan; Keller, Sebastian; Ma, Yingjin; Reiher, Markus
2015-01-28
We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.
Self-consistent-field calculations of proteinlike incorporations in polyelectrolyte complex micelles
Lindhoud, S.; Cohen Stuart, M.A.; Norde, W.; Leermakers, F.A.M.
2009-01-01
Self-consistent field theory is applied to model the structure and stability of polyelectrolyte complex micelles with incorporated protein (molten globule) molecules in the core. The electrostatic interactions that drive the micelle formation are mimicked by nearest-neighbor interactions using
Lauw, Y.; Leermakers, F.A.M.; Cohen Stuart, M.A.
2007-01-01
The persistence length of a wormlike micelle composed of ionic surfactants CnEmXk in an aqueous solvent is predicted by means of the self-consistent-field theory where CnEm is the conventional nonionic surfactant and X-k is an additional sequence of k weakly charged (pH-dependent) segments. By
Pressure variation of the valence band width in Ge: A self-consistent GW study
DEFF Research Database (Denmark)
Modak, Paritosh; Svane, Axel; Christensen, Niels Egede
2009-01-01
. In the present work we report results of quasiparticle self-consistent GW (QSGW) band calculations for diamond- as well as β-tin-type Ge under pressure. For both phases we find that the band width increases with pressure. For β-tin Ge this agrees with experiment and density-functional theory, but for diamond Ge...
Renormalization of self-consistent Schwinger-Dyson equations at finite temperature
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2002-01-01
We show that Dyson resummation schemes based on Baym's Φ-derivable approximations can be renormalized with counter term structures solely defined on the vacuum level. First applications to the self-consistent solution of the sunset self-energy in φ 4 -theory are presented. (orig.)
Self-consistent approximations beyond the CPA: Part II
International Nuclear Information System (INIS)
Kaplan, T.; Gray, L.J.
1982-01-01
This paper concentrates on a self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl. The construction of the augmented space formalism for a binary alloy is sketched, and the notation to be used derived. Using the operator methods of the augmented space, the self-consistent approximation is derived for the average Green's function, and for evaluating the self-energy, taking into account the scattering by clusters of excitations. The particular cluster approximation desired is derived by treating the scattering by the excitations with S /SUB T/ exactly. Fourier transforms on the disorder-space clustersite labels solve the self-consistent set of equations. Expansion to short range order in the alloy is also discussed. A method to reduce the problem to a computationally tractable form is described
Linear augmented plane wave method for self-consistent calculations
International Nuclear Information System (INIS)
Takeda, T.; Kuebler, J.
1979-01-01
O.K. Andersen has recently introduced a linear augmented plane wave method (LAPW) for the calculation of electronic structure that was shown to be computationally fast. A more general formulation of an LAPW method is presented here. It makes use of a freely disposable number of eigenfunctions of the radial Schroedinger equation. These eigenfunctions can be selected in a self-consistent way. The present formulation also results in a computationally fast method. It is shown that Andersen's LAPW is obtained in a special limit from the present formulation. Self-consistent test calculations for copper show the present method to be remarkably accurate. As an application, scalar-relativistic self-consistent calculations are presented for the band structure of FCC lanthanum. (author)
Self-consistency and coherent effects in nonlinear resonances
International Nuclear Information System (INIS)
Hofmann, I.; Franchetti, G.; Qiang, J.; Ryne, R. D.
2003-01-01
The influence of space charge on emittance growth is studied in simulations of a coasting beam exposed to a strong octupolar perturbation in an otherwise linear lattice, and under stationary parameters. We explore the importance of self-consistency by comparing results with a non-self-consistent model, where the space charge electric field is kept 'frozen-in' to its initial values. For Gaussian distribution functions we find that the 'frozen-in' model results in a good approximation of the self-consistent model, hence coherent response is practically absent and the emittance growth is self-limiting due to space charge de-tuning. For KV or waterbag distributions, instead, strong coherent response is found, which we explain in terms of absence of Landau damping
An approach to a self-consistent nuclear energy system
International Nuclear Information System (INIS)
Fujii-e, Yoichi; Arie, Kazuo; Endo, Hiroshi
1992-01-01
A nuclear energy system should provide a stable supply of energy without endangering the environment or humans. If there is fear about exhausting world energy resources, accumulating radionuclides, and nuclear reactor safety, tension is created in human society. Nuclear energy systems of the future should be able to eliminate fear from people's minds. In other words, the whole system, including the nuclear fuel cycle, should be self-consistent. This is the ultimate goal of nuclear energy. If it can be realized, public acceptance of nuclear energy will increase significantly. In a self-consistent nuclear energy system, misunderstandings between experts on nuclear energy and the public should be minimized. The way to achieve this goal is to explain using simple logic. This paper proposes specific targets for self-consistent nuclear energy systems and shows that the fast breeder reactor (FBR) lies on the route to attaining the final goal
The influence of thermodynamic self-consistency on the phase behaviour of symmetric binary mixtures
Scholl-Paschinger, E; Kahl, G
2004-01-01
We have investigated the phase behaviour of a symmetric binary mixture with particles interacting via hard-core Yukawa potentials. To calculate the thermodynamic properties we have used the mean spherical approximation (MSA), a conventional liquid state theory, and the closely related self-consistent Ornstein-Zernike approximation which is defined via an MSA-type closure relation, requiring, in addition, thermodynamic self-consistency between the compressibility and the energy-route. We investigate on a quantitative level the effect of the self-consistency requirement on the phase diagram and on the critical behaviour and confirm the existence of three archetypes of phase diagram, which originate from the competition between the first order liquid/vapour transition and the second order demixing transition.
Multiplicative renormalizability and self-consistent treatments of the Schwinger-Dyson equations
International Nuclear Information System (INIS)
Brown, N.; Dorey, N.
1989-11-01
Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched quantum electrodynamics, (QED), checking the consistency of various approximations. In particular, we show that the much used 'ladder' approximation is self-consistent, provided that the coupling constant is renormalized in a particular way. We also propose another approximation which satisfies this self-consistency test, but requires that the coupling be unrenormalized, as should be the case in the full quenched approximation. This new approximation admits an exact solution, which also satisfies the renormalization group equation for the quenched approximation. (author)
Thermodynamically self-consistent integral equations and the structure of liquid metals
International Nuclear Information System (INIS)
Pastore, G.; Kahl, G.
1987-01-01
We discuss the application of the new thermodynamically self-consistent integral equations for the determination of the structural properties of liquid metals. We present a detailed comparison of the structure (S(q) and g(r)) for models of liquid alkali metals as obtained from two thermodynamically self-consistent integral equations and some published exact computer simulation results; the range of states extends from the triple point to the expanded metal. The theories which only impose thermodynamic self-consistency without any fitting of external data show an excellent agreement with the simulation results, thus demonstrating that this new type of integral equation is definitely superior to the conventional ones (hypernetted chain, Percus-Yevick, mean spherical approximation, etc). (author)
Mean field games for cognitive radio networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2012-01-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing
Bauso, Dario
2014-05-07
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.
Mean field approach to nuclear structure
International Nuclear Information System (INIS)
Nazarewicz, W.; Tennessee Univ., Knoxville, TN
1993-01-01
Several examples of mean-field calculations, relevant to the recent and planned low-spin experimental works, are presented. The perspectives for future studies (mainly related to spectroscopy of exotic nuclei) are reviewd
Weakly coupled mean-field game systems
Gomes, Diogo A.; Patrizi, Stefania
2016-01-01
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being. © 2014 Bauso et al.
Mean-field games for marriage.
Directory of Open Access Journals (Sweden)
Dario Bauso
Full Text Available This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.
Virtual-site correlation mean field approach to criticality in spin systems
International Nuclear Information System (INIS)
Sen, Aditi; Sen, Ujjwal
2013-01-01
We propose a virtual-site correlation mean field theory for dealing with interacting many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the virtual-site correlation mean field theory deals with single- as well as two-body ones, and involves a virtual site for every interaction term in the Hamiltonian. We generalize the theory to a cluster virtual-site correlation mean field, that works with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are generally much better in the proposed theories as compared to the corresponding ones in mean field theories
SOCIAL COMPARISON, SELF-CONSISTENCY AND THE PRESENTATION OF SELF.
MORSE, STANLEY J.; GERGEN, KENNETH J.
TO DISCOVER HOW A PERSON'S (P) SELF-CONCEPT IS AFFECTED BY THE CHARACTERISTICS OF ANOTHER (O) WHO SUDDENLY APPEARS IN THE SAME SOCIAL ENVIRONMENT, SEVERAL QUESTIONNAIRES, INCLUDING THE GERGEN-MORSE (1967) SELF-CONSISTENCY SCALE AND HALF THE COOPERSMITH SELF-ESTEEM INVENTORY, WERE ADMINISTERED TO 78 UNDERGRADUATE MEN WHO HAD ANSWERED AN AD FOR WORK…
Final Report Fermionic Symmetries and Self consistent Shell Model
International Nuclear Information System (INIS)
Zamick, Larry
2008-01-01
In this final report in the field of theoretical nuclear physics we note important accomplishments.We were confronted with 'anomoulous' magnetic moments by the experimetalists and were able to expain them. We found unexpected partial dynamical symmetries--completely unknown before, and were able to a large extent to expain them. The importance of a self consistent shell model was emphasized.
Analytical relativistic self-consistent-field calculations for atoms
International Nuclear Information System (INIS)
Barthelat, J.C.; Pelissier, M.; Durand, P.
