A bilocal picture of quantum mechanics
Withers, L. P., Jr.; Narducci, F. A.
2015-04-01
A new, bilocal picture of quantum mechanics is developed. We show that Born’s rule supports a virtual probability for a particle to arrive, as a wave, at any two locations (but no more). We discuss two ways to implement twin detectors suitable for detecting bilocal arrivals. The bilocal picture sheds light on currents in quantum mechanics. We find there are two types of bilocal current density, whose polar form and related mean velocities are given. In the bilocal context, the definitions of both current types simplify. In the unilocal case, the two types become the usual current and a fluctuation current. Their respective mean velocity fields are the usual de Broglie-Madelung-Bohm velocity and the imaginary (osmotic) velocity. We obtain a new, probabilistic Schrödinger equation for the bilocal probability by itself, solve the example of a free particle, develop the dyadic stationary states, and find that the von Neumann equation for time-varying density of states follows directly from the new equation. We also show how to include the electromagnetic potentials in this probabilistic Schrödinger equation.
Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs
Directory of Open Access Journals (Sweden)
Ruimin Xu
2014-01-01
Full Text Available We obtain the existence and uniqueness result of the mild solutions to mean-field backward stochastic evolution equations (BSEEs in Hilbert spaces under a weaker condition than the Lipschitz one. As an intermediate step, the existence and uniqueness result for the mild solutions of mean-field BSEEs under Lipschitz condition is also established. And then a maximum principle for optimal control problems governed by backward stochastic partial differential equations (BSPDEs of mean-field type is presented. In this control system, the control domain need not to be convex and the coefficients, both in the state equation and in the cost functional, depend on the law of the BSPDE as well as the state and the control. Finally, a linear-quadratic optimal control problem is given to explain our theoretical results.
On the dynamics of mean-field equations for stochastic neural fields with delays
Touboul, Jonathan
2011-01-01
The cortex is composed of large-scale cell assemblies sharing the same individual properties and receiving the same input, in charge of certain functions, and subject to noise. Such assemblies are characterized by specific space locations and space-dependent delayed interactions. The mean-field equations for such systems were rigorously derived in a recent paper for general models, under mild assumptions on the network, using probabilistic methods. We summarize and investigate general implications of this result. We then address the dynamics of these stochastic neural field equations in the case of firing-rate neurons. This is a unique case where the very complex stochastic mean-field equations exactly reduce to a set of delayed differential or integro-differential equations on the two first moments of the solutions, this reduction being possible due to the Gaussian nature of the solutions. The obtained equations differ from more customary approaches in that it incorporates intrinsic noise levels nonlinearly ...
The Schrödinger Equation in the Mean-Field and Semiclassical Regime
Golse, François; Paul, Thierry
2017-01-01
In this paper, we establish (1) the classical limit of the Hartree equation leading to the Vlasov equation, (2) the classical limit of the N-body linear Schrödinger equation uniformly in N leading to the N-body Liouville equation of classical mechanics and (3) the simultaneous mean-field and classical limit of the N-body linear Schrödinger equation leading to the Vlasov equation. In all these limits, we assume that the gradient of the interaction potential is Lipschitz continuous. All our results are formulated as estimates involving a quantum analogue of the Monge-Kantorovich distance of exponent 2 adapted to the classical limit, reminiscent of, but different from the one defined in Golse et al. [Commun Math Phys 343:165-205, 2016]. As a by-product, we also provide bounds on the quadratic Monge-Kantorovich distance between the classical densities and the Husimi functions of the quantum density matrices.
Vrettas, Michail D; Opper, Manfred; Cornford, Dan
2015-01-01
This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
Mean-field potential calculations of high-pressure equation of state for BeO
Institute of Scientific and Technical Information of China (English)
Zhang Qi-Li; Zhang Ping; Song Hai-Feng; Liu Hai-Feng
2008-01-01
A systematic study of the Hugoniot equation of state, phase transition, and the other thermodynamic properties including the Hugoniot temperature, the electronic and ionic heat capacities, and the Griineisen parameter for shockcompressed BeO, has been carried out by calculating the total free energy. The method of calculations combines first-principles treatment for 0 K and finite-T electronic contribution and the mean-field-potential approach for the vibrational contribution of the lattice ion to the total energy. Our calculated Hugoniot is in good agreement with the experimental data.
Tidal deformability of neutron and hyperon star with relativistic mean field equations of state
Kumar, Bharat; Patra, S K
2016-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field (RMF) equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various love numbers kl (l=2, 3, 4), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through advanced LIGO detector from the final stages of inspiraling binary neutron star (BNS) merger.
Chavanis, Pierre-Henri
2008-01-01
We consider a generalized class of Keller-Segel models describing the chemotaxis of biological populations (bacteria, amoebae, endothelial cells, social insects,...). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). We also discuss the analogy between biological populations described by the Keller-Segel model and self-gravitating Brownian particles described by the Smoluchowski-Poisson system.
Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state
Kumar, Bharat; Biswal, S. K.; Patra, S. K.
2017-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers kl(l =2 ,3 ,4 ), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.
Nonequilibrium dynamical mean-field theory: an auxiliary quantum master equation approach.
Arrigoni, Enrico; Knap, Michael; von der Linden, Wolfgang
2013-02-22
We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.
Mean-field equations for stochastic neural fields with spatio-temporal delays
Touboul, Jonathan
2011-01-01
Neurons form large-scale cell assemblies sharing the same individual properties and receiving the same input, in charge of certain functions. Such assemblies have specific space locations and hence interact after some (space dependent) delay due the transport and transfer of the information. Both delays and spatial connectivity structures are understood to shape the collective response of neural assemblies and brain states that are observed through usual recording techniques. Abstracting this setting, we consider here the problem of the asymptotics, as the number of neurons increases, of bio-inspired neuronal networks composed of several populations (up to a continuum), interacting with spatio-temporal delays. The propagation of chaos property is proved under mild assumptions on the neuronal dynamics, valid for most models used in neuroscience, in both the case of finite number and infinite continuum populations (called neural fields). The mean-field equations in these cases are derived and analyzed from the ...
A Second Relativistic Mean Field and Virial Equation of State for Astrophysical Simulations
Shen, G; O'Connor, E
2011-01-01
We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the Virial expansion of a non-ideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100,000 grid points in the temperature range $T$ = 0 to 80 MeV, the density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$, and the proton fraction range $Y_p$ = 0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3 ba...
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.
Lahiri, T.; Pal Majumder, T.; Ghosh, N. K.
2014-07-01
Commercialization of ferroelectric liquid crystal displays (FLCDs) suffers from mechanical and electro-convective instabilities. Impurity ions play a pivotal role in the latter case, and therefore we developed a mean-field type model to understand the complex role of space charges, particularly ions in a ferroelectric liquid crystal. Considering an effective ion-chirality relation, we obtained a modified Poisson-Boltzmann equation for ions dissolved into a chiral solvent like the ferroelectric smectic phase. A nonuniform director profile induced by the mean electrostatic potential of the ions is then calculated by solving an Euler-Lagrange equation for a helically twisted smectic state. A combination of effects resulting from molecular chirality and an electrostatically driven twist created by the ions seems to produce this nonuniform fluctuation in the director orientation. Finally, both theoretical and experimental points of view are presented on the prediction of this mean-field model.
Mocák, Miroslav; Viallet, Maxime; Arnett, David
2014-01-01
We present a statistical analysis of turbulent convection in stars within our Reynolds-Averaged Navier Stokes (RANS) framework in spherical geometry which we derived from first principles. The primary results reported in this document include: (1) an extensive set of mean-field equations for compressible, multi-species hydrodynamics, and (2) corresponding mean-field data computed from various simulation models. Some supplementary scale analysis data is also presented. The simulation data which is presented includes: (1) shell convection during oxygen burning in a 23 solar mass supernova progenitor, (2) envelope convection in a 5 solar mass red giant, (3) shell convection during the helium flash, and (4) a hydrogen injection flash in a 1.25 solar mass star. These simulations have been partially described previously in Meakin [2006], Meakin and Arnett [2007a,b, 2010], Arnett et al. [2009, 2010], Viallet et al. [2011, 2013a,b] and Mocak et al. [2009, 2011]. New data is also included in this document with several...
Malik, G P
2016-01-01
Given the Debye temperature of an elemental superconductor (SC) and its Tc, BCS theory enables one to predict the value of its gap 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {Tc, 10, 20 > 10}, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO3, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the Tcs, s and other properties (e.g., number densities of charge carriers) of high-Tc SCs via GBCSE...
Bi-local Fields in Noncommutative Field Theory
Iso, S; Kitazawa, Y; Iso, Satoshi; Kawai, Hikaru; Kitazawa, Yoshihisa
2000-01-01
We propose a bi-local representation in noncommutative field theory. It provides a simple description for high momentum degrees of freedom. It also shows that the low momentum modes can be well approximated by ordinary local fields. Long range interactions are generated in the effective action for the lower momentum modes after integrating out the high momentum bi-local fields. The low momentum modes can be represented by diagonal blocks in the matrix model picture and the high momentum bi-local fields correspond to off-diagonal blocks. This block-block interaction picture simply reproduces the infrared singular behaviors of nonplanar diagrams in noncommutative field theory.
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.
Bi-local holography in the SYK model
Jevicki, Antal; Suzuki, Kenta; Yoon, Junggi
2016-07-01
We discuss large N rules of the Sachdev-Ye-Kitaev model and the bi-local representation of holography of this theory. This is done by establishing 1 /N Feynman rules in terms of bi-local propagators and vertices, which can be evaluated following the recent procedure of Polchinski and Rosenhaus. These rules can be interpreted as Witten type diagrams of the dual AdS theory, which we are able to define at IR fixed point and off.
DEFF Research Database (Denmark)
Petersen, Kaare Brandt
2006-01-01
This thesis describes investigations and improvements of a technique for Independent Component Analysis (ICA), called "Mean Field ICA". The main focus of the thesis is the optimization part of the algorithm, the so-called "EM algorithm". Using different approaches it is demonstrated that the EM...... Gradient Recipe is applicable to a wide selection of models. Furthermore, the Mean Field ICA model is extended to incorporate ltering over time in a so-called "convolutive ICA" model. Finally, by using mixture of Gaussians as source priors, the generative and ltering approach to ICA is compared...
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.
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.
Pais, Helena
2016-01-01
The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear $\\omega\\rho$ and $\\sigma\\rho$ coupling terms on the crust-core transition density and pressure, and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure, and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6$\\pm$0.3 km and a crust thickness of $1.36\\pm 0.06$km for a 1.4 $M_\\odot$ star.