1980-01-01
A new second-order representation of the Dirac equation is presented. This representation which is exact for a hydrogen atom is applied to approximate analytical self-consistent-field calculations for atoms. Results are given for the rare-gas atoms from helium to radon and for lead. The results compare favorably with numerical Dirac-Hartree-Fock solutions
Self-consistent description of the isospin mixing
International Nuclear Information System (INIS)
Gabrakov, S.I.; Pyatov, N.I.; Baznat, M.I.; Salamov, D.I.
1978-03-01
The properties of collective 0 + states built of unlike particle-hole excitations in spherical nuclei have been investigated in a self-consistent microscopic approach. These states arise when the broken isospin symmetry of the nuclear shell model Hamiltonian is restored. The numerical calculations were performed with Woods-Saxon wave functions
Self-consistent collective coordinate method for large amplitude collective motions
International Nuclear Information System (INIS)
Sakata, F.; Hashimoto, Y.; Marumori, T.; Une, T.
1982-01-01
A recent development of the self-consistent collective coordinate method is described. The self-consistent collective coordinate method was proposed on the basis of the fundamental principle called the invariance principle of the Schroedinger equation. If this is formulated within a framework of the time dependent Hartree Fock (TDHF) theory, a classical version of the theory is obtained. A quantum version of the theory is deduced by formulating it within a framework of the unitary transformation method with auxiliary bosons. In this report, the discussion is concentrated on a relation between the classical theory and the quantum theory, and an applicability of the classical theory. The aim of the classical theory is to extract a maximally decoupled collective subspace out of a huge dimensional 1p - 1h parameter space introduced by the TDHF theory. An intimate similarity between the classical theory and a full quantum boson expansion method (BEM) was clarified. Discussion was concentrated to a simple Lipkin model. Then a relation between the BEM and the unitary transformation method with auxiliary bosons was discussed. It became clear that the quantum version of the theory had a strong relation to the BEM, and that the BEM was nothing but a quantum analogue of the present classical theory. The present theory was compared with the full TDHF calculation by using a simple model. (Kato, T.)
Pairing gaps from nuclear mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Maruhn, J.A.
2000-01-01
We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei. (orig.)
The mean field in many body quantum physics
International Nuclear Information System (INIS)
Llano, M. de
1984-01-01
As an introduction to the quantum problem of many bodies we present a panoramic view of the most elementary theories called mean field theories. They comprise: i) the fermions ideal gas theory which implies, in a simple manner, the stability of white dwarf stars and of neutron stars, ii) the Hartree-Fock approximation for thermodynamical systems which is presented here in the context of a liquid-crystal phase transition, and iii) the Thomas-Fermi theory which is applied to the total binding energy of neutral atoms. (author)
van Vlimmeren, BAC; Maurits, NM; Zvelindovsky, AV; Sevink, GJA; Fraaije, JGEM
1999-01-01
We simulate the microphase separation dynamics of aqueous solutions of the triblock polymer surfactants (ethylene oxide)(13)(propylene oxide)(30)(ethylene oxide)(13) and (propylene oxide)(19)(ethylene oxide)(33)(propylene oxide)(19) by a dynamic variant of mean-field density functional theory for
Obstacle mean-field game problem
Gomes, Diogo A.; Patrizi, Stefania
2015-01-01
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Self-consistent studies of magnetic thin film Ni (001)
International Nuclear Information System (INIS)
Wang, C.S.; Freeman, A.J.
1979-01-01
Advances in experimental methods for studying surface phenomena have provided the stimulus to develop theoretical methods capable of interpreting this wealth of new information. Of particular interest have been the relative roles of bulk and surface contributions since in several important cases agreement between experiment and bulk self-consistent (SC) calculations within the local spin density functional formalism (LSDF) is lacking. We discuss our recent extension of the (LSDF) approach to the study of thin films (slabs) and the role of surface effects on magnetic properties. Results are described for Ni (001) films using our new SC numerical basis set LCAO method. Self-consistency within the superposition of overlapping spherical atomic charge density model is obtained iteratively with the atomic configuration as the adjustable parameter. Results are presented for the electronic charge densities and local density of states. The origin and role of (magnetic) surface states is discussed by comparison with results of earlier bulk calculations
Self-consistent equilibria in the pulsar magnetosphere
International Nuclear Information System (INIS)
Endean, V.G.
1976-01-01
For a 'collisionless' pulsar magnetosphere the self-consistent equilibrium particle distribution functions are functions of the constants of the motion ony. Reasons are given for concluding that to a good approximation they will be functions of the rotating frame Hamiltonian only. This is shown to result in a rigid rotation of the plasma, which therefore becomes trapped inside the velocity of light cylinder. The self-consistent field equations are derived, and a method of solving them is illustrated. The axial component of the magnetic field decays to zero at the plasma boundary. In practice, some streaming of particles into the wind zone may occur as a second-order effect. Acceleration of such particles to very high energies is expected when they approach the velocity of light cylinder, but they cannot be accelerated to very high energies near the star. (author)
Self-consistent modelling of resonant tunnelling structures
DEFF Research Database (Denmark)
Fiig, T.; Jauho, A.P.
1992-01-01
We report a comprehensive study of the effects of self-consistency on the I-V-characteristics of resonant tunnelling structures. The calculational method is based on a simultaneous solution of the effective-mass Schrödinger equation and the Poisson equation, and the current is evaluated...... applied voltages and carrier densities at the emitter-barrier interface. We include the two-dimensional accumulation layer charge and the quantum well charge in our self-consistent scheme. We discuss the evaluation of the current contribution originating from the two-dimensional accumulation layer charges......, and our qualitative estimates seem consistent with recent experimental studies. The intrinsic bistability of resonant tunnelling diodes is analyzed within several different approximation schemes....
A regularized stationary mean-field game
Yang, Xianjin
2016-01-01
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
A regularized stationary mean-field game
Yang, Xianjin
2016-04-19
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
Weakly coupled mean-field game systems
Gomes, Diogo A.
2016-07-14
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. © 2016 Elsevier Ltd
Mean-field Ensemble Kalman Filter
Law, Kody; Tembine, Hamidou; Tempone, Raul
2015-01-01
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature
DEFF Research Database (Denmark)
Norman, Patrick; Bishop, David M.; Jensen, Hans Jørgen Aa
2001-01-01
Computationally tractable expressions for the evaluation of the linear response function in the multiconfigurational self-consistent field approximation were derived and implemented. The finite lifetime of the electronically excited states was considered and the linear response function was shown...... to be convergent in the whole frequency region. This was achieved through the incorporation of phenomenological damping factors that lead to complex response function values....
Homogenization of Periodic Masonry Using Self-Consistent Scheme and Finite Element Method
Kumar, Nitin; Lambadi, Harish; Pandey, Manoj; Rajagopal, Amirtham
2016-01-01
Masonry is a heterogeneous anisotropic continuum, made up of the brick and mortar arranged in a periodic manner. Obtaining the effective elastic stiffness of the masonry structures has been a challenging task. In this study, the homogenization theory for periodic media is implemented in a very generic manner to derive the anisotropic global behavior of the masonry, through rigorous application of the homogenization theory in one step and through a full three-dimensional behavior. We have considered the periodic Eshelby self-consistent method and the finite element method. Two representative unit cells that represent the microstructure of the masonry wall exactly are considered for calibration and numerical application of the theory.
Self-consistent Hartree-Fock RPA calculations in 208Pb
Taqi, Ali H.; Ali, Mohammed S.
2018-01-01
The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree-Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even-even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.
Self-consistent finite-temperature model of atom-laser coherence properties
International Nuclear Information System (INIS)
Fergusson, J.R.; Geddes, A.J.; Hutchinson, D.A.W.
2005-01-01
We present a mean-field model of a continuous-wave atom laser with Raman output coupling. The noncondensate is pumped at a fixed input rate which, in turn, pumps the condensate through a two-body scattering process obeying the Fermi golden rule. The gas is then coupled out by a Gaussian beam from the system, and the temperature and particle number are self-consistently evaluated against equilibrium constraints. We observe the dependence of the second-order coherence of the output upon the width of the output-coupling beam, and note that even in the presence of a highly coherent trapped gas, perfect coherence of the output matter wave is not guaranteed
Self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the Δ distribution function
International Nuclear Information System (INIS)
Mao, G.; Li, Z.; Zhuo, Y.
1996-01-01
We derive the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) equation for the delta distribution function within the framework which we have done for nucleon close-quote s. In our approach, the Δ isobars are treated in essentially the same way as nucleons. Both mean field and collision terms of Δ close-quote s RBUU equation are derived from the same effective Lagrangian and presented analytically. We calculate the in-medium NΔ elastic and inelastic scattering cross sections up to twice nuclear matter density and the results show that the in-medium cross sections deviate substantially from Cugnon close-quote s parametrization that is commonly used in the transport model. copyright 1996 The American Physical Society
DEFF Research Database (Denmark)
Zecevic, Miroslav; Pantleon, Wolfgang; Lebensohn, Ricardo A.
2017-01-01
In a recent paper, we reported the methodology to calculate intragranular fluctuations in the instantaneous lattice rotation rates in polycrystalline materials within the mean-field viscoplastic self-consistent (VPSC) model. This paper is concerned with the time integration and subsequent use......, we calculate intragranular misorientations in face-centered cubic polycrystals deformed in tension and plane-strain compression. These predictions are tested by comparison with corresponding experiments for polycrystalline copper and aluminum, respectively, and with full-field calculations....... It is observed that at sufficiently high strains some grains develop large misorientations that may lead to grain fragmentation and/or act as driving forces for recrystallization. The proposed VPSC-based prediction of intragranular misorientations enables modeling of grain fragmentation, as well as a more...