Moghrabi, Kassem; Roca-Maza, Xavier; Colo', Gianluca
2012-01-01
In a quantum Fermi system the energy per particle calculated at the second order beyond the mean-field approximation diverges if a zero-range interaction is employed. We have previously analyzed this problem in symmetric nuclear matter by using a simplified nuclear Skyrme interaction, and proposed a strategy to treat such a divergence. In the present work, we extend the same strategy to the case of the full nuclear Skyrme interaction. Moreover we show that, in spite of the strong divergence ($\\sim$ $\\Lambda^5$, where $\\Lambda$ is the momentum cutoff) related to the velocity-dependent terms of the interaction, the adopted cutoff regularization can be always simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratio. This paves the way to applications to finite nuclei.
Karkheck, John; Stell, George
1981-08-01
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras
Directory of Open Access Journals (Sweden)
Dangui Yan
2011-01-01
Full Text Available Let H be a complex Hilbert space and B(H the collection of all linear bounded operators, A is the closed subspace lattice including 0 an H, then A is a nest, accordingly alg A={T∈B(H:TN⊆N, ∀N∈A} is a nest algebra. It will be shown that of nest algebra, generalized derivations are generalized inner derivations, and bilocal Jordan derivations are inner derivations.
Obstacle mean-field game problem
Gomes, Diogo A.
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.
Bosonic Dynamical Mean-Field Theory
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
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.
Mean field games systems of first order
Cardaliaguet, Pierre; Graber, Philip Jameson
2014-01-01
International audience; We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.
A mean field approach to watershed hydrology
Bartlett, Mark; Porporato, Amilcare
2016-04-01
Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect for all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages, resulting in a consistent method for linking the average watershed fluxes to the local fluxes at each point. We apply this approach to the spatial distribution of soil moisture, and as a result, the numerous local interactions related to lateral fluxes of soil water are parameterized in terms of the average soil moisture. The mean field approach provides a basis for unifying and extending common event-based models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). We obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff, and the average runoff value (i.e., the so-called runoff curve). The resulting space time distribution of soil moisture offers a concise description of the variability of watershed fluxes.
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.
A Bilocal Model for the Relativistic Spinning Particle
Rempel, Trevor
2016-01-01
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for spinning particles allows for a natural description of particle interactions as a local interaction at each of the constituents. This form of the interaction vertex provides a resolution to a long standing issue on the nature of relativistic interactions for spinning objects in the context of the worldline formalism. It also potentially brings a dynamical explanation for why massive fundamental objects are naturally of lowest spin. We analyze first a non-relativistic system where spin is modeled as an entangled state of two particles with the entanglement encoded into a set of constraints. It is shown that these constraints can be made relativistic and that the resulting description is isomorphic to the usual description of the phase space of massive relativistic particles ...
Vollhardt, D.; Byczuk, K.; Kollar, M.
2011-01-01
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the ...
The bilocated mind: new perspectives on self-localization and self-identification
Furlanetto, Tiziano; Bertone, Cesare; Becchio, Cristina
2013-01-01
Does the human mind allow for self-locating at more than one place at a time? Evidence from neurology, cognitive neuroscience, and experimental psychology suggests that mental bilocation is a complex, but genuine experience, occurring more frequently than commonly thought. In this article, we distinguish between different components of bilocated self-representation: self-localization in two different places at the same time, self-identification with another body, reduplication of first-person perspective. We argue that different forms of mental bilocation may result from the combination of these components. To illustrate this, we discuss evidence of mental bilocation in pathological conditions such as heautoscopy, during immersion in virtual environments, and in everyday life, during social interaction. Finally, we consider the conditions for mental bilocation and speculate on the possible role of mental bilocation in the context of social interaction, suggesting that self-localization at two places at the same time may prove advantageous for the construction of a shared space. PMID:23482653
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.
Mean-field models for disordered crystals
Cancès, Eric; Lewin, Mathieu
2012-01-01
In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.
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.
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.
2013-11-20
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
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.)
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.)
Large amplitude motion with a stochastic mean-field approach
Directory of Open Access Journals (Sweden)
Yilmaz Bulent
2012-12-01
Full Text Available In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
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)
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; 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.
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.
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.)
Degenerate second order mean field games systems
Tonon, Daniela; Cardaliaguet, Pierre; Graber, Philip,; Poretta, Alessio
2014-01-01
Parallel session; International audience; We consider degenerate second order mean field games systems with a local coupling. The starting point is the idea that mean field games systems can be understood as an optimality condition for optimal control of PDEs. Developing this strategy for the degenerate second order case, we discuss the existence and uniqueness of a weak solution as well as its stability (vanishing viscosity limit). Speaker: Daniela TONON
From infinity to one: The reduction of some mean field games to a global control problem
Guéant, Olivier
2011-01-01
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced by J.M. Lasry and P.L. Lions and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation, from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.
Pion mean fields and heavy baryons
Yang, Ghil-Seok; Polyakov, Maxim V; Praszałowicz, Michał
2016-01-01
We show that the masses of the lowest-lying heavy baryons can be very well described in a pion mean-field approach. We consider a heavy baryon as a system consisting of the $N_c-1$ light quarks that induce the pion mean field, and a heavy quark as a static color source under the influence of this mean field. In this approach we derive a number of \\textit{model-independent} relations and calculate the heavy baryon masses using those of the lowest-lying light baryons as input. The results are in remarkable agreement with the experimental data. In addition, the mass of the $\\Omega_b^*$ baryon is predicted.
Schrödinger Approach to Mean Field Games
Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis
2016-03-01
Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.
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
Back-reaction beyond the mean field approximation
Energy Technology Data Exchange (ETDEWEB)
Kluger, Y.
1993-12-01
A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N{sub f} expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N{sub f} is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e{sup +}e{sup {minus}} plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N{sub f} expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation.
Propagation peculiarities of mean field massive gravity
Directory of Open Access Journals (Sweden)
S. Deser
2015-10-01
Full Text Available Massive gravity (mGR describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m‾GR propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS theory. The fiducial and mGR mean field background metrics in the m‾GR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR which is at least a consistent classical theory. Moreover, even though both m‾GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. This applies both to m‾GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.
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
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.
Mean-field games with logistic population dynamics
Gomes, Diogo A.
2013-12-01
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
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.
'Phase diagram' of a mean field game
Swiecicki, Igor; Ullmo, Denis
2015-01-01
Mean field games were introduced by J-M.Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the 'seminar problem' introduced by O.Gu\\'eant, J-M Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agent are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space...
Mean-field theory of echo state networks
Massar, Marc; Massar, Serge
2013-04-01
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.
Mean-field theory of a recurrent epidemiological model.
Nagy, Viktor
2009-06-01
Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity.
Relativistic mean field description of cluster radioactivity
Bhagwat, A.; Gambhir, Y. K.
2005-01-01
Comprehensive investigations of the observed cluster radioactivity are carried out. First, the relativistic mean field (RMF) theory is employed for the calculations of the ground-state properties of relevant nuclei. The calculations reproduce the experiment well. The calculated RMF point densities are folded with the density-dependent M3Y nucleon-nucleon interaction to obtain the cluster-daughter interaction potential. This, along with the calculated and experimental Q values, is used in the WKB approximation for estimating the half-lives of the parent nuclei against cluster decay. The calculations qualitatively agree with the experiment. Sensitive dependence of the half-lives on Q values is explicitly demonstrated.
Mean-field behavior of cluster dynamics
Persky, N.; Ben-Av, R.; Kanter, I.; Domany, E.
1996-09-01
The dynamic behavior of cluster algorithms is analyzed in the classical mean-field limit. Rigorous analytical results below Tc establish that the dynamic exponent has the value zSW=1 for the Swendsen-Wang algorithm and zW=0 for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below Tc demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.
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...
Diabatic constrained relativistic mean field approach
L"u, H F; Meng, J
2005-01-01
A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. The potential energy surfaces of $^{208}$Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. The diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to define the single particle orbits at very deformed region by their quantum numbers, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.
Dynamical mean-field theory for flat-band ferromagnetism
Nguyen, Hong-Son; Tran, Minh-Tien
2016-09-01
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
Control and Nash Games with Mean Field Effect
Institute of Scientific and Technical Information of China (English)
Alain BENSOUSSAN; Jens FREHSE
2013-01-01
Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of applications.In general,the applications concern approximating an infinite number of players with common behavior by a representative agent.This agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of agents.This approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite challenging.In this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential games.Thus the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-11-01
I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.
Mean-field theory and self-consistent dynamo modeling
Energy Technology Data Exchange (ETDEWEB)
Yoshizawa, Akira; Yokoi, Nobumitsu [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Sanae-I [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
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 Field Evolution of Fermions with Coulomb Interaction
Porta, Marcello; Rademacher, Simone; Saffirio, Chiara; Schlein, Benjamin
2017-03-01
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree-Fock dynamics. Our result holds under a condition on the solution of the Hartree-Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree-Fock evolution is trivial), but that we expect to hold more generally.
Directory of Open Access Journals (Sweden)
Jürgen Dorbritz
2013-03-01
When looking at wave one and wave two in comparison (i.e. a time period of one year, profound changes have already occurred regarding continuation or breakup. From those bilocal relationships found in wave one, more than half of the age-group questioned had not changed their chosen relationship type. The smaller portion of respondents had separated and thus ended bilocality (just over 10 %. The remaining bilocal relationships had increased their level of institutionalisation by becoming spouses or cohabitants. As regarding the development from wave one to wave two, it becomes apparent through the results of a multivariate analysis that the general circumstances of older respondents should be judged differently than those of younger ones. The work-related constellation between the two partners, spatial proximity, educational homogamy, previous experience in cohabitating and intentions in regard to separation or moving in together are explaining factors for the continuation of a bilocal relationship, the set-up of a shared household or a breakup.
Invisible dynamo in mean-field models
Reshetnyak, M. Yu.
2016-07-01
The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.
Mean field magnetization of gapped anisotropic multiplet
Paixão, L. S.; Reis, M. S.
2014-06-01
Some materials have a large gap between the ground and first excited states. At temperatures smaller than the gap value, the thermodynamic properties of such materials are mainly ruled by the ground state. It is also common to find materials with magnetocrystalline anisotropy, which arises due to interatomic interactions. The present paper uses a classical approach to deal large angular momenta in such materials. Based on analytical expressions for the thermodynamics of paramagnetic gapped anisotropic multiplets, we use mean field theory to study the influence of the anisotropy upon the properties of interacting systems. We also use Landau theory to determine the influence of the anisotropy in first and second order phase transitions. It is found that the anisotropy increases the critical temperature, and enlarges the hysteresis of first order transitions. We present analytical expressions for the quantities analyzed.
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-01-01
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat. Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that models also the geometric Brownian motion and can be studied analytically. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate. The relationship between the kinetic and the diffusion models allow to introduce an easy-to- implement expression for computing the Fourier transform o...