The numerical multiconfiguration self-consistent field approach for atoms
International Nuclear Information System (INIS)
Stiehler, Johannes
1995-12-01
The dissertation uses the Multiconfiguration Self-Consistent Field Approach to specify the electronic wave function of N electron atoms in a static electrical field. It presents numerical approaches to describe the wave functions and introduces new methods to compute the numerical Fock equations. Based on results computed with an implemented computer program the universal application, flexibility and high numerical precision of the presented approach is shown. RHF results and for the first time MCSCF results for polarizabilities and hyperpolarizabilities of various states of the atoms He to Kr are discussed. In addition, an application to interpret a plasma spectrum of gallium is presented. (orig.)
Self-consistent potential variations in magnetic wells
International Nuclear Information System (INIS)
Kesner, J.; Knorr, G.; Nicholson, D.R.
1981-01-01
Self-consistent electrostatic potential variations are considered in a spatial region of weak magnetic field, as in the proposed tandem mirror thermal barriers (with no trapped ions). For some conditions, equivalent to ion distributions with a sufficiently high net drift speed along the magnetic field, the desired potential depressions are found. When the net drift speed is not high enough, potential depressions are found only in combination with strong electric fields on the boundaries of the system. These potential depressions are not directly related to the magnetic field depression. (author)
A self-consistent model of an isothermal tokamak
McNamara, Steven; Lilley, Matthew
2014-10-01
Continued progress in liquid lithium coating technologies have made the development of a beam driven tokamak with minimal edge recycling a feasibly possibility. Such devices are characterised by improved confinement due to their inherent stability and the suppression of thermal conduction. Particle and energy confinement become intrinsically linked and the plasma thermal energy content is governed by the injected beam. A self-consistent model of a purely beam fuelled isothermal tokamak is presented, including calculations of the density profile, bulk species temperature ratios and the fusion output. Stability considerations constrain the operating parameters and regions of stable operation are identified and their suitability to potential reactor applications discussed.
Self-consistent calculation of 208Pb spectrum
International Nuclear Information System (INIS)
Pal'chik, V.V.; Pyatov, N.I.; Fayans, S.A.
1981-01-01
The self-consistent model with exact accounting for one-particle continuum is applied to calculate all discrete particle-hole natural parity states with 2 208 Pb nucleus (up to the neutron emission threshold, 7.4 MeV). Contributions to the energy-weighted sum rules S(EL) of the first collective levels and total contributions of all discrete levels are evaluated. Most strongly the collectivization is manifested for octupole states. With multipolarity growth L contributions of discrete levels are sharply reduced. The results are compared with other models and the experimental data obtained in (e, e'), (p, p') reactions and other data [ru
Poisson solvers for self-consistent multi-particle simulations
International Nuclear Information System (INIS)
Qiang, J; Paret, S
2014-01-01
Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density distribution in the multi-particle simulation. In this paper, we review a number of numerical methods that can be used to solve the Poisson equation efficiently. The computational complexity of those numerical methods will be O(N log(N)) or O(N) instead of O(N2), where N is the total number of grid points used to solve the Poisson equation
Wavelets in self-consistent electronic structure calculations
International Nuclear Information System (INIS)
Wei, S.; Chou, M.Y.
1996-01-01
We report the first implementation of orthonormal wavelet bases in self-consistent electronic structure calculations within the local-density approximation. These local bases of different scales efficiently describe localized orbitals of interest. As an example, we studied two molecules, H 2 and O 2 , using pseudopotentials and supercells. Considerably fewer bases are needed compared with conventional plane-wave approaches, yet calculated binding properties are similar. Our implementation employs fast wavelet and Fourier transforms, avoiding evaluating any three-dimensional integral numerically. copyright 1996 The American Physical Society
Tunneling in a self-consistent dynamic image potential
International Nuclear Information System (INIS)
Rudberg, B.G.R.; Jonson, M.
1991-01-01
We have calculated the self-consistent effective potential for an electron tunneling through a square barrier while interacting with surface plasmons. This potential reduces to the classical image potential in the static limit. In the opposite limit, when the ''velocity'' of the tunneling electron is large, it reduces to the unperturbed square-barrier potential. For a wide variety of parameters the dynamic effects on the transmission coefficient T=|t 2 | can, for instance, be related to the Buettiker-Landauer traversal time for tunneling, given by τ BL =ℎ|d lnt/dV|
On the hydrodynamic limit of self-consistent field equations
International Nuclear Information System (INIS)
Pauli, H.C.
1980-01-01
As an approximation to the nuclear many-body problem, the hydrodynamical limit of self-consistent field equations is worked out and applied to the treatment of vibrational and rotational motion. Its validity is coupled to the value of a smallness parameter, behaving as 20Asup(-2/3) with the number of nucleons. For finite nuclei, this number is not small enough as compared to 1, and indeed one observes a discrepancy of roughly a factor of 5 between the hydrodynamic frequencies and the relevant experimental numbers. (orig.)
Mean-field learning for satisfactory solutions
Tembine, Hamidou
2013-12-01
One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.
Stochastic quantization and mean field approximation
International Nuclear Information System (INIS)
Jengo, R.; Parga, N.
1983-09-01
In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)
Self-consistent viscous heating of rapidly compressed turbulence
Campos, Alejandro; Morgan, Brandon
2017-11-01
Given turbulence subjected to infinitely rapid deformations, linear terms representing interactions between the mean flow and the turbulence dictate the evolution of the flow, whereas non-linear terms corresponding to turbulence-turbulence interactions are safely ignored. For rapidly deformed flows where the turbulence Reynolds number is not sufficiently large, viscous effects can't be neglected and tend to play a prominent role, as shown in the study of Davidovits & Fisch (2016). For such a case, the rapid increase of viscosity in a plasma-as compared to the weaker scaling of viscosity in a fluid-leads to the sudden viscous dissipation of turbulent kinetic energy. As shown in Davidovits & Fisch, increases in temperature caused by the direct compression of the plasma drive sufficiently large values of viscosity. We report on numerical simulations of turbulence where the increase in temperature is the result of both the direct compression (an inviscid mechanism) and the self-consistent viscous transfer of energy from the turbulent scales towards the thermal energy. A comparison between implicit large-eddy simulations against well-resolved direct numerical simulations is included to asses the effect of the numerical and subgrid-scale dissipation on the self-consistent viscous This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Self-consistent modeling of electron cyclotron resonance ion sources
International Nuclear Information System (INIS)
Girard, A.; Hitz, D.; Melin, G.; Serebrennikov, K.; Lecot, C.
2004-01-01
In order to predict the performances of electron cyclotron resonance ion source (ECRIS), it is necessary to perfectly model the different parts of these sources: (i) magnetic configuration; (ii) plasma characteristics; (iii) extraction system. The magnetic configuration is easily calculated via commercial codes; different codes also simulate the ion extraction, either in two dimension, or even in three dimension (to take into account the shape of the plasma at the extraction influenced by the hexapole). However the characteristics of the plasma are not always mastered. This article describes the self-consistent modeling of ECRIS: we have developed a code which takes into account the most important construction parameters: the size of the plasma (length, diameter), the mirror ratio and axial magnetic profile, whether a biased probe is installed or not. These input parameters are used to feed a self-consistent code, which calculates the characteristics of the plasma: electron density and energy, charge state distribution, plasma potential. The code is briefly described, and some of its most interesting results are presented. Comparisons are made between the calculations and the results obtained experimentally
Self-consistent modeling of electron cyclotron resonance ion sources
Girard, A.; Hitz, D.; Melin, G.; Serebrennikov, K.; Lécot, C.
2004-05-01
In order to predict the performances of electron cyclotron resonance ion source (ECRIS), it is necessary to perfectly model the different parts of these sources: (i) magnetic configuration; (ii) plasma characteristics; (iii) extraction system. The magnetic configuration is easily calculated via commercial codes; different codes also simulate the ion extraction, either in two dimension, or even in three dimension (to take into account the shape of the plasma at the extraction influenced by the hexapole). However the characteristics of the plasma are not always mastered. This article describes the self-consistent modeling of ECRIS: we have developed a code which takes into account the most important construction parameters: the size of the plasma (length, diameter), the mirror ratio and axial magnetic profile, whether a biased probe is installed or not. These input parameters are used to feed a self-consistent code, which calculates the characteristics of the plasma: electron density and energy, charge state distribution, plasma potential. The code is briefly described, and some of its most interesting results are presented. Comparisons are made between the calculations and the results obtained experimentally.
Self-consistent chaos in the beam-plasma instability
International Nuclear Information System (INIS)
Tennyson, J.L.; Meiss, J.D.