Nonlinear regimes in mean-field full-sphere dynamo
Pipin, V V
2016-01-01
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\\odot}$ rotating with period of 10 days. The differential rotation law was estimated using the mean-field hydrodynamic and heat transport equations. For the intermediate parameter of the turbulent magnetic Reynolds number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. The meridional circulation has one cell per hemisphere. It is counter-clockwise in the Northen hemisphere. The amplitude of the flow at the surface around 1 m/s. Tne models with regards for meridional circulation show the anti-symmetric relative to equator magnetic field. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $\\alpha$effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear $\\alpha$-effect. The situation pe...
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.
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.
Generalized continuity equations from two-field Schrödinger Lagrangians
Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.
2016-11-01
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.
Neural Population Dynamics Modeled by Mean-Field Graphs
Kozma, Robert; Puljic, Marko
2011-09-01
In this work we apply random graph theory approach to describe neural population dynamics. There are important advantages of using random graph theory approach in addition to ordinary and partial differential equations. The mathematical theory of large-scale random graphs provides an efficient tool to describe transitions between high- and low-dimensional spaces. Recent advances in studying neural correlates of higher cognition indicate the significance of sudden changes in space-time neurodynamics, which can be efficiently described as phase transitions in the neuropil medium. Phase transitions are rigorously defined mathematically on random graph sequences and they can be naturally generalized to a class of percolation processes called neuropercolation. In this work we employ mean-field graphs with given vertex degree distribution and edge strength distribution. We demonstrate the emergence of collective oscillations in the style of brains.
Thermal Effects in Dense Matter Beyond Mean Field Theory
Constantinou, Constantinos; Prakash, Madappa
2016-01-01
The formalism of next-to-leading order Fermi Liquid Theory is employed to calculate the thermal properties of symmetric nuclear and pure neutron matter in a relativistic many-body theory beyond the mean field level which includes two-loop effects. For all thermal variables, the semi-analytical next-to-leading order corrections reproduce results of the exact numerical calculations for entropies per baryon up to 2. This corresponds to excellent agreement down to sub-nuclear densities for temperatures up to $20$ MeV. In addition to providing physical insights, a rapid evaluation of the equation of state in the homogeneous phase of hot and dense matter is achieved through the use of the zero-temperature Landau effective mass function and its derivatives.
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.
Metastability for the Exclusion Process with Mean-Field Interaction
Asselah, Amine; Giacomin, Giambattista
1998-12-01
We consider an exclusion particle system with long-range, mean-field-type interactions at temperature 1/β. The hydrodynamic limit of such a system is given by an integrodifferential equation with one conservation law on the circle C: it is the gradient flux of the Kac free energy functional F β. For β≤1, any constant function with value m ∈ [-1, +1] is the global minimizer of F β in the space \\{ u:int_C {u(x)} dx = m\\} . For β>1, F β restricted to \\{ u:int_C {u(x)} dx = m\\} may have several local minima: in particular, the constant solution may not be the absolute minimizer of F β. We therefore study the long-time behavior of the particle system when the initial condition is close to a homogeneous stable state, giving results on the time of exit from (suitable) subsets of its domain of attraction. We follow the Freidlin-Wentzell approach: first, we study in detail F β together with the time asymptotics of the solution of the hydrodynamic equation; then we study the probability of rare events for the particle system, i.e., large deviations from the hydrodynamic limit.
Mean-field approximation for spacing distribution functions in classical systems
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials
Vollhardt, Dieter
2010-11-01
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many-body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean-field theory for correlated fermions, the dynamical mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.
Time-Dependent Mean-Field Games in the Subquadratic Case
Gomes, Diogo A.
2014-10-14
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
Finite-size and correlation-induced effects in Mean-field Dynamics
Touboul, Jonathan
2010-01-01
The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon a recent approach that includes correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of...
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bos...
Modified Mean Field approximation for the Ising Model
Di Bartolo, Cayetano
2009-01-01
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the Mean-Field or the Bethe-Peierls-Weiss methods, we take an infinite chain of fluctuating spins coupled to the mean field of the rest of the lattice. This results in a significative improvement of the Mean-Field approximation with a small extra effort.
Exact mean field dynamics for epidemic-like processes on heterogeneous networks
Lucas, Andrew
2012-01-01
We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a solution in terms of an integral over functions dependent on the degree distribution of the network, and reconstructing all mean field functions of interest from this integral. Irreversibility of the SIR epidemic is crucial for the solution. We also find exact solutions to the sexually transmitted disease SI epidemic on bipartite graphs, to a simplified rumor spreading model, and to a new model for recommendation spreading, via similar techniques. Numerical simulations of these processes on scale free networks demonstrate the qualitative validity of mean field theory in most regimes.
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...
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem
2015-02-24
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
Modeling distributed axonal delays in mean-field brain dynamics
Roberts, J. A.; Robinson, P. A.
2008-11-01
The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.
2016-11-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Hot and dense matter beyond relativistic mean field theory
Zhang, Xilin
2016-01-01
Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\\odot$ neutron star req...
Verbalization of Mean Field Utterances in German Instructions
Directory of Open Access Journals (Sweden)
Tayupova O. I.
2013-01-01
Full Text Available The article investigates ways of actualization of mean field utterances used in modern German instructions considering the type of the text. The author determines and analyzes similarities and differences in linguistic means used in mean field utterances in the context of such text subtypes as instructions to household appliances, cosmetic products directions and prescribing information for pharmaceutical drugs use.
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2013-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combinatio...
Mean-field Approach to the Derivation of Baryon Superpotential from Matrix Model
Suzuki, H
2003-01-01
We discuss how to obtain the superpotential of the baryons and mesons for SU(N) gauge theories with N flavour matter fields from matrix integral. We apply the mean-field approximation for the matrix integral. Assuming the planar limit of the self-consistency equation, we show that the result almost agrees with the field theoretical result.
Frank, T. D.; Daffertshofer, A.; Beek, P. J.
2001-01-01
We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.
2014-10-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
Quantum correlations in nuclear mean field theory through source terms
Lee, S J
1996-01-01
Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence, the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing further approximation, the result can be reduced to Hartree-Fock or Hartree approximation. The role of the source dependence in a mean field theory is examined.
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.
Mean-field instabilities and cluster formation in nuclear reactions
Colonna, M; Baran, V
2016-01-01
We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to...
Simplified method for including spatial correlations in mean-field approximations
Markham, Deborah C.; Simpson, Matthew J.; Baker, Ruth E.
2013-06-01
Biological systems involving proliferation, migration, and death are observed across all scales. For example, they govern cellular processes such as wound healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration, and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behavior. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behavior in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.
Test-field method for mean-field coefficients with MHD background
Rheinhardt, M
2010-01-01
Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results: Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electr...
Short-time existence of solutions for mean-field games with congestion
Gomes, Diogo A.
2015-11-20
We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.
Mean-Field Semantics for a Process Calculus for Spatially-Explicit Ecological Models
Directory of Open Access Journals (Sweden)
Mauricio Toro
2016-03-01
Full Text Available We define a mean-field semantics for S-PALPS, a process calculus for spatially-explicit, individual-based modeling of ecological systems. The new semantics of S-PALPS allows an interpretation of the average behavior of a system as a set of recurrence equations. Recurrence equations are a useful approximation when dealing with a large number of individuals, as it is the case in epidemiological studies. As a case study, we compute a set of recurrence equations capturing the dynamics of an individual-based model of the transmission of dengue in Bello (Antioquia, Colombia.
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
Energy Technology Data Exchange (ETDEWEB)
Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)
2012-12-15
We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Blackman, Eric G
2012-01-01
Conversion of gravitational energy into radiation near stars and compact objects in accretion disks the origin of large scale magnetic fields in astrophysical rotators have long been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such distinct pursuits. Both are presently incomplete, but 21st century MFD theory has nonlinear predictive power compared to 20th century MFD. in contrast, alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory ar...
Mean field limit for bosons and propagation of Wigner measures
Ammari, Z
2008-01-01
We consider the N-body Schr\\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \\cite{AmNi}, the mean field limit is translated into a semiclassical problem with a small parameter $\\epsilon\\to 0$, after introducing an $\\epsilon$-dependent bosonic quantization. The limit is expressed as a push-forward by a nonlinear flow (e.g. Hartree) of the associated Wigner measures. These object and their basic properties were introduced in \\cite{AmNi} in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for rather general class of quantum states in their mean field limit.
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.
Neutron Stars in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S; Stachniewicz, S
1998-01-01
We study the equation of state of beta-stable dense matter and models of neutron stars in the relativistic mean field theory with the isovector scalar mean field corresponding to the delta-meson [a_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_s=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 equation of state becomes slightly stiffer and the maximum neutron star mass increases for stronger delta-meson coupling.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou
2012-01-01
In this paper we present analytical mean field techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean field optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean field propagation models which focus on deterministic equations, we show that the mean field limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean field limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.
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.
Suppression of oscillations in mean-field diffusion
Indian Academy of Sciences (India)
Neeraj Kumar Kamal; Pooja Rani Sharma; Manish Dev Shrimali
2015-02-01
We study the role of mean-field diffusive coupling on suppression of oscillations for systems of limit cycle oscillators. We show that this coupling scheme not only induces amplitude death (AD) but also oscillation death (OD) in coupled identical systems. The suppression of oscillations in the parameter space crucially depends on the value of mean-field diffusion parameter. It is also found that the transition from oscillatory solutions to OD in conjugate coupling case is different from the case when the coupling is through similar variable. We rationalize our study using linear stability analysis.
Point-coupling models from mesonic hyper massive limit and mean-field approaches
Energy Technology Data Exchange (ETDEWEB)
Lourenco, O.; Dutra, M., E-mail: odilon@ita.br [Departamento de Fisica, Instituto Tecnologico da Aeronautica - CTA, Sao Jose dos Campos, SP (Brazil); Delfino, Antonio, E-mail: delfino@if.uff.br [Instituto de Fisica, Universidade Federal Fluminense, Niteroi, RJ (Brazil); Amaral, R.L.P.G. [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)
2012-08-15
t In this work, we show how nonlinear point coupling models, described by a Lagrangian density containing only terms up to fourth order in the fermion condensate ({Psi}-bar{Psi}), are derived from a modified meson exchange nonlinear Walecka model. We present two methods of derivation, namely the hyper massive meson limit within a functional integral approach and the mean-field approximation, in which equations of state at zero temperature of the nonlinear point-coupling models are directly obtained. (author)
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.
Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Greg; O' Brien, John; Chou, Tom [Department of Biomathematics and Institute for Pure and Applied Mathematics, UCLA, Los Angeles, CA 90095 (United States)
2006-03-10
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.
Merging Belief Propagation and the Mean Field Approximation
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence) as a ...
Mean-Field Versus Microconvection Effects in Nanofluid Thermal Conduction
Eapen, Jacob; Williams, Wesley C.; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
2007-08-01
Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.
Mean Field Approach to the Giant Wormhole Problem
Gamba, A.; Kolokolov, I.; Martellini, M.
We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.
Mean-field dynamo action in renovating shearing flows.
Kolekar, Sanved; Subramanian, Kandaswamy; Sridhar, S
2012-08-01
We study mean-field dynamo action in renovating flows with finite and nonzero correlation time (τ) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and nonhelical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly nonhelical, then such mean-field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval τ. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the α(2)Ω dynamo, in the small τ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean-field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.
Condition monitoring with Mean field independent components analysis
DEFF Research Database (Denmark)
Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan
2005-01-01
We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...
Mean-field versus microconvection effects in nanofluid thermal conduction.
Eapen, Jacob; Williams, Wesley C; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
2007-08-31
Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Critical fluctuations for quantum mean-field models
Energy Technology Data Exchange (ETDEWEB)
Fannes, M.; Kossakowski, A.; Verbeure, A. (Univ. Louvain (Belgium))
1991-11-01
A Ginzburg-Landau-type approximation is proposed for the local Gibbs states for quantum mean-field models that leads to the exact thermodynamics. Using this approach, the spin fluctuations are computed for some spin-1/2 models. At the critical temperature, the distribution function showing abnormal fluctuations is found explicitly.
Robust mean field games for coupled Markov jump linear systems
Moon, Jun; Başar, Tamer
2016-07-01
We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.
Model-checking mean-field models: algorithms & applications
Kolesnichenko, Anna Victorovna
2014-01-01
Large systems of interacting objects are highly prevalent in today's world. In this thesis we primarily address such large systems in computer science. We model such large systems using mean-field approximation, which allows to compute the limiting behaviour of an infinite population of identical o
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion
de Andrade, L Garcia
2009-01-01
Mean-field cosmological dynamos in Riemannian space with isotropic diffusion}} Previous attempts for building a cosmic dynamo including preheating in inflationary universes [Bassett et al Phys Rev (2001)] has not included mean field or turbulent dynamos. In this paper a mean field dynamo in cosmic scales on a Riemannian spatial cosmological section background, is set up. When magnetic fields and flow velocities are parallel propagated along the Riemannian space dynamo action is obtained. Turbulent diffusivity ${\\beta}$ is coupled with the Ricci magnetic curvature, as in Marklund and Clarkson [MNRAS (2005)], GR-MHD dynamo equation. Mean electric field possesses an extra term where Ricci tensor couples with magnetic vector potential in Ohm's law. In Goedel universe induces a mean field dynamo growth rate ${\\gamma}=2{\\omega}^{2}{\\beta}$. In this frame kinetic helicity vanishes. In radiation era this yields ${\\gamma}\\approx{2{\\beta}{\\times}10^{-12}s^{-1}}$. In non-comoving the magnetic field is expressed as $B\\ap...
Chaotic time series prediction using mean-field theory for support vector machine
Institute of Scientific and Technical Information of China (English)
Cui Wan-Zhao; Zhu Chang-Chun; Bao Wen-Xing; Liu Jun-Hua
2005-01-01
This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach, and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Going Beyond a Mean-field Model for the Learning Cortex: Second-Order Statistics
Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.
2008-01-01
Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the “up” and “down” states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories. PMID:19669541
Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model
Chen, Li; Göttlich, Simone; Yin, Qitao
2016-11-01
In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale. For stochastic initial data, it is proved that the solution of the N-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation. Furthermore, the result on propagation of chaos is also deduced in terms of bounded Lipschitz distance.
Maslov, K A; Voskresensky, D N
2016-01-01
Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and $\\Delta$ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the $\\Delta$ isobars. We analyze available empirical information to put constraints on coupling constants of $\\Delta$s to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.
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)
Mean field theory for fermion-based U(2) anyons
McGraw, P
1996-01-01
The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless fermion, we find that this energy is independent of the two Chern-Simons coupling constants and is minimized when the non-Abelian charge density is zero. This suggests that there is no spontaneous breaking of the SU(2) subgroup of the symmetry, at least in this mean-field approximation. For spin-1/2 fermions, we find self-consistent mean-field states with a small non-Abelian charge density, which vanishes as the theory of free fermions is approached.
Characterizing the mean-field dynamo in turbulent accretion disks
Gressel, Oliver
2015-01-01
The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale depen...
Analytic Beyond-Mean-Field BEC Wave Functions
Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.
2006-05-01
We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata; Gangopadhyay, G.
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been ca...
Dynamical mean field theory of optical third harmonic generation
Jafari, S. A.; Tohyama, T.; Maekawa, S.
2006-01-01
We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation...
Communication patterns in mean field models for wireless sensor networks
2015-01-01
Wireless sensor networks are usually composed of a large number of nodes, and with the increasing processing power and power consumption efficiency they are expected to run more complex protocols in the future. These pose problems in the field of verification and performance evaluation of wireless networks. In this paper, we tailor the mean-field theory as a modeling technique to analyze their behavior. We apply this method to the slotted ALOHA protocol, and establish results on the long term...
Time-dependent mean-field games in the superquadratic case
Gomes, Diogo A.
2016-04-06
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as key techniques used in the subquadratic case, which was studied in a previous publication of the authors, do not extend to the superquadratic setting. The main objective of the present paper is to address these difficulties. Because of the superquadratic structure of the Hamiltonian, Lipschitz estimates for the solutions of the Hamilton−Jacobi equation are obtained here through a novel set of techniques. These explore the parabolic nature of the problem through the nonlinear adjoint method. Well-posedness is proven by combining Lipschitz regularity for the Hamilton−Jacobi equation with polynomial estimates for solutions of the Fokker−Planck equation. Existence of classical solutions is then established under conditions depending only on the growth of the Hamiltonian and the dimension. Our results also add to current understanding of superquadratic Hamilton−Jacobi equations.
HBT Pion Interferometry with Phenomenological Mean Field Interaction
Hattori, K.
2010-11-01
To extract information on hadron production dynamics in the ultrarelativistic heavy ion collision, the space-time structure of the hadron source has been measured using Hanbury Brown and Twiss interferometry. We study the distortion of the source images due to the effect of a final state interaction. We describe the interaction, taking place during penetrating through a cloud formed by evaporating particles, in terms of a one-body mean field potential localized in the vicinity of the source region. By adopting the semiclassical method, the modification of the propagation of an emitted particle is examined. In analogy to the optical model applied to nuclear reactions, our phenomenological model has an imaginary part of the potential, which describes the absorption in the cloud. In this work, we focus on the pion interferometry and mean field interaction obtained using a phenomenological pipi forward scattering amplitude in the elastic channels. The p-wave scattering wit h rho meson resonance leads to an attractive mean field interaction, and the presence of the absorptive part is mainly attributed to the formation of this resonance. We also incorporate a simple time dependence of the potential reflecting the dynamics of the evaporating source. Using the obtained potential, we examine how and to what extent the so-called HBT Gaussian radius is varied by the modification of the propagation.
Resummed mean-field inference for strongly coupled data
Jacquin, Hugo; Rançon, A.
2016-10-01
We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for N auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z; Simon, Péter L
2016-04-01
An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models.
Relativistic heavy ion collisions with realistic non-equilibrium mean fields
Fuchs, C; Wolter, H H
1996-01-01
We study the influence of non-equilibrium phase space effects on the dynamics of heavy ion reactions within the relativistic BUU approach. We use realistic Dirac-Brueckner-Hartree-Fock (DBHF) mean fields determined for two-Fermi-ellipsoid configurations, i.e. for colliding nuclear matter, in a local phase space configuration approximation (LCA). We compare to DBHF mean fields in the local density approximation (LDA) and to the non-linear Walecka model. The results are further compared to flow data of the reaction Au on Au at 400 MeV per nucleon measured by the FOPI collaboration. We find that the DBHF fields reproduce the experiment if the configuration dependence is taken into account. This has also implications on the determination of the equation of state from heavy ion collisions.
Modeling and computation of mean field equilibria in producers' game with emission permits trading
Zhang, Shuhua; Wang, Xinyu; Shanain, Aleksandr
2016-08-01
In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our model, in which each enterprise can trade its own permits flexibly. By means of the mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equation coupled with a Kolmogorov equation, which are satisfied by the adjoint state and the density of producers (agents), respectively. Then, we propose a so-called fitted finite volume method to solve the HJB equation and the Kolmogorov equation. The efficiency and the usefulness of this method are illustrated by the numerical experiments. Under different conditions, the equilibrium states as well as the effects of the emission permits price are examined, which demonstrates that the emission permits trading scheme influences the producers' behaviors, that is, more populations would like to choose a lower rather than a higher emission level when the emission permits are expensive.
Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics
Silva, A Castro e
2009-01-01
We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.
Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics
Energy Technology Data Exchange (ETDEWEB)
Castro e Silva, A [Departamento de Fisica, Universidade Federal de Ouro Preto, Campus Universitario, 35.400-000 Ouro Preto, Minas Gerais (Brazil); Kamphorst Leal da Silva, J, E-mail: alcidescs@gmail.co, E-mail: jaff@fisica.ufmg.b [Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.161-970, Belo Horizonte, Minas Gerais (Brazil)
2010-06-04
We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.
Dynamical mean-field theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
2011-03-04
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.
Mean field approaches for $\\Xi^-$ hypernuclei and current experimental data
Sun, T T; Sagawa, H; Schulze, H -J; Meng, J
2016-01-01
Motivated by the recently observed hypernucleus (Kiso event) $^{15}_{\\Xi}$C ($^{14}$N$+\\Xi^-$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The $\\Xi N$ interactions are constructed to reproduce the two possibly observed $\\Xi^-$ removal energies, $4.38\\pm 0.25$ MeV or $1.11\\pm 0.25$ MeV. The present result is preferable to be $^{14}{\\rm N}({\\rm g.s.})+\\Xi^-(1p)$, corresponding to the latter value.
A mean-field game economic growth model
Gomes, Diogo A.
2016-08-05
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize his/her utility by taking into account statistical data about the whole population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.
Relativistic Mean Field Study on Halo Structures of Mirror Nuclei
Institute of Scientific and Technical Information of China (English)
LIANG Yu-Jie; LI Yan-Song; LIU Zu-Hua; ZHOU Hong-Yu
2009-01-01
Halo structures of some light mirror nuclei are investigated with the relativistic mean field (RMF) theory.The calculations show that the dispersion of the valence proton is larger than that of the valence neutron in its mirror nucleus,the difference between the root-mean-square (rms) radius of the valence nucleon in each pair of mirror nuclei becomes smailer with the increase of the mass number A,and all the ratios of the rms radius of the valence nucleon to that of the matter in each pair o~ mirror nuclei decrease almost linearly with the increase of the mass number A.
Skymapping with OSSE via the Mean Field Annealing Pixon Technique
Dixon, D D; Zych, A D; Cheng, L X; Johnson, W N; Kurfess, J D; Pina, R K; Pütter, R C; Purcell, W R; Wheaton, W A; Wheaton, Wm. A.