1993-01-01
The effect of self-consistency on Hamiltonian systems with a large number of degrees-of-freedom is investigated for the beam-plasma instability using the single-wave model of O'Neil, Winfrey, and Malmberg.The single-wave model is reviewed and then rederived within the Hamiltonian context, which leads naturally to canonical action- angle variables. Simulations are performed with a large (10 4 ) number of beam particles interacting with the single wave. It is observed that the system relaxes into a time asymptotic periodic state where only a few collective degrees are active; namely, a clump of trapped particles oscillating in a modulated wave, within a uniform chaotic sea with oscillating phase space boundaries. Thus self-consistency is seen to effectively reduce the number of degrees- of-freedom. A simple low degree-of-freedom model is derived that treats the clump as a single macroparticle, interacting with the wave and chaotic sea. The uniform chaotic sea is modeled by a fluid waterbag, where the waterbag boundaries correspond approximately to invariant tori. This low degree-of-freedom model is seen to compare well with the simulation
Self-consistent electron transport in collisional plasmas
International Nuclear Information System (INIS)
Mason, R.J.
1982-01-01
A self-consistent scheme has been developed to model electron transport in evolving plasmas of arbitrary classical collisionality. The electrons and ions are treated as either multiple donor-cell fluids, or collisional particles-in-cell. Particle suprathermal electrons scatter off ions, and drag against fluid background thermal electrons. The background electrons undergo ion friction, thermal coupling, and bremsstrahlung. The components move in self-consistent advanced E-fields, obtained by the Implicit Moment Method, which permits Δt >> ω/sub p/ -1 and Δx >> lambda/sub D/ - offering a 10 2 - 10 3 -fold speed-up over older explicit techniques. The fluid description for the background plasma components permits the modeling of transport in systems spanning more than a 10 7 -fold change in density, and encompassing contiguous collisional and collisionless regions. Results are presented from application of the scheme to the modeling of CO 2 laser-generated suprathermal electron transport in expanding thin foils, and in multi-foil target configurations
Efficient self-consistency for magnetic tight binding
Soin, Preetma; Horsfield, A. P.; Nguyen-Manh, D.
2011-06-01
Tight binding can be extended to magnetic systems by including an exchange interaction on an atomic site that favours net spin polarisation. We have used a published model, extended to include long-ranged Coulomb interactions, to study defects in iron. We have found that achieving self-consistency using conventional techniques was either unstable or very slow. By formulating the problem of achieving charge and spin self-consistency as a search for stationary points of a Harris-Foulkes functional, extended to include spin, we have derived a much more efficient scheme based on a Newton-Raphson procedure. We demonstrate the capabilities of our method by looking at vacancies and self-interstitials in iron. Self-consistency can indeed be achieved in a more efficient and stable manner, but care needs to be taken to manage this. The algorithm is implemented in the code PLATO. Program summaryProgram title:PLATO Catalogue identifier: AEFC_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 228 747 No. of bytes in distributed program, including test data, etc.: 1 880 369 Distribution format: tar.gz Programming language: C and PERL Computer: Apple Macintosh, PC, Unix machines Operating system: Unix, Linux, Mac OS X, Windows XP Has the code been vectorised or parallelised?: Yes. Up to 256 processors tested RAM: Up to 2 Gbytes per processor Classification: 7.3 External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTW Catalogue identifier of previous version: AEFC_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 2616 Does the new version supersede the previous version?: Yes Nature of problem: Achieving charge and spin self-consistency in magnetic tight binding can be very
Martins, Cyril; Lenz, Benjamin; Perfetti, Luca; Brouet, Veronique; Bertran, François; Biermann, Silke
2018-03-01
We address the role of nonlocal Coulomb correlations and short-range magnetic fluctuations in the high-temperature phase of Sr2IrO4 within state-of-the-art spectroscopic and first-principles theoretical methods. Introducing an "oriented-cluster dynamical mean-field scheme", we compute momentum-resolved spectral functions, which we find to be in excellent agreement with angle-resolved photoemission spectra. We show that while short-range antiferromagnetic fluctuations are crucial to accounting for the electronic properties of Sr2IrO4 even in the high-temperature paramagnetic phase, long-range magnetic order is not a necessary ingredient of the insulating state. Upon doping, an exotic metallic state is generated, exhibiting cuprate-like pseudo-gap spectral properties, for which we propose a surprisingly simple theoretical mechanism.
Directory of Open Access Journals (Sweden)
Michael Brown
2015-11-01
Full Text Available Approximations based on two-particle irreducible (2PI effective actions (also known as Φ-derivable, Cornwall–Jackiw–Tomboulis or Luttinger–Ward functionals depending on context have been widely used in condensed matter and non-equilibrium quantum/statistical field theory because this formalism gives a robust, self-consistent, non-perturbative and systematically improvable approach which avoids problems with secular time evolution. The strengths of 2PI approximations are often described in terms of a selective resummation of Feynman diagrams to infinite order. However, the Feynman diagram series is asymptotic and summation is at best a dangerous procedure. Here we show that, at least in the context of a toy model where exact results are available, the true strength of 2PI approximations derives from their self-consistency rather than any resummation. This self-consistency allows truncated 2PI approximations to capture the branch points of physical amplitudes where adjustments of coupling constants can trigger an instability of the vacuum. This, in effect, turns Dyson's argument for the failure of perturbation theory on its head. As a result we find that 2PI approximations perform better than Padé approximation and are competitive with Borel–Padé resummation. Finally, we introduce a hybrid 2PI–Padé method.
Exciton spectrum of surface-corrugated quantum wells: the adiabatic self-consistent approach
International Nuclear Information System (INIS)
Atenco A, N.; Perez R, F.; Makarov, N.M.
2005-01-01
A theory for calculating the relaxation frequency ν and the shift δ ω of exciton resonances in quantum wells with finite potential barriers and adiabatic surface disorder is developed. The adiabaticity implies that the correlation length R C for the well width fluctuations is much larger than the exciton radius a 0 (R C >> a 0 ). Our theory is based on the self-consistent Green's function method, and therefore takes into account the inherent action of the exciton scattering on itself. The self-consistent approach is shown to describe quantitatively the sharp exciton resonance. It also gives the qualitatively correct resonance picture for the transition to the classical limit, as well as within the domain of the classical limit itself. We present and analyze results for h h-exciton in a GaAs quantum well with Al 0.3 Ga 0.7 As barriers. It is established that the self-consistency and finite height of potential barriers significantly influence on the line-shape of exciton resonances, and make the values of ν and δ ω be quite realistic. In particular, the relaxation frequency ν for the ground-state resonance has a broad, almost symmetric maximum near the resonance frequency ω 0 , while the surface-induced resonance shift δ ω vanishes near ω 0 , and has different signs on the sides of the exciton resonance. (Author) 43 refs., 4 figs
Communication: A difference density picture for the self-consistent field ansatz
Energy Technology Data Exchange (ETDEWEB)
Parrish, Robert M.; Liu, Fang; Martínez, Todd J., E-mail: toddjmartinez@gmail.com [Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305 (United States); SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)
2016-04-07
We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this “difference self-consistent field (dSCF)” picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TERACHEM SCF implementation.
Communication: A difference density picture for the self-consistent field ansatz
International Nuclear Information System (INIS)
Parrish, Robert M.; Liu, Fang; Martínez, Todd J.
2016-01-01
We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this “difference self-consistent field (dSCF)” picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TERACHEM SCF implementation.
Communication: A difference density picture for the self-consistent field ansatz
Parrish, Robert M.; Liu, Fang; Martínez, Todd J.
2016-04-01
We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this "difference self-consistent field (dSCF)" picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TeraChem SCF implementation.
Liang, Y Y; Chen, H; Mizuseki, H; Kawazoe, Y
2011-04-14
We use density functional theory based nonequilibrium Green's function to self-consistently study the current through the 1,4-benzenedithiol (BDT). The elastic and inelastic tunneling properties through this Au-BDT-Au molecular junction are simulated, respectively. For the elastic tunneling case, it is found that the current through the tilted molecule can be modulated effectively by the external gate field, which is perpendicular to the phenyl ring. The gate voltage amplification comes from the modulation of the interaction between the electrodes and the molecules in the junctions. For the inelastic case, the electron tunneling scattered by the molecular vibrational modes is considered within the self-consistent Born approximation scheme, and the inelastic electron tunneling spectrum is calculated.
Analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field method
Directory of Open Access Journals (Sweden)
N.Yoshida
2007-09-01
Full Text Available An analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field (MOZ-SCF method is presented. MOZ-SCF theory is one of the theories to considering the solvent effects on the solute electronic structure in solution. [Yoshida N. et al., J. Chem. Phys., 2000, 113, 4974] Molecular geometries of water, formaldehyde, acetonitrile and acetone in water are optimized by analytical energy gradient formula. The results are compared with those from the polarizable continuum model (PCM, the reference interaction site model (RISM-SCF and the three dimensional (3D RISM-SCF.
Simulations of tokamak disruptions including self-consistent temperature evolution
International Nuclear Information System (INIS)
Bondeson, A.
1986-01-01
Three-dimensional simulations of tokamaks have been carried out, including self-consistent temperature evolution with a highly anisotropic thermal conductivity. The simulations extend over the transport time-scale and address the question of how disruptive current profiles arise at low-q or high-density operation. Sharply defined disruptive events are triggered by the m/n=2/1 resistive tearing mode, which is mainly affected by local current gradients near the q=2 surface. If the global current gradient between q=2 and q=1 is sufficiently steep, the m=2 mode starts a shock which accelerates towards the q=1 surface, leaving stochastic fields, a flattened temperature profile and turbulent plasma behind it. For slightly weaker global current gradients, a shock may form, but it will dissipate before reaching q=1 and may lead to repetitive minidisruptions which flatten the temperature profile in a region inside the q=2 surface. (author)
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Manchon, Aurelien; Praetorius, Dirk; Suess, Dieter
2016-01-01
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
Self-consistent determination of quasiparticle properties in nuclear matter
International Nuclear Information System (INIS)
Oset, E.; Palanques-Mestre, A.