1997-01-01
We present progress toward using scanned OSSE observations for mapping and sky survey work. To this end, we have developed a technique for detecting pointlike sources of unknown number and location, given that they appear in a background which is relatively featureless or which can be modeled. The technique, based on the newly developed concept and mean field annealing, is described, with sample reconstructions of data from the OSSE Virgo Survey. The results demonstrate the capability of reconstructing source information without any a priori information about the number and/or location of pointlike sources in the field-of-view.
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.)
Small-world network spectra in mean-field theory.
Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc
2012-05-25
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean-field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering, and social science.
Asymptotics of Mean-Field O( N) Models
Kirkpatrick, Kay; Nawaz, Tayyab
2016-12-01
We study mean-field classical N-vector models, for integers N≥2. We use the theory of large deviations and Stein's method to study the total spin and its typical behavior, specifically obtaining non-normal limit theorems at the critical temperatures and central limit theorems away from criticality. Important special cases of these models are the XY (N=2) model of superconductors, the Heisenberg (N=3) model [previously studied in Kirkpatrick and Meckes (J Stat Phys 152:54-92, 2013) but with a correction to the critical distribution here], and the Toy (N=4) model of the Higgs sector in particle physics.
Asymptotics of the mean-field Heisenberg model
Kirkpatrick, Kay
2012-01-01
We consider the mean-field classical Heisenberg model and obtain detailed information about the magnetization by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cram\\`er- and Sanov-type large deviations principles for the magnetization and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the magnetization throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.
A mechanical approach to mean field spin models
Genovese, Giuseppe
2008-01-01
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models defined on lattice, whose order parameters self average. We show the whole procedure by analyzing in full details the simplest test case, namely the Curie-Weiss model. Further we report some applications also to models whose order parameters do not self-average, by using the Sherrington-Kirkpatrick spin glass as a guide.
Nuclear Density-Dependent Effective Coupling Constants in the Mean-Field Theory
Lee, J H; Lee, S J; Lee, Jae Hwang; Lee, Young Jae; Lee, Suk-Joon
1996-01-01
It is shown that the equation of state of nuclear matter can be determined within the mean-field theory of $\\sigma \\omega$ model provided only that the nucleon effective mass curve is given. We use a family of the possible nucleon effective mass curves that reproduce the empirical saturation point in the calculation of the nuclear binding energy curves in order to obtain density-dependent effective coupling constants. The resulting density-dependent coupling constants may be used to study a possible equation of state of nuclear system at high density or neutron matter. Within the constraints used in this paper to $M^*$ of nuclear matter at saturation point and zero density, neutron matter of large incompressibility is strongly bound at high density while soft neutron matter is weakly bound at low density. The study also exhibits the importance of surface vibration modes in the study of nuclear equation of state.
Mean Field Limit of Interacting Filaments and Vector Valued Non-linear PDEs
Bessaih, Hakima; Coghi, Michele; Flandoli, Franco
2017-03-01
Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new set-up, a mean field result is proven, as N→ ∞. The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result. The results are local in time for general interaction kernel, global in time under some additional restriction. Our main motivation is the approximation of 3D-inviscid flow dynamics by the interacting dynamics of a large number of vortex filaments, as observed in certain turbulent fluids; in this respect, the present paper is restricted to smoothed interaction kernels, instead of the true Biot-Savart kernel.
Combining Few-Body Cluster Structures with Many-Body Mean-Field Methods
Hove, D.; Garrido, E.; Jensen, A. S.; Sarriguren, P.; Fynbo, H. O. U.; Fedorov, D. V.; Zinner, N. T.
2017-03-01
Nuclear cluster physics implicitly assumes a distinction between groups of degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated) relative cluster motion. We formulate a realistic and practical method to describe the coupled motion of these two sets of degrees-of-freedom. We derive a coupled set of differential equations for the system using the phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon interaction. We select a two-nucleon plus core system where the mean-field approximation corresponding to the Skyrme interaction is used for the core. A hyperspherical adiabatic expansion of the Faddeev equations is used for the relative cluster motion. We shall specifically compare both the structure and the decay mechanism found from the traditional three-body calculations with the result using the new boundary condition provided by the full microscopic structure at small distance. The extended Hilbert space guaranties an improved wave function compared to both mean-field and three-body solutions. We shall investigate the structures and decay mechanism of ^{22}C (^{20}C+n+n). In conclusion, we have developed a method combining nuclear few- and many-body techniques without losing the descriptive power of each approximation at medium-to-large distances and small distances respectively. The coupled set of equations are solved self-consistently, and both structure and dynamic evolution are studied.
Baladron, Javier; Fasoli, Diego; Faugeras, Olivier; Touboul, Jonathan
2012-05-31
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons' initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes place, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial differential equations resembling the McKean-Vlasov-Fokker-Planck equations. We prove the well-posedness of the McKean-Vlasov equations, i.e. the existence and uniqueness of a solution. We also show the results of some numerical experiments that indicate that the mean-field equations are a good representation of the mean activity of a finite size network, even for modest sizes. These experiments also indicate that the McKean-Vlasov-Fokker-Planck equations may be a good way to understand the mean-field dynamics through, e.g. a bifurcation analysis.Mathematics Subject Classification (2000): 60F99, 60B10, 92B20, 82C32, 82C80, 35Q80.
Topological properties of the mean-field ϕ4 model
Andronico, A.; Angelani, L.; Ruocco, G.; Zamponi, F.
2004-10-01
We study the thermodynamics and the properties of the stationary points (saddles and minima) of the potential energy for a ϕ4 mean-field model. We compare the critical energy vc [i.e., the potential energy v(T) evaluated at the phase transition temperature Tc ] with the energy vθ at which the saddle energy distribution show a discontinuity in its derivative. We find that, in this model, vc≫vθ , at variance to what has been found in different mean-field and short ranged systems, where the thermodynamic phase transitions take place at vc=vθ [Casetti, Pettini and Cohen, Phys. Rep. 337, 237 (2000)]. By direct calculation of the energy vs(T) of the “inherent saddles,” i.e., the saddles visited by the equilibrated system at temperature T , we find that vs(Tc)˜vθ . Thus, we argue that the thermodynamic phase transition is related to a change in the properties of the inherent saddles rather than to a change of the topology of the potential energy surface at T=Tc . Finally, we discuss the approximation involved in our analysis and the generality of our method.
Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter
Institute of Scientific and Technical Information of China (English)
ZHANG Qi-Ren; GAO Chun-Yuan
2011-01-01
We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field Φ is introduced.The equivalence of this procedure with the usual one is proven for any given value of Φ.By use of this procedure, the scalar meson field in the Walecka's MFA and in Chin's RHA are quantized around the mean field.Its corrections on these theories are considered by perturbation up to the second order.The arbitrariness of Φ makes us free to fix it at any stage in the calculation.When we fix it in the way of Walecka's MFA, the quantum corrections are big, and the result does not converge.When we fix it in the way of Chin's RHA, the quantum correction is negligibly small, and the convergence is excellent.It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka's MFA does not.We suggest to fix the parameter Φ at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory (QRMFT) a variational method.
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.)
Benchmarking mean-field approximations to level densities
Alhassid, Y; Gilbreth, C N; Nakada, H
2015-01-01
We assess the accuracy of finite-temperature mean-field theory using as a standard the Hamiltonian and model space of the shell model Monte Carlo calculations. Two examples are considered: the nucleus $^{162}$Dy, representing a heavy deformed nucleus, and $^{148}$Sm, representing a nearby heavy spherical nucleus with strong pairing correlations. The errors inherent in the finite-temperature Hartree-Fock and Hartree-Fock-Bogoliubov approximations are analyzed by comparing the entropies of the grand canonical and canonical ensembles, as well as the level density at the neutron resonance threshold, with shell model Monte Carlo (SMMC) calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are seen to be: (i) the extraction of number-projected densities from the grand canonical ensembles, and (ii) the symmetry breaking by deformation or by the pairing condensate. In the absence of a pairing condensate, we confirm that the usual saddle-point appr...
Simulated Tempering and Swapping on Mean-Field Models
Bhatnagar, Nayantara; Randall, Dana
2016-08-01
Simulated and parallel tempering are families of Markov Chain Monte Carlo algorithms where a temperature parameter is varied during the simulation to overcome bottlenecks to convergence due to multimodality. In this work we introduce and analyze the convergence for a set of new tempering distributions which we call entropy dampening. For asymmetric exponential distributions and the mean field Ising model with an external field simulated tempering is known to converge slowly. We show that tempering with entropy dampening distributions mixes in polynomial time for these models. Examining slow mixing times of tempering more closely, we show that for the mean-field 3-state ferromagnetic Potts model, tempering converges slowly regardless of the temperature schedule chosen. On the other hand, tempering with entropy dampening distributions converges in polynomial time to stationarity. Finally we show that the slow mixing can be very expensive practically. In particular, the mixing time of simulated tempering is an exponential factor longer than the mixing time at the fixed temperature.
Mean field theory for U(n) dynamical groups
Energy Technology Data Exchange (ETDEWEB)
Rosensteel, G, E-mail: george.rosensteel@tulane.edu [Department of Physics, Tulane University, New Orleans, LA 70118 (United States)
2011-04-22
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick su(2) model and the Elliott su(3) model. When the energy in the su(3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
The effectiveness of mean-field theory for avalanche distributions
Lee, Edward; Raju, Archishman; Sethna, James
We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.
Second-order corrections to mean-field evolution of weakly interacting Bosons, II
Grillakis, M; Margetis, D
2010-01-01
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I, in which we derived a second-order correction to a mean-field evolution law for coherent states in the presence of small interaction potential. Here, we remove the assumption of smallness of the interaction potential and prove global existence of solutions to the equation for the second-order correction. This implies an improved Fock-space estimate for our approximation of the N-body state.
Mean field mutation dynamics and the continuous Luria-Delbrück distribution.
Kashdan, Eugene; Pareschi, Lorenzo
2012-12-01
The Luria-Delbrück mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbrück distribution. Numerical results confirming the theoretical analysis are also presented.
Mean field mutation dynamics and the continuous Luria-Delbr\\"uck distribution
Kashdan, Eugene
2011-01-01
The Luria-Delbr\\"uck mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbr\\"uck distribution. Numerical results confirming the theoretical analysis are also presented.
Delta isobars in relativistic mean-field models with $\\sigma$-scaled hadron masses and couplings
Kolomeitsev, E E; Voskresensky, D N
2016-01-01
We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\\sigma$ field, studied previously to incorporate $\\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\\Delta$s with meson fields. Conditions for the appearance of $\\Delta$s are studied. We demonstrate that with inclusion of the $\\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.
Pasta phases in neutron star studied with extended relativistic mean field models
Gupta, Neha
2013-01-01
To explain several properties of finite nuclei, infinite matter, and neutron stars in a unified way within the relativistic mean field models, it is important to extend them either with higher order couplings or with density-dependent couplings. These extensions are known to have strong impact in the high-density regime. Here we explore their role on the equation of state at densities lower than the saturation density of finite nuclei which govern the phase transitions associated with pasta structures in the crust of neutron stars.
DEFF Research Database (Denmark)
Lerchner, Alexander; Sterner, G.; Hertz, J.
2006-01-01
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......, without being restricted to specific neuron models. Here, we solve the 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...
Energy Technology Data Exchange (ETDEWEB)
Withers, L. P., E-mail: lpwithers@mitre.org [School of Physics, Astronomy, and Computational Science, George Mason University, Fairfax, Virginia 22030-4444 (United States); Narducci, F. A., E-mail: francesco.narducci@navy.mil [Naval Air Systems Command, Patuxent River, Maryland 20670 (United States)
2015-06-15
The recent single-photon double-slit experiment of Steinberg et al., based on a weak measurement method proposed by Wiseman, showed that, by encoding the photon’s transverse momentum behind the slits into its polarization state, the momentum profile can subsequently be measured on average, from a difference of the separated fringe intensities for the two circular polarization components. They then integrated the measured average velocity field, to obtain the average trajectories of the photons enroute to the detector array. In this paper, we propose a modification of their experiment, to demonstrate that the average particle velocities and trajectories change when the mode of detection changes. The proposed experiment replaces a single detector by a pair of detectors with a given spacing between them. The pair of detectors is configured so that it is impossible to distinguish which detector received the particle. The pair of detectors is then analogous to the simple pair of slits, in that it is impossible to distinguish which slit the particle passed through. To establish the paradoxical outcome of the modified experiment, the theory and explicit three-dimensional formulas are developed for the bilocal probability and current densities, and for the average velocity field and trajectories as the particle wavefunction propagates in the volume of space behind the Gaussian slits. Examples of these predicted results are plotted. Implementation details of the proposed experiment are discussed.
Metabifurcation analysis of a mean field model of the cortex
Frascoli, Federico; Bojak, Ingo; Liley, David T J
2010-01-01
Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space capturing neurobiological attributes relevant to brain dynamics. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two families. After investigating and characterizing these, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli, distribution of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs ...
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been calculated in the WKB approximation and the spectroscopic factors have been extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions have been made for some possible decays.
Quasi-isotropic cascade in MHD turbulence with mean field
Grappin, Roland; Gürcan, Özgür
2012-01-01
We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\\parallel,k_\\bot)$ has the same slope in all directions. The ratio between the extents of the inertial range in the parallel and perpendicular directions is equal to $b_{rms}/B_0$. These properties match those found in recent 3D MHD simulations with isotropic forcing reported in [R. Grappin and W.-C. M\\"uller, Phys. Rev. E \\textbf{82}, 26406 (2010)].
Nuclear Level Density: Shell Model vs Mean Field
Sen'kov, Roman
2015-01-01
The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally...
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Relativistic Mean-Field Models and Nuclear Matter Constraints
Dutra, M; Carlson, B V; Delfino, A; Menezes, D P; Avancini, S S; Stone, J R; Providência, C; Typel, S
2013-01-01
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear \\sigma^3+\\sigma^4 models, (iii) \\sigma^3+\\sigma^4+\\omega^4 models, (iv) models containing mixing terms in the fields \\sigma and \\omega, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the \\sigma (\\omega) field. The isospin dependence of the interaction is modeled by the \\rho meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Mean-field vs. Stochastic Models for Transcriptional Regulation
Blossey, Ralf; Giuraniuc, Claudiu
2009-03-01
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Mean-field versus stochastic models for transcriptional regulation
Blossey, R.; Giuraniuc, C. V.
2008-09-01
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ODE’s representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results that both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: The repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Double binding energy differences: Mean-field or pairing effect?
Qi, Chong
2012-10-01
In this Letter we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction Vpn thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the Vpn in even-even nuclei with N ≠ Z are dominated by the contribution from the proton-neutron monopole interactions. A strong additional contribution from the isoscalar monopole interaction and isovector proton-neutron pairing interaction is seen in the Vpn for even-even N = Z nuclei and for the adjacent odd-A nuclei with one neutron or proton being subtracted.
Non-mean-field screening by multivalent counterions
Energy Technology Data Exchange (ETDEWEB)
Loth, M S; Shklovskii, B I, E-mail: loth@physics.umn.ed [Department of Physics, University of Minnesota, Minneapolis, MN 55455 (United States)
2009-10-21
Screening of a strongly charged macroion by its multivalent counterions cannot be described in the framework of a mean-field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that, due to the negative screening length of the SCL, -2xi, the effective metallic surface is actually above the SCL by |xi|.
Spectral Synthesis via Mean Field approach Independent Component Analysis
Hu, Ning; Kong, Xu
2015-01-01
In this paper, we apply a new statistical analysis technique, Mean Field approach to Bayesian Independent Component Analysis (MF-ICA), on galaxy spectral analysis. This algorithm can compress the stellar spectral library into a few Independent Components (ICs), and galaxy spectrum can be reconstructed by these ICs. Comparing to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, MF-ICA approach offers a large improvement in the efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter-recover for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters from the Sloan Digital Sky Survey galaxies. We find that our MF-ICA method not only can fit the observed galaxy spectra efficiently, but also can recover the physical parameters of galaxies accurately. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find...
Mean field theory for U(n) dynamical groups
Rosensteel, G.
2011-04-01
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick {\\mathfrak s}{\\mathfrak u} (2) model and the Elliott {\\mathfrak s}{\\mathfrak u} (3) model. When the energy in the {\\mathfrak s}{\\mathfrak u} (3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
Conserving Gapless Mean-Field Theory for Weakly Interacting Bose Gases
Kita, Takafumi
2006-04-01
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 \\Psi and the Nambu Green’s function \\hat{G} for the quasiparticle field. Imposing its stationarity respect to \\Psi and \\hat{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 Tc inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature Tc shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case Tc increases from the ideal gas value T0 as Tc/T0= 1+ 2.33 an1/3, whereas it decreases in the latter as Tc/T0= 1- 3.84a(m p/2π\\hbar2)1/5. Temperature dependences of basic thermodynamic quantities are clarified explicitly.
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
Trimborn, F.; Werner, R. F.; Witthaut, D.
2016-04-01
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
Second-order corrections to mean field evolution for weakly interacting Bosons. I
Grillakis, Manoussos G; Margetis, Dionisios
2009-01-01
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential $v(x)= \\epsilon \\chi(x) |x|^{-1}$, where $\\epsilon$ is sufficiently small and $\\chi \\in C_0^{\\infty}$, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (part II) of this paper.
Chen, Xuwen
2010-01-01
In this paper, we consider the Hamiltonian evolution of N weakly interacting Bosons. Assuming triple collisions with singular potentials, its mean field approximation is given by a quintic Hartree equation. We construct a second order correction to the mean field approximation using a kernel k(t,x,y) and derive an evolution equation for k. We show the global existence for the resulting evolution equation for the correction and establish an apriori estimate comparing the approximation to the exact Hamiltonian evolution. Our error estimate is global and uniform in time. Comparing with the work in [20,11,12] where the error estimate grows in time, our approximation tracks the exact dynamics for all time with an error of the order O(1/$\\sqrt{N}$).
Wen, Jiayi; Zhou, Shenggao; Xu, Zhenli; Li, Bo
2012-04-01
Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling.
Relativistic mean-field models and nuclear matter constraints
Energy Technology Data Exchange (ETDEWEB)
Dutra, M.; Lourenco, O.; Carlson, B. V. [Departamento de Fisica, Instituto Tecnologico de Aeronautica-CTA, 12228-900, Sao Jose dos Campos, SP (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminense, 24210-150, Boa Viagem, Niteroi, RJ (Brazil); Menezes, D. P.; Avancini, S. S. [Departamento de Fisica, CFM, Universidade Federal de Santa Catarina, CP. 476, CEP 88.040-900, Florianopolis, SC (Brazil); Stone, J. R. [Oxford Physics, University of Oxford, OX1 3PU Oxford (United Kingdom) and Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States); Providencia, C. [Centro de Fisica Computacional, Department of Physics, University of Coimbra, P-3004-516 Coimbra (Portugal); Typel, S. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Theorie, Planckstrasse 1,D-64291 Darmstadt (Germany)
2013-05-06
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear {sigma}{sup 3}+{sigma}{sup 4} models, (iii) {sigma}{sup 3}+{sigma}{sup 4}+{omega}{sup 4} models, (iv) models containing mixing terms in the fields {sigma} and {omega}, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the {sigma} ({omega}) field. The isospin dependence of the interaction is modeled by the {rho} meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Mean-field study of $^{12}$C+$^{12}$C fusion
Chien, Le Hoang; Khoa, Dao T
2016-01-01
The nuclear mean-field potential arising from the $^{12}$C+$^{12}$C interaction at the low energies relevant for the astrophysical carbon burning process has been constructed within the double-folding model, using the realistic nuclear ground-state density of the $^{12}$C nucleus and the effective M3Y nucleon-nucleon (NN) interaction constructed from the G-matrix of the Paris (free) NN potential. To explore the nuclear medium effect, both the original density independent M3Y-Paris interaction and its density dependent CDM3Y6 version have been used in the folding model calculation of the $^{12}$C+$^{12}$C potential. The folded potentials at the different energies were used in the optical model description of the elastic $^{12}$C+$^{12}$C scattering at the energies around and below the Coulomb barrier, as well as in the barrier penetration model to estimate the fusion cross section and astrophysical $S$ factor of the $^{12}$C+$^{12}$C reactions at the low energies. The obtained results are in good agreement wit...
A Mean-Field Theory for Coarsening Faceted Surfaces
Norris, Scott A
2009-01-01
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von S...
Nuclear mean field from chiral pion-nucleon dynamics
Kaiser, N; Weise, W
2002-01-01
Using the two-loop approximation of chiral perturbation theory, we calculate the momentum- and density-dependent single-particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give rise to a potential depth for a nucleon at rest of U(0,k sub f sub 0)=-53.2 MeV at saturation density. The momentum dependence of the real part of the single-particle potential U(p,k sub f sub 0) is nonmonotonic and can be translated into a mean effective nucleon mass of M*bar approx =0.8M. The imaginary part of the single-particle potential W(p,k sub f) is generated to that order entirely by iterated one-pion exchange. The resulting half width of a nucleon hole-state at the bottom of the Fermi sea comes out as W(0,k sub f sub 0)=29.7 MeV. The basic theorems of Hugenholtz-Van-Hove and Luttinger are satisfied in our perturbative two-loop calculation of the nuclear mean field.