1981-01-01
The self-energy of nuclear matter is calculated by directing the attention to the energy and momentum dependent pieces which determine the quasiparticle properties. A microscopic approach is followed which starts from the boson exchange picture for the NN interaction, then the π-and p-mesons are shown to play a major role in the nucleon renormalization. The calculation is done self-consistently and the effective mass and pole strength determined as a function of the nuclear density and momentum. Particular emphasis is put on the non-static character of the interaction and its consequences. Finally a comparison is made with other calculations and with experimental results. The consequences of the nucleon renormalization in pion condensation are also examined with the result that the critical density is pushed up appreciably. (orig.)
Self-Consistent Dynamical Model of the Broad Line Region
Energy Technology Data Exchange (ETDEWEB)
Czerny, Bozena [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Li, Yan-Rong [Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing (China); Sredzinska, Justyna; Hryniewicz, Krzysztof [Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw (Poland); Panda, Swayam [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw (Poland); Wildy, Conor [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Karas, Vladimir, E-mail: bcz@cft.edu.pl [Astronomical Institute, Czech Academy of Sciences, Prague (Czech Republic)
2017-06-22
We develop a self-consistent description of the Broad Line Region based on the concept of a failed wind powered by radiation pressure acting on a dusty accretion disk atmosphere in Keplerian motion. The material raised high above the disk is illuminated, dust evaporates, and the matter falls back toward the disk. This material is the source of emission lines. The model predicts the inner and outer radius of the region, the cloud dynamics under the dust radiation pressure and, subsequently, the gravitational field of the central black hole, which results in asymmetry between the rise and fall. Knowledge of the dynamics allows us to predict the shapes of the emission lines as functions of the basic parameters of an active nucleus: black hole mass, accretion rate, black hole spin (or accretion efficiency) and the viewing angle with respect to the symmetry axis. Here we show preliminary results based on analytical approximations to the cloud motion.
Self-consistent modeling of amorphous silicon devices
International Nuclear Information System (INIS)
Hack, M.
1987-01-01
The authors developed a computer model to describe the steady-state behaviour of a range of amorphous silicon devices. It is based on the complete set of transport equations and takes into account the important role played by the continuous distribution of localized states in the mobility gap of amorphous silicon. Using one set of parameters they have been able to self-consistently simulate the current-voltage characteristics of p-i-n (or n-i-p) solar cells under illumination, the dark behaviour of field-effect transistors, p-i-n diodes and n-i-n diodes in both the ohmic and space charge limited regimes. This model also describes the steady-state photoconductivity of amorphous silicon, in particular, its dependence on temperature, doping and illumination intensity
Self-consistent Langmuir waves in resonantly driven thermal plasmas
Lindberg, R. R.; Charman, A. E.; Wurtele, J. S.
2007-12-01
The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly invariant in the canonical particle action, provided both a spatially uniform term and higher-order spatial harmonics are included along with the fundamental in the longitudinal electric field. Requirements of self-consistency with the electrostatic potential yield the basic properties of the nonlinear distribution function, including a frequency shift that agrees closely with driven, electrostatic particle simulations over a range of temperatures. This extends earlier work on nonlinear Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] and Dewar [R. L. Dewar, Phys. Plasmas 15, 712 (1972)], and could form the basis of a reduced kinetic treatment of plasma dynamics for accelerator applications or Raman backscatter.
Self-consistent Langmuir waves in resonantly driven thermal plasmas
International Nuclear Information System (INIS)
Lindberg, R. R.; Charman, A. E.; Wurtele, J. S.
2007-01-01
The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly invariant in the canonical particle action, provided both a spatially uniform term and higher-order spatial harmonics are included along with the fundamental in the longitudinal electric field. Requirements of self-consistency with the electrostatic potential yield the basic properties of the nonlinear distribution function, including a frequency shift that agrees closely with driven, electrostatic particle simulations over a range of temperatures. This extends earlier work on nonlinear Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] and Dewar [R. L. Dewar, Phys. Plasmas 15, 712 (1972)], and could form the basis of a reduced kinetic treatment of plasma dynamics for accelerator applications or Raman backscatter
Self-consistent, relativistic, ferromagnetic band structure of gadolinium
International Nuclear Information System (INIS)
Harmon, B.N.; Schirber, J.; Koelling, D.D.
1977-01-01
An initial self-consistent calculation of the ground state magnetic band structure of gadolinium is described. A linearized APW method was used which included all single particle relativistic effects except spin-orbit coupling. The spin polarized potential was obtained in the muffin-tin form using the local spin density approximation for exchange and correlation. The most striking and unorthodox aspect of the results is the position of the 4f spin-down ''bands'' which are required to float just on top of the Fermi level in order to obtain convergence. If the 4f states (l = 3 resonance) are removed from the occupied region of the conduction bands the magnetic moment is approximately .75 μ/sub B//atom; however, as the 4f spin-down states are allowed to find their own position they hybridize with the conduction bands at the Fermi level and the moment becomes smaller. Means of improving the calculation are discussed
Self-consistent simulation of the CSR effect
International Nuclear Information System (INIS)
Li, R.; Bohn, C.L.; Bisogano, J.J.
1998-01-01
When a microbunch with high charge traverses a curved trajectory, the curvature-induced bunch self-interaction, by way of coherent synchrotron radiation (CSR) and space-charge forces, may cause serious emittance degradation. In this paper, the authors present a self-consistent simulation for the study of the impact of CSR on beam optics. The dynamics of the bunch under the influence of the CSR forces is simulated using macroparticles, where the CSR force in turn depends on the history of bunch dynamics in accordance with causality. The simulation is benchmarked with analytical results obtained for a rigid-line bunch. Here they present the algorithm used in the simulation, along with the simulation results obtained for bending systems in the Jefferson Lab (JLab) free-electron-laser (FEL) lattice
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas
2016-12-17
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
Self-Consistent Dynamical Model of the Broad Line Region
Directory of Open Access Journals (Sweden)
Bozena Czerny
2017-06-01
Full Text Available We develop a self-consistent description of the Broad Line Region based on the concept of a failed wind powered by radiation pressure acting on a dusty accretion disk atmosphere in Keplerian motion. The material raised high above the disk is illuminated, dust evaporates, and the matter falls back toward the disk. This material is the source of emission lines. The model predicts the inner and outer radius of the region, the cloud dynamics under the dust radiation pressure and, subsequently, the gravitational field of the central black hole, which results in asymmetry between the rise and fall. Knowledge of the dynamics allows us to predict the shapes of the emission lines as functions of the basic parameters of an active nucleus: black hole mass, accretion rate, black hole spin (or accretion efficiency and the viewing angle with respect to the symmetry axis. Here we show preliminary results based on analytical approximations to the cloud motion.
A self-consistent nuclear energy supply system
International Nuclear Information System (INIS)
Fujii-e, Y.; Morita, T.; Kawakami, H.; Arie, K.; Suzuki, M.; Iida, M.; Yamazaki, H.
1992-01-01
A self-consistent nuclear energy supply system (SCNESS) is investigated for a Fast Reactor. SCNESS is proposed as a future stable energy supplier with no harmful influence on humans or environment for the ultimate goal of nuclear energy development. SCNESS should be inherently safe, be able to breed fissionable material, and transmute long-lived radioactive nuclides (i.e., minor actinides and long-lived fission products). The relationship between these characteristics and the spatial assignment of excess neutrons (v-1) for each characteristic are analyzed. The analysis shows that excess neutrons play an intrinsic role in realizing SCNESS. The reactor concept of SCNESS is investigated by considering utilization of excess neutrons. Results show that a small-size axially double-layered annular core with metal fuel is a choice candidate for SCNESS. SCNESS is concluded feasible. (author). 4 refs., 9 figs
Self-consistent equilibria in cylindrical reversed-field pinch
International Nuclear Information System (INIS)
Lo Surdo, C.; Paccagnella, R.; Guo, S.
1995-03-01
The object of this work is to study the self-consistent magnetofluidstatic equilibria of a 2-region (plasma + gas) reversed-field pinch (RFP) in cylindrical approximation (namely, with vanishing inverse aspect ratio). Differently from what happens in a tokamak, in a RFP a significant part of the plasma current is driven by a dynamo electric field (DEF), in its turn mainly due to plasma turbulence. So, it is worked out a reasonable mathematical model of the above self-consistent equilibria under the following main points it has been: a) to the lowest order, and according to a standard ansatz, the turbulent DEF say ε t , is expressed as a homogeneous transform of the magnetic field B of degree 1, ε t =(α) (B), with α≡a given 2-nd rank tensor, homogeneous of degree 0 in B and generally depending on the plasma state; b) ε t does not explicitly appear in the plasma energy balance, as it were produced by a Maxwell demon able of extract the corresponding Joule power from the plasma. In particular, it is showed that, if both α and the resistivity tensor η are isotropic and constant, the magnetic field is force-free with abnormality equal to αη 0 /η, in the limit of vanishing β; that is, the well-known J.B. Taylor'result is recovered, in this particular conditions, starting from ideas quite different from the usual ones (minimization of total magnetic energy under constrained total elicity). Finally, the general problem is solved numerically under circular (besides cylindrical) symmetry, for simplicity neglecting the existence of gas region (i.e., assuming the plasma in direct contact with the external wall)
Sums over geometries and improvements on the mean field approximation
International Nuclear Information System (INIS)
Sacksteder, Vincent E. IV
2007-01-01
The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-11-01
We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
Effective masses and the nuclear mean field
International Nuclear Information System (INIS)
Mahaux, C.; Sartor, R.