Spectral Synthesis via Mean Field approach to Independent Component Analysis
Hu, Ning; Su, Shan-Shan; Kong, Xu
2016-03-01
We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis (MF-ICA) in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components (ICs), and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter recovery for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.
Quark mean field model with pion and gluon corrections
Xing, Xueyong; Hu, Jinniu; Shen, Hong
2016-10-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.
Individual based and mean-field modeling of direct aggregation
Burger, Martin
2013-10-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.
The quark mean field model with pion and gluon corrections
Xing, Xueyong; Shen, Hong
2016-01-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pion and gluon into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pion and gluon on the nucleon structure are treated in second-order perturbation theory. For the nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determine three parameter sets about the coupling constants between mesons and quarks, named as QMF-NK1, QMF-NK2, and QMF-NK3 by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give satisfactory description on properties of nuclear matter and finite nuclei, meanwhile they can also predict the larger neutron star mass around $2.3M_\\odot$ without the hypero...
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Elementary proof of convergence to the mean-field model for the SIR process.
Armbruster, Benjamin; Beck, Ekkehard
2016-12-21
The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field approximation of the underlying stochastic SIR process on contact networks, only few rigorous approaches exist and these use complex semigroup and martingale techniques to prove that the expected fraction of the susceptible and infected nodes of the stochastic SIR process on a complete graph converges as the number of nodes increases to the solution of the mean-field ODE model. Extending the elementary proof of convergence for the SIS process introduced by Armbruster and Beck (IMA J Appl Math, doi: 10.1093/imamat/hxw010 , 2016) to the SIR process, we show convergence using only a system of three ODEs, simple probabilistic inequalities, and basic ODE theory. Our approach can also be generalized to many other types of compartmental models (e.g., susceptible-infected-recovered-susceptible (SIRS)) which are linear ODEs with the addition of quadratic terms for the number of new infections similar to the SI term in the SIR model.
Mean-field approximation for the Sznajd model in complex networks
Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.
2015-02-01
This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.
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.
Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks
Gomez, Sergio; Moreno, Yamir; Arenas, Alex
2011-01-01
Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by proposing a non-perturbative formulation of the heterogeneous mean field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. The non-perturbative equations we propose have no assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description at the node level of the epidemic propagation for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. We propose to use the full extension of the approach instead of pruning the expansion to first order, which leads to a non-perturbative formulation that can be solved by fixed point it...
Mean field spin glasses treated with PDE techniques
Barra, Adriano; Del Ferraro, Gino; Tantari, Daniele
2013-07-01
Following an original idea of Guerra, in these notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of the model (e.g. solving for the free energy) to well-known partial differential equation (PDE) problems (in suitable spaces). The plan is then to solve the related PDE using techniques involved in their native field and lastly bringing back the solution in the proper statistical mechanics framework. Within this strand, after a streamlined test-case on the Curie-Weiss model to highlight the methods more than the physics behind, we solve the SK both at the replica symmetric and at the 1-RSB level, obtaining the correct expression for the free energy via an analogy to a Fourier equation and for the self-consistencies with an analogy to a Burger equation, whose shock wave develops exactly at critical noise level (triggering the phase transition). Our approach, beyond acting as a new alternative method (with respect to the standard routes) for tackling the complexity of spin glasses, links symmetries in PDE theory with constraints in statistical mechanics and, as a novel result from the theoretical physics perspective, we obtain a new class of polynomial identities (namely of Aizenman-Contucci type, but merged within the Guerra's broken replica measures), whose interest lies in understanding, via the recent Panchenko breakthroughs, how to force the overlap organization to the ultrametric tree predicted by Parisi.
Economic dynamics with financial fragility and mean-field interaction: A model
Di Guilmi, C.; Gallegati, M.; Landini, S.
2008-06-01
Following Aoki’s statistical mechanics methodology [Masanao Aoki, New Approaches to Macroeconomic Modeling, Cambridge University Press, 1996; Masanao Aoki, Modeling Aggregate Behaviour and Fluctuations in Economics, Cambridge University Press, 2002; Masanao Aoki, and Hiroshi Yoshikawa, Reconstructing Macroeconomics, Cambridge University Press, 2006], we provide some insights into the well-known works of [Bruce Greenwald, Joseph Stiglitz, Macroeconomic models with equity and credit rationing, in: R. Hubbard (Ed.), Information, Capital Markets and Investment, Chicago University Press, Chicago, 1990; Bruce Greenwald, Joseph Stiglitz, Financial markets imperfections and business cycles, Quarterly journal of Economics (1993)]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can be partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean-field interaction modeling and master equation techniques.
A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games
Cao, Ke-cai; Stuart, Dan
2016-01-01
Modeling of crowds of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micro-macro model for crowds of pedestrians are obtained in the end. Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model respectively.
On the binding of small polarons in a mean-field quantum crystal
Lewin, Mathieu
2012-01-01
We consider a small multi-polaron model obtained by coupling the many-body Schr\\"odinger equation for N interacting electrons with the energy functional of a mean- field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitue a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background. We first prove that a single polaron always binds, i.e. the energy functional has a minimizer for N = 1. Then we discuss the case of multi-polarons containing two electrons or more. We show that their existence is guaranteed when certain quantized binding inequalities of HVZ type are satisfied.
Hamiltonian-based impurity solver for nonequilibrium dynamical mean-field theory
Gramsch, Christian; Balzer, Karsten; Eckstein, Martin; Kollar, Marcus
2013-12-01
We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.
Hayasaka, K; Hayasaka, Kiyoshi; Nakayama, Ryuichi
2002-01-01
We point out that when a D-brane is placed in an NS-NS B field background with non-vanishing field strength (H=dB) along the D-brane worldvolume, the coordinate of one end of the open string does not commute with that of the other in the low energy limit. The degrees of the freedom associated with both ends are not decoupled and accordingly, the effective action must be quite different from that of the ordinary noncommutative gauge theory for a constant B background. We construct an associative and noncommutative product which operates on the coordinates of both ends of the string and propose a new type of noncommutative gauge action for the low energy effective theory of a Dp-brane. This effective theory is bi-local and lives in twice as large dimensions (2D=2(p+1)) as in the H=0 case. When viewed as a theory in the D-dimensional space, this theory is non-local and we must force the two ends of the string to coincide. We will then propose a prescription for reducing this bi-local effective action to that in ...
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.
Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo
Schrinner, M; Schmitt, D; Rheinhardt, M; Christensen, U R
2006-01-01
A comparison is made between mean-field models and direct numerical simulations of rotating magnetoconvection and the geodynamo. The mean-field coefficients are calculated with the fluid velocity taken from the direct numerical simulations. The magnetic fields resulting from mean-field models are then compared with the mean magnetic field from the direct numerical simulations.
Exact mean-field theory of ionic solutions: non-Debye screening
Varela, Luis M.; García, Manuel; Mosquera, Víctor
2003-07-01
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 Hückel (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
Exact mean-field theory of ionic solutions: non-Debye screening
Energy Technology Data Exchange (ETDEWEB)
Varela, L.M.; Garcia, Manuel; Mosquera, Victor
2003-07-01
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
Quantum corrections to the Relativistic mean-field theory
Maydanyuk, Sergei P; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{\\rm shell}$. But, a difference between $V_{RMF}$ and $V_{\\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indica...
Mean-field and Monte Carlo studies of the magnetization-reversal transition in the Ising model
Energy Technology Data Exchange (ETDEWEB)
Misra, Arkajyoti [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India)]. E-mail: arko@cmp.saha.ernet.in; Chakrabarti, Bikas K. [Saha Institute of Nuclear Physics, Bidhannagar, Calcutta (India)]. E-mail: bikas@cmp.saha.ernet.in
2000-06-16
Detailed mean-field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. An approximate analytical treatment of the mean-field equations of motion shows the existence of diverging length and time scales across this dynamic transition phase boundary. These are also supported by numerical solutions of the complete mean-field equations of motion and the Monte Carlo study of the system evolving under Glauber dynamics in both two and three dimensions. Classical nucleation theory predicts different mechanisms of domain growth in two regimes marked by the strength of the external field, and the nature of the Monte Carlo phase boundary can be comprehended satisfactorily using the theory. The order of the transition changes from a continuous to a discontinuous one as one crosses over from coalescence regime (stronger field) to a nucleation regime (weaker field). Finite-size scaling theory can be applied in the coalescence regime, where the best-fit estimates of the critical exponents are obtained for two and three dimensions. (author)
Compression induced phase transition of nematic brush: A mean-field theory study
Energy Technology Data Exchange (ETDEWEB)
Tang, Jiuzhou [Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190 (China); Zhang, Xinghua, E-mail: zhangxh@bjtu.edu.cn [School of Science, Beijing Jiaotong University, Beijing 100044 (China); Yan, Dadong, E-mail: yandd@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2015-11-28
Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.
Mean-field analysis of an inductive reasoning game: application to influenza vaccination.
Breban, Romulus; Vardavas, Raffaele; Blower, Sally
2007-09-01
Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.
Dynamo action due to alpha fluctuations in a shear flow: mean--field theory
Sridhar, S
2013-01-01
We present an analytical theory of the growth of a large-scale mean magnetic field in a linear shear flow with fluctuations in time of the alpha parameter (equivalently, kinetic helicity). Using shearing coordinates and Fourier variables we derive a set of coupled integro-differential equations, governing the dynamics of the mean magnetic field, that are non perturbative in the rate of shear. When the alpha fluctuations are of white-noise form, the mean electromotive force (EMF) is identical to the negative diffusive form derived by Kraichnan for the case of no shear; the physical reason is that shear takes time to act, and white-noise fluctuations have zero correlation time. We demonstrate that the white-noise case does not allow for large-scale dynamo action. We then allow for a small but non zero correlation time and show that, for a slowly varying mean magnetic field, the mean EMF has additional terms that depend on a combination of shear and alpha fluctuations; the mean-field equations now reduce to a se...
The Accuracy of Mean-Field Approximation for Susceptible-Infected-Susceptible Epidemic Spreading
Qu, Bo
2016-01-01
The epidemic spreading has been studied for years by applying the mean-field approach in both homogeneous case, where each node may get infected by an infected neighbor with the same rate, and heterogeneous case, where the infection rates between different pairs of nodes are different. Researchers have discussed whether the mean-field approaches could accurately describe the epidemic spreading for the homogeneous cases but not for the heterogeneous cases. In this paper, we explore under what conditions the mean-field approach could perform well when the infection rates are heterogeneous. In particular, we employ the Susceptible-Infected-Susceptible (SIS) model and compare the average fraction of infected nodes in the metastable state obtained by the continuous-time simulation and the mean-field approximation. We concentrate on an individual-based mean-field approximation called the N-intertwined Mean Field Approximation (NIMFA), which is an advanced approach considered the underlying network topology. Moreove...
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.
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek
2009-01-01
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.
Nuclear matter EOS with light clusters within the mean-field approximation
Ferreira, Márcio
2013-01-01
The crust of a neutron star is essentially determined by the low-density region ($\\rho<\\rho_0\\approx0.15-0.16\\unit{fm}^{-3}$) of the equation of state. At the bottom of the inner crust, where the density is $\\rho\\lesssim0.1\\rho_0$, the formation of light clusters in nuclear matter will be energetically favorable at finite temperature. At very low densities and moderate temperatures, the few body correlations are expected to become important and light nuclei like deuterons, tritons, helions and $\\alpha$-particles will form. Due to Pauli blocking, these clusters will dissolve at higher densities $\\rho\\gtrsim 0.1\\rho_0$. The presence of these clusters influences the cooling process and quantities, such as the neutrino emissivity and gravitational waves emission. The dissolution density of these light clusters, treated as point-like particles, will be studied within the Relativistic Mean Field approximation. In particular, the dependence of the dissolution density on the clusters-meson couplings is studied.
Nuclear matter fourth-order symmetry energy in relativistic mean field models
Cai, Bao-Jun
2011-01-01
Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{4}(\\rho)$. Our results show that the value of $E_{4}(\\rho)$ at normal nuclear matter density $\\rho_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $\\rho_{0}$. On the other hand, we find that the $E_{4}(\\rho)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{4}(\\rho)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{\\mathrm{sat}}(\\delta)=K_{0}+K_{\\mathrm{{sat},2}}\\delta ^{2}+K_{\\mathrm{{sat},4}}\\delta ^{4}+\\mathcal{O}(\\delta ^{6})$ where $\\delta =(\\rho_{n}-\\rho_{p})/\\rho $ is the isospin asymmetry, and we find that the value of $K_{\\mathrm{{sat},4}}$ is generally comparable with that of the $K_{\\mathrm{{sat},2}}$. In addition, we study the effects of the $E...
Open-source tools for dynamical analysis of Liley's mean-field cortex model
Green, Kevin R
2012-01-01
Mean-field models of the mammalian cortex treat this part of the brain as a two-dimensional excitable medium. The electrical potentials, generated by the excitatory and inhibitory neuron populations, are described by nonlinear, coupled, partial differential equations, that are known to generate complicated spatio-temporal behaviour. We focus on the model by Liley {\\sl et al.} (Network: Comput. Neural Syst. (2002) 13, 67-113). Several reductions of this model have been studied in detail, but a direct analysis of its spatio-temporal dynamics has, to the best of our knowledge, never been attempted before. Here, we describe the implementation of implicit time-stepping of the model and the tangent linear model, and solving for equilibria and time-periodic solutions, using the open-source library PETSc. By using domain decomposition for parallelization, and iterative solving of linear problems, the code is capable of parsing some dynamics of a macroscopic slice of cortical tissue with a sub-millimetre resolution.
Impact of fraud on the mean-field dynamics of cooperative social systems
Röhl, Torsten; Röhl, Claudia; Schuster, Heinz Georg; Traulsen, Arne
2007-08-01
The evolution of costly cooperation between selfish individuals seems to contradict Darwinian selection, as it reduces the fitness of a cooperating individual. However, several mechanisms such as repeated interactions or spatial structure can lead to the evolution of cooperation. One such mechanism for the evolution of cooperation, in particular among humans, is indirect reciprocity, in which individuals base their decision to cooperate on the reputation of the potential receiver, which has been established in previous interactions. Cooperation can evolve in these systems if individuals preferably cooperate with those that have shown to be cooperative in the past. We analyze the impact of fake reputations or fraud on the dynamics of reputation and on the success of the reputation system itself, using a mean-field description for evolutionary games given by the replicator equation. This allows us to classify the qualitative dynamics of our model analytically. Our results show that cooperation based on indirect reciprocity is robust with respect to fake reputations and can even be enhanced by them. We conclude that fraud per se does not necessarily have a detrimental effect on social systems.
Hamiltonian mean field model: Effect of network structure on synchronization dynamics.
Virkar, Yogesh S; Restrepo, Juan G; Meiss, James D
2015-11-01
The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors. When K is just beyond the transition to synchronization, we find that the degree of synchronization is highly dependent on the network's heterogeneity, but that for large K the degree of synchronization is robust to changes in the degree distribution. Our results are illustrated with numerical simulations on Erdös-Renyi networks and networks with power-law degree distributions.
Mean-field Density Functional Theory of a Three-Phase Contact Line
Lin, Chang-You
A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive over-relaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change. We develop a geometrical interpretation to generalize our potential in order to study less symmetric systems as occur in some practical phase diagrams. A set of special cases of this new potential are linear transformations from our original potential. In those special cases, we can obtain solutions by scaling of our former results.
Singular-potential random-matrix model arising in mean-field glassy systems.
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Symmetry-unrestricted Skyrme mean-field study of heavy nuclei
Ryssens, W; Bender, M
2016-01-01
In the light of recent experimental developments, increasing attention is devoted to nuclear phenomena related to rotational excitations of exotic intrinsic nuclear configurations that often lack symmetries present in the majority of nuclei. Examples include configurations with a non-vanishing octupole moment. In order to describe this kind of states, we have developed a new computer code to solve the self-consistent mean-field equations, able to use most of today's effective Skyrme interactions and working in coordinate-space. We report on the development of MOCCa, a code based on the same principles as EV8, but offering the user individual control on many symmetry assumptions. In addition, the HF+BCS pairing treatment of EV8 has been generalised to the full machinery of Hartree-Fock-Bogoliubov transformations. We discuss as example the static fission barrier of $^{226}$Ra, prefacing extended studies in the region, using the recent series of Skyrme parameterizations SLy5s1 through SLy5s8.
Nucleon Finite Volume Effect and Nuclear Matter Properties in a Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
R. Costa; A.J. Santiago; H. Rodrigues; J. Sa Borges
2006-01-01
Effects of excluded volume of nucleons on nuclear matter are studied, and the nuclear properties that follow from different relativistic mean-field model parametrizations are compared. We show that, for all tested parametrizations,the resulting volume energy a1 and the symmetry energy J are around the acceptable values of 16 MeV and 30 MeV,and the density symmetry L is around 100 Me V. On the other hand, models that consider only linear terms lead to incompressibility K0 much higher than expected. For most parameter sets there exists a critical point (ρc,δc), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero. This critical point depends on the excluded volume parameter r. If this parameter is larger than 0.5 fm, there is no critical point and the pure neutron matter is predicted to be bound. The maximum value for neutron star mass is 1.85M⊙, which is in agreement with the mass of the heaviest observed neutron star 4U0900-40 and corresponds to r = 0.72 fm. We also show that the light neutron star mass (1.2M⊙) is obtained for r (≌) 0.9 fm.
Energy Technology Data Exchange (ETDEWEB)
Bassi, G.; /Liverpool U. /Cockroft Inst.; Ellison, J.A.; Heinemann, K.; /New Mexico U.; Warnock, R.; /SLAC
2009-05-07
Bunch compressors, designed to increase the peak current, can lead to a microbunching instability with detrimental effects on the beam quality. This is a major concern for free electron lasers (FELs) where very bright electron beams are required, i.e. beams with low emittance and energy spread. In this paper, we apply our self-consistent, parallel solver to study the microbunching instability in the first bunch compressor system of FERMI{at}Elettra. Our basic model is a 2D Vlasov-Maxwell system. We treat the beam evolution through a bunch compressor using our Monte Carlo mean field approximation. We randomly generate N points from an initial phase space density. We then calculate the charge density using a smooth density estimation procedure, from statistics, based on Fourier series. The electric and magnetic fields are calculated from the smooth charge/current density using a novel field formula that avoids singularities by using the retarded time as a variable of integration. The points are then moved forward in small time steps using the beam frame equations of motion, with the fields frozen during a time step, and a new charge density is determined using our density estimation procedure. We try to choose N large enough so that the charge density is a good approximation to the density that would be obtained from solving the 2D Vlasov-Maxwell system exactly. We call this method the Monte Carlo Particle (MCP) method.
Singular-potential random-matrix model arising in mean-field glassy systems
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Amplitude pattern synthesis for conformal array antennas using mean-field neural networks
Castaldi, G.; Gerini, G.
2001-01-01
In this paper, we deal with the synthesis problem of conformai array antennas using a mean-field neural network. We applied a discrete version of mean-field neural network proposed by Vidyasagar [1], This technique is used to find the global minimum of the objective function, which represents the sq
Rigorous mean-field dynamics of lattice bosons: quenches from the Mott insulator
M. Snoek
2011-01-01
We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator
State-of-the-art of beyond mean field theories with nuclear density functionals
Egido, J. Luis
2016-07-01
We present an overview of different beyond mean field theories (BMFTs) based on the generator coordinate method (GCM) and the recovery of symmetries used in many body nuclear physics with effective forces. In a first step a short reminder of the Hartree-Fock-Bogoliubov (HFB) theory is given. A general discussion of the shortcomings of any mean field approximation (MFA), stemming either from the lack of the elementary symmetries (like particle number and angular momentum) or the absence of fluctuations around the mean values, is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is also needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. A whole chapter is devoted to illustrate with examples the convenience of recovering symmetries and the differences between the projection before and after the variation. The lack of fluctuations around the average values of the MFA is a big shortcoming inherent to this approach. To build in correlations in BMFT one selects the relevant degrees of freedom of the atomic nucleus. In the low energy part of the spectrum these are the quadrupole, octupole and the pairing vibrations as well as the single particle degrees of freedom. In the GCM the operators representing these degrees of freedom are used as coordinates to generate, by the constrained (projected) HFB theory, a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. The flexibility of the GCM Ansatz allows to describe a whole palette of physical situations by conveniently choosing the generator coordinates. We discuss the
Merino-Aceituno, Sara
2016-12-01
The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation-fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).
Sereda, Yuriy V.; Ortoleva, Peter J.
2014-04-01
A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.
MODEL STUDY OF THE SIGN PROBLEM IN A MEAN-FIELD APPROXIMATION.
Energy Technology Data Exchange (ETDEWEB)
HIDAKA,Y.
2007-07-30
We study the sign problem of the fermion determinant at nonzero baryon chemical potential. For this purpose we apply a simple model derived from Quantum Chromodynamics, in the limit of large chemical potential and mass. For SU(2) color, there is no sign problem and the mean-field approximation is similar to data from the lattice. For SU(3) color the sign problem is unavoidable, even in a mean-field approximation. We apply a phase-reweighting method, combined with the mean-field approximation, to estimate thermodynamic quantities. We also investigate the meanfield free energy using a saddle-point approximation [1].
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Mean-field dynamos: the old concept and some recent developments
Rädler, K -H
2014-01-01
This article reproduces the Karl Schwarzschild lecture 2013. Some of the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids are explained. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of $\\alpha^2$ and