1985-01-01
The effective mass characterizes the energy dependence of the empirical average nuclear potential. This energy dependence has two different sources, namely the nonlocality in space of the microscopic mean field on the one hand, and its true energy dependence on the other hand. Correspondingly it is convenient to divide the effective mass into two components, the k-mass and the ω-mass. The latter is responsible for the existence of a peak in the energy dependence of the effective mass. This peak is located near the Fermi energy in nuclear matter and in nuclei, as well as in the electron gas, the hard sphere Fermi gas and liquid helium 3. A related phenomenon is the existence of a low energy anomaly in the energy dependence of the optical model potential between two heavy ions. (orig.)
Self-consistent approach for neutral community models with speciation
Haegeman, Bart; Etienne, Rampal S.
2010-03-01
Hubbell’s neutral model provides a rich theoretical framework to study ecological communities. By incorporating both ecological and evolutionary time scales, it allows us to investigate how communities are shaped by speciation processes. The speciation model in the basic neutral model is particularly simple, describing speciation as a point-mutation event in a birth of a single individual. The stationary species abundance distribution of the basic model, which can be solved exactly, fits empirical data of distributions of species’ abundances surprisingly well. More realistic speciation models have been proposed such as the random-fission model in which new species appear by splitting up existing species. However, no analytical solution is available for these models, impeding quantitative comparison with data. Here, we present a self-consistent approximation method for neutral community models with various speciation modes, including random fission. We derive explicit formulas for the stationary species abundance distribution, which agree very well with simulations. We expect that our approximation method will be useful to study other speciation processes in neutral community models as well.
A self-consistent upward leader propagation model
International Nuclear Information System (INIS)
Becerra, Marley; Cooray, Vernon
2006-01-01
The knowledge of the initiation and propagation of an upward moving connecting leader in the presence of a downward moving lightning stepped leader is a must in the determination of the lateral attraction distance of a lightning flash by any grounded structure. Even though different models that simulate this phenomenon are available in the literature, they do not take into account the latest developments in the physics of leader discharges. The leader model proposed here simulates the advancement of positive upward leaders by appealing to the presently understood physics of that process. The model properly simulates the upward continuous progression of the positive connecting leaders from its inception to the final connection with the downward stepped leader (final jump). Thus, the main physical properties of upward leaders, namely the charge per unit length, the injected current, the channel gradient and the leader velocity are self-consistently obtained. The obtained results are compared with an altitude triggered lightning experiment and there is good agreement between the model predictions and the measured leader current and the experimentally inferred spatial and temporal location of the final jump. It is also found that the usual assumption of constant charge per unit length, based on laboratory experiments, is not valid for lightning upward connecting leaders
International Nuclear Information System (INIS)
Hojsik, M.; Gmuca, S.
1998-01-01
Relativistic microscopic calculations are presented for proton elastic scattering from 40 Ca at 500 MeV. The underlying target densities are calculated within the framework of the relativistic mean-field theory with several parameter sets commonly in use. The self consistency of the scalar and vector densities (and thus to relativistic mean-field parameters) is investigated. Recently, the relativistic impulse approximation (RIA) has been widely and repeatedly used for the calculations of proton-nucleus scattering at intermediate energies. These calculations have exhibited significant improvements over the nonrelativistic approaches. The relativistic impulse approximation calculations. in particular, provide a dramatically better description of the spin observables, namely the analyzing power, A y , and the spin-rotation function, Q, at least for energies higher than 400 MeV. In the relativistic impulse approximation, the Dirac optical potential is obtained by folding of the local Lorentz-invariant amplitudes with the corresponding nuclear densities. For the spin zero targets the scalar and vector terms give the dominant contributions. Thus the scalar and vector nuclear densities (both, proton and neutron ones) play the dominant role in the relativistic impulse approximation. While the proton vector densities can be obtained by unfolding from the empirically known charge densities, all other densities used rely to a great extent on theoretical models. The various recipes are used to construct the neutron vector densities and the scalar densities for both, neutrons and protons. In this paper we will study the sensitivity of the relativistic impulse approximation results on the various sets of relativistic mean-field parameters currently in use
Self-consistent RPA calculations with Skyrme-type interactions: The skyrme_rpa program
Colò, Gianluca; Cao, Ligang; Van Giai, Nguyen; Capelli, Luigi
2013-01-01
Random Phase Approximation (RPA) calculations are nowadays an indispensable tool in nuclear physics studies. We present here a complete version implemented with Skyrme-type interactions, with the spherical symmetry assumption, that can be used in cases where the effects of pairing correlations and of deformation can be ignored. The full self-consistency between the Hartree-Fock mean field and the RPA excitations is enforced, and it is numerically controlled by comparison with energy-weighted sum rules. The main limitations are that charge-exchange excitations and transitions involving spin operators are not included in this version. Program summaryProgram title: skyrme_rpa (v 1.00) Catalogue identifier: AENF_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5531 No. of bytes in distributed program, including test data, etc.: 39435 Distribution format: tar.gz Programming language: FORTRAN-90/95; easily downgradable to FORTRAN-77. Computer: PC with Intel Celeron, Intel Pentium, AMD Athlon and Intel Core Duo processors. Operating system: Linux, Windows. RAM: From 4 MBytes to 150 MBytes, depending on the size of the nucleus and of the model space for RPA. Word size: The code is written with a prevalent use of double precision or REAL(8) variables; this assures 15 significant digits. Classification: 17.24. Nature of problem: Systematic observations of excitation properties in finite nuclear systems can lead to improved knowledge of the nuclear matter equation of state as well as a better understanding of the effective interaction in the medium. This is the case of the nuclear giant resonances and low-lying collective excitations, which can be described as small amplitude collective motions in the framework of
Self-consistent electronic structure of the contracted tungsten (001) surface
International Nuclear Information System (INIS)
Posternak, M.; Krakauer, H.; Freeman, A.J.
1982-01-01
Self-consistent linearized-augmented-plane-wave energy-band studies using the warped muffin-tin approximation for a seven-layer W(001) single slab with the surface-layer separation contracted by 6% of the bulk interlayer spacing are reported. Surface electronic structure, local densities of states, generalized susceptibility for the surface, work function, and core-level shifts are found to have insignificant differences with corresponding results for the unrelaxed surface. Several differences in surface states between theory and recent angle-resolved photoemission experiments are discussed in the light of new proposed models of the actual unreconstructed surface structure at high temperatures
Generating functional of the mean field in quantum electrodynamics with non-stable vacuum
International Nuclear Information System (INIS)
Gitman, D.M.; Kuchin, V.A.
1981-01-01
Generating functional for calculating a mean field, in the case of unstable vacuum, in quantum field theory has been suggested. Continual representation for the generating functional of the mean field has been found in the case of quantum electrodynamics with an external field. Generating electron-positron pairs from vacuum [ru
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
2016-06-03
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
Instabilities constraint and relativistic mean field parametrization
International Nuclear Information System (INIS)
Sulaksono, A.; Kasmudin; Buervenich, T.J.; Reinhard, P.-G.; Maruhn, J.A.
2011-01-01
Two parameter sets (Set 1 and Set 2) of the standard relativistic mean field (RMF) model plus additional vector isoscalar nonlinear term, which are constrained by a set of criteria 20 determined by symmetric nuclear matter stabilities at high densities due to longitudinal and transversal particle–hole excitation modes are investigated. In the latter parameter set, δ meson and isoscalar as well as isovector tensor contributions are included. The effects in selected finite nuclei and nuclear matter properties predicted by both parameter sets are systematically studied and compared with the ones predicted by well-known RMF parameter sets. The vector isoscalar nonlinear term addition and instability constraints have reasonably good effects in the high-density properties of the isoscalar sector of nuclear matter and certain finite nuclei properties. However, even though the δ meson and isovector tensor are included, the incompatibility with the constraints from some experimental data in certain nuclear properties at saturation point and the excessive stiffness of the isovector nuclear matter equation of state at high densities as well as the incorrect isotonic trend in binding the energies of finite nuclei are still encountered. It is shown that the problem may be remedied if we introduce additional nonlinear terms not only in the isovector but also in the isoscalar vectors. (author)
Exciton spectrum of surface-corrugated quantum wells: the adiabatic self-consistent approach
Energy Technology Data Exchange (ETDEWEB)
Atenco A, N.; Perez R, F. [lnstituto de Fisica, Universidad Autonoma de Puebla, A.P. J-48, 72570 Puebla (Mexico); Makarov, N.M. [lnstituto de Ciencias, Universidad Autonoma de Puebla, Priv. 17 Norte No 3417, Col. San Miguel Hueyotlipan, 72050 Puebla (Mexico)
2005-07-01
A theory for calculating the relaxation frequency {nu} and the shift {delta} {omega} of exciton resonances in quantum wells with finite potential barriers and adiabatic surface disorder is developed. The adiabaticity implies that the correlation length R{sub C} for the well width fluctuations is much larger than the exciton radius a{sub 0} (R{sub C} >> a{sub 0}). Our theory is based on the self-consistent Green's function method, and therefore takes into account the inherent action of the exciton scattering on itself. The self-consistent approach is shown to describe quantitatively the sharp exciton resonance. It also gives the qualitatively correct resonance picture for the transition to the classical limit, as well as within the domain of the classical limit itself. We present and analyze results for h h-exciton in a GaAs quantum well with Al{sub 0.3} Ga{sub 0.7}As barriers. It is established that the self-consistency and finite height of potential barriers significantly influence on the line-shape of exciton resonances, and make the values of {nu} and {delta} {omega} be quite realistic. In particular, the relaxation frequency {nu} for the ground-state resonance has a broad, almost symmetric maximum near the resonance frequency {omega}{sub 0}, while the surface-induced resonance shift {delta} {omega} vanishes near {omega}{sub 0}, and has different signs on the sides of the exciton resonance. (Author) 43 refs., 4 figs.
Relativistic mean-field mass models
Energy Technology Data Exchange (ETDEWEB)
Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2016-10-15
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)
Self-consistent Modeling of Elastic Anisotropy in Shale
Kanitpanyacharoen, W.; Wenk, H.; Matthies, S.; Vasin, R.
2012-12-01
Elastic anisotropy in clay-rich sedimentary rocks has increasingly received attention because of significance for prospecting of petroleum deposits, as well as seals in the context of nuclear waste and CO2 sequestration. The orientation of component minerals and pores/fractures is a critical factor that influences elastic anisotropy. In this study, we investigate lattice and shape preferred orientation (LPO and SPO) of three shales from the North Sea in UK, the Qusaiba Formation in Saudi Arabia, and the Officer Basin in Australia (referred to as N1, Qu3, and L1905, respectively) to calculate elastic properties and compare them with experimental results. Synchrotron hard X-ray diffraction and microtomography experiments were performed to quantify LPO, weight proportions, and three-dimensional SPO of constituent minerals and pores. Our preliminary results show that the degree of LPO and total amount of clays are highest in Qu3 (3.3-6.5 m.r.d and 74vol%), moderately high in N1 (2.4-5.6 m.r.d. and 70vol%), and lowest in L1905 (2.3-2.5 m.r.d. and 42vol%). In addition, porosity in Qu3 is as low as 2% while it is up to 6% in L1605 and 8% in N1, respectively. Based on this information and single crystal elastic properties of mineral components, we apply a self-consistent averaging method to calculate macroscopic elastic properties and corresponding seismic velocities for different shales. The elastic model is then compared with measured acoustic velocities on the same samples. The P-wave velocities measured from Qu3 (4.1-5.3 km/s, 26.3%Ani.) are faster than those obtained from L1905 (3.9-4.7 km/s, 18.6%Ani.) and N1 (3.6-4.3 km/s, 17.7%Ani.). By making adjustments for pore structure (aspect ratio) and single crystal elastic properties of clay minerals, a good agreement between our calculation and the ultrasonic measurement is obtained.
A self-consistency check for unitary propagation of Hawking quanta
Baker, Daniel; Kodwani, Darsh; Pen, Ue-Li; Yang, I.-Sheng
2017-11-01
The black hole information paradox presumes that quantum field theory in curved space-time can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum-gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman’s analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern is projected is infinitely far away. We argue for an analogous self-consistency check for quantum field theory in curved space-time. We apply it to the propagation of Hawking quanta and test whether ignoring the entanglement with the geometry also becomes arbitrarily reliable in the limit of a large black hole. We present curious results to suggest a negative answer, and we discuss how this loss of naive unitarity in QFT might be related to a solution of the paradox based on the soft-hair-memory effect.
Abram, M; Zegrodnik, M; Spałek, J
2017-09-13
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
Self-consistent ECCD calculations with bootstrap current
International Nuclear Information System (INIS)
Decker, J.; Bers, A.; Ram, A. K; Peysson, Y.
2003-01-01
To achieve high performance, steady-state operation in tokamaks, it is increasingly important to find the appropriate means for modifying and sustaining the pressure and magnetic shear profiles in the plasma. In such advanced scenarios, especially in the vicinity of internal transport barrier, RF induced currents have to be calculated self-consistently with the bootstrap current, thus taking into account possible synergistic effects resulting from the momentum space distortion of the electron distribution function f e . Since RF waves can cause the distribution of electrons to become non-Maxwellian, the associated changes in parallel diffusion of momentum between trapped and passing particles can be expected to modify the bootstrap current fraction; conversely, the bootstrap current distribution function can enhance the current driven by RF waves. For this purpose, a new, fast and fully implicit solver has been recently developed to carry out computations including new and detailed evaluations of the interactions between bootstrap current (BC) and Electron Cyclotron current drive (ECCD). Moreover, Ohkawa current drive (OKCD) appears to be an efficient method for driving current when the fraction of trapped particles is large. OKCD in the presence of BC is also investigated. Here, results are illustrated around projected tokamak parameters in high performance scenarios of AlcatorC-MOD. It is shown that by increasing n // , the EC wave penetration into the bulk of the electron distribution is greater, and since the resonance extends up to high p // values, this situation is the usual ECCD based on the Fisch-Boozer mechanism concerning passing particles. However, because of the close vicinity of the trapped boundary at r/a=0.7, this process is counterbalanced by the Ohkawa effect, possibly leading to a negative net current. Therefore, by injecting the EC wave in the opposite toroidal direction (n // RF by OKCD may be 70% larger than that of ECCD, with a choice of EC
Self-consistent study of localization near band edges
International Nuclear Information System (INIS)
Brezini, A.
1982-02-01
The localization criterion of Kumar et al. is applied to the case of a uniform distribution for the site energies and particular attention is given to the behaviour of the mobility edge in the limit of weak disorder. The results are similar to other theories but disagree with that of Abou-Chacra and Thouless in the limit of zero disorder. (author)
A mean field approach to the Ising chain in a transverse magnetic field
Osácar, C.; Pacheco, A. F.
2017-07-01
We evaluate a mean field method to describe the properties of the ground state of the Ising chain in a transverse magnetic field. Specifically, a method of the Bethe-Peierls type is used by solving spin blocks with a self-consistency condition at the borders. The computations include the critical point for the phase transition, exponent of magnetisation and energy density. All results are obtained using basic quantum mechanics at an undergraduate level. The advantages and the limitations of the approach are emphasised.
Energy Technology Data Exchange (ETDEWEB)
Liu, Z.; Bessa, M. A.; Liu, W.K.
2017-10-25
A predictive computational theory is shown for modeling complex, hierarchical materials ranging from metal alloys to polymer nanocomposites. The theory can capture complex mechanisms such as plasticity and failure that span across multiple length scales. This general multiscale material modeling theory relies on sound principles of mathematics and mechanics, and a cutting-edge reduced order modeling method named self-consistent clustering analysis (SCA) [Zeliang Liu, M.A. Bessa, Wing Kam Liu, “Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials,” Comput. Methods Appl. Mech. Engrg. 306 (2016) 319–341]. SCA reduces by several orders of magnitude the computational cost of micromechanical and concurrent multiscale simulations, while retaining the microstructure information. This remarkable increase in efficiency is achieved with a data-driven clustering method. Computationally expensive operations are performed in the so-called offline stage, where degrees of freedom (DOFs) are agglomerated into clusters. The interaction tensor of these clusters is computed. In the online or predictive stage, the Lippmann-Schwinger integral equation is solved cluster-wise using a self-consistent scheme to ensure solution accuracy and avoid path dependence. To construct a concurrent multiscale model, this scheme is applied at each material point in a macroscale structure, replacing a conventional constitutive model with the average response computed from the microscale model using just the SCA online stage. A regularized damage theory is incorporated in the microscale that avoids the mesh and RVE size dependence that commonly plagues microscale damage calculations. The SCA method is illustrated with two cases: a carbon fiber reinforced polymer (CFRP) structure with the concurrent multiscale model and an application to fatigue prediction for additively manufactured metals. For the CFRP problem, a speed up estimated to be about
Self-Consistent Criteria for Evaluation of Neutron Interaction
International Nuclear Information System (INIS)
Henry, H.F.; Newlon, C.E.; Knight, J.R.
2007-01-01
New safe interaction criteria for containers of fissionable materials handled at the Oak Ridge Gaseous Diffusion Plant have been developed on the basis of an interaction theory using the basic concepts of a safe solid angle subtended by interacting containers, and the multiplication factor as determined by two-group theory for an individually safe containers The calculated results agree satisfactorily with experimental data obtained with identical interacting units involving both cylinders and slabs containing highly enriched uranium, the core compositions of which were varied between H/U-235 atomic ratios of 44.3 and 337. The application of the derived interaction criteria to items containing material with low moderation or low U-235 assay, and to containers for which nuclear safety is dependent upon control of the U-235 mass or U-235 concentration is discussed.
Efficient 3D/1D self-consistent integral-equation analysis of ICRH antennae
International Nuclear Information System (INIS)
Maggiora, R.; Vecchi, G.; Lancellotti, V.; Kyrytsya, V.
2004-01-01
This work presents a comprehensive account of the theory and implementation of a method for the self-consistent numerical analysis of plasma-facing ion-cyclotron resonance heating (ICRH) antenna arrays. The method is based on the integral-equation formulation of the boundary-value problem, solved via a weighted-residual scheme. The antenna geometry (including Faraday shield bars and a recess box) is fairly general and three-dimensional (3D), and the plasma is in the one-dimensional (1D) 'slab' approximation; finite-Larmor radius effects, as well as plasma density and temperature gradients, are considered. Feeding via the voltages in the access coaxial lines is self consistently accounted throughout and the impedance or scattering matrix of the antenna array obtained therefrom. The problem is formulated in both the dual space (physical) and spectral (wavenumber) domains, which allows the extraction and simple handling of the terms that slow the convergence in the spectral domain usually employed. This paper includes validation tests of the developed code against measured data, both in vacuo and in the presence of plasma. An example of application to a complex geometry is also given. (author)
Effects of self-consistency in a Green's function description of saturation in nuclear matter
International Nuclear Information System (INIS)
Dewulf, Y.; Neck, D. van; Waroquier, M.
2002-01-01
The binding energy in nuclear matter is evaluated within the framework of self-consistent Green's function theory, using a realistic nucleon-nucleon interaction. The two-body dynamics is solved at the level of summing particle-particle and hole-hole ladders. We go beyond the on-shell approximation and use intermediary propagators with a discrete-pole structure. A three-pole approximation is used, which provides a good representation of the quasiparticle excitations, as well as reproducing the zeroth- and first-order energy-weighted moments in both the nucleon removal and addition domains of the spectral function. Results for the binding energy are practically independent of the details of the discretization scheme. The main effect of the increased self-consistency is to introduce an additional density dependence, which causes a shift towards lower densities and smaller binding energies, as compared to a (continuous choice) Brueckner calculation with the same interaction. Particle number conservation and the Hugenholz-Van Hove theorem are satisfied with reasonable accuracy
A pedestal temperature model with self-consistent calculation of safety factor and magnetic shear
International Nuclear Information System (INIS)
Onjun, T; Siriburanon, T; Onjun, O
2008-01-01
A pedestal model based on theory-motivated models for the pedestal width and the pedestal pressure gradient is developed for the temperature at the top of the H-mode pedestal. The pedestal width model based on magnetic shear and flow shear stabilization is used in this study, where the pedestal pressure gradient is assumed to be limited by first stability of infinite n ballooning mode instability. This pedestal model is implemented in the 1.5D BALDUR integrated predictive modeling code, where the safety factor and magnetic shear are solved self-consistently in both core and pedestal regions. With the self-consistently approach for calculating safety factor and magnetic shear, the effect of bootstrap current can be correctly included in the pedestal model. The pedestal model is used to provide the boundary conditions in the simulations and the Multi-mode core transport model is used to describe the core transport. This new integrated modeling procedure of the BALDUR code is used to predict the temperature and density profiles of 26 H-mode discharges. Simulations are carried out for 13 discharges in the Joint European Torus and 13 discharges in the DIII-D tokamak. The average root-mean-square deviation between experimental data and the predicted profiles of the temperature and the density, normalized by their central values, is found to be about 14%
Stochastic mean-field dynamics for fermions in the weak coupling limit
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D
2005-09-15
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |{phi}{sub a}> <|{phi}{sub b}| / <|{phi}{sub b} | |{phi} {sub a}> where |{phi}{sub a}> and |{phi}{sub b}> are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
Stochastic mean-field dynamics for fermions in the weak coupling limit
International Nuclear Information System (INIS)
Lacroix, D.
2005-09-01
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |Φ a > b | / b | |Φ a > where |Φ a > and |Φ b > are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical 40 Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
Self-consistent treatment of transport in tokamak plasmas
International Nuclear Information System (INIS)
Wilhelmsson, H.
1993-01-01
A theory is developed for the dynamics of tokamak plasmas considering the influence of combinations of simultaneous heating processes (alpha particle, auxiliary and ohmic), thermal conduction and particle diffusion, thermal and particle pinches, thermalization of alpha particles as well as the effects of boundary conditions. The analysis is based on a generalization of the central expansion technique which transforms the partial differential equations to a set of nonlinear coupled equations in time for the dynamic variables. Oscillatory solutions are found, but only in the presence of alpha particle heating. Examples of extensive computer simulations are included which support and complete the analytic results. (26 refs.)
International Nuclear Information System (INIS)
Hamed Hassani, S; Macris, Nicolas; Urbanke, Ruediger
2012-01-01
We consider a collection of Curie–Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of the chain and by an infinite-range interaction in the direction transverse to the chain. Our motivations for studying this model come from recent findings in the theory of error-correcting codes based on spatially coupled graphs. We find that, although much simpler than the codes, the model studied here already displays similar behavior. We are interested in the van der Waals curve in a regime where the size of each Curie–Weiss model tends to infinity, and the length of the chain and range of the Kac interaction are large but finite. Below the critical temperature, and with appropriate boundary conditions, there appears a series of equilibrium states representing kink-like interfaces between the two equilibrium states of the individual system. The van der Waals curve oscillates periodically around the Maxwell plateau. These oscillations have a period inversely proportional to the chain length and an amplitude exponentially small in the range of the interaction; in other words, the spinodal points of the chain model lie exponentially close to the phase transition threshold. The amplitude of the oscillations is closely related to a Peierls–Nabarro free energy barrier for the motion of the kink along the chain. Analogies to similar phenomena and their possible algorithmic significance for graphical models of interest in coding theory and theoretical computer science are pointed out
Physically self-consistent basis for modern cosmology
International Nuclear Information System (INIS)
Khlopov, M.Yu.
2000-01-01
Cosmoparticle physics appeared as a natural result of internal development of cosmology seeking physical grounds for inflation, baryosynthesis, and nonbaryonic dark matter and of particle physics going outside the Standard Model of particle interactions. Its aim is to study the foundations of particle physics and cosmology and their fundamental relationship in the combination of respective indirect cosmological, astrophysical, and physical effects. The ideas on new particles and fields predicted by particle theory and on their cosmological impact are discussed, as well as the methods of cosmoparticle physics to probe these ideas, are considered with special analysis of physical mechanisms for inflation, baryosynthesis, and nonbaryonic dark matter. These mechanisms are shown to reflect the main principle of modern cosmology, putting, instead of formal parameters of cosmological models, physical processes governing the evolution of the big-bang universe. Their realization on the basis of particle theory induces additional model-dependent predictions, accessible to various methods of nonaccelerator particle physics. Probes for such predictions, with the use of astrophysical data, are the aim of cosmoarcheology studying astrophysical effects of new physics. The possibility of finding quantitatively definite relationships between cosmological and laboratory effects on the basis of cosmoparticle approach, as well as of obtaining a unique solution to the problem of physical candidates for inflation, mechanisms of baryogenesis, and multicomponent dark matter, is exemplified in terms of gauge model with broken family symmetry, underlying horizontal unification and possessing quantitatively definite physical grounds for inflation, baryosynthesis, and effectively multicomponent dark-matter scenarios
Trapped Bose gas. Mean-field approximation and beyond
International Nuclear Information System (INIS)
Pitaevskii, L.P.
1998-01-01
The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for observation of macroscopic quantum phenomena. There are two important features of the system - weak interaction and significant spatial inhomogeneity. Because of this inhomogeneity a non-trivial 'zeroth-order' theory exists, compared to the 'first-order' Bogoliubov theory. This theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ -function. The equation is classical in its essence but contains the ℎ constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. The study of deviations from the zeroth-order theory arising from zero-point and thermal fluctuations is also of great interest. Thermal fluctuations are described by elementary excitations which define the thermodynamic behaviour of the system and result in Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in the quantum collapse-revival of the collective oscillations. This phenomenon is considered in some details. Collapse time for the JILA experimental conditions turns out to be of the order of seconds. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Mean field dynamics of networks of delay-coupled noisy excitable units
Energy Technology Data Exchange (ETDEWEB)
Franović, Igor, E-mail: franovic@ipb.ac.rs [Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Todorović, Kristina; Burić, Nikola [Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade (Serbia); Vasović, Nebojša [Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, PO Box 162, Belgrade (Serbia)
2016-06-08
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
Warm and cold pasta phase in relativistic mean field theory
International Nuclear Information System (INIS)
Avancini, S. S.; Menezes, D. P.; Alloy, M. D.; Marinelli, J. R.; Moraes, M. M. W.; Providencia, C.
2008-01-01
In the present article we investigate the onset of the pasta phase with different parametrizations of the nonlinear Walecka model. At zero temperature two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature only the coexistence phases method is used. matter with fixed proton fractions and in β equilibrium is studied. The pasta phase decreases with the increase of temperature. The internal pasta structure and the beginning of the homogeneous phase vary depending on the proton fraction (or the imposition of β equilibrium), on the method used, and on the chosen parametrization. It is shown that a good parametrization of the surface tension with dependence on the temperature, proton fraction, and geometry is essential to describe correctly large isospin asymmetries and the transition from pasta to homogeneous matter
Warm and cold pasta phase in relativistic mean field theory
Avancini, S. S.; Menezes, D. P.; Alloy, M. D.; Marinelli, J. R.; Moraes, M. M. W.; Providência, C.
2008-07-01
In the present article we investigate the onset of the pasta phase with different parametrizations of the nonlinear Walecka model. At zero temperature two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature only the coexistence phases method is used. npe matter with fixed proton fractions and in β equilibrium is studied. The pasta phase decreases with the increase of temperature. The internal pasta structure and the beginning of the homogeneous phase vary depending on the proton fraction (or the imposition of β equilibrium), on the method used, and on the chosen parametrization. It is shown that a good parametrization of the surface tension with dependence on the temperature, proton fraction, and geometry is essential to describe correctly large isospin asymmetries and the transition from pasta to homogeneous matter.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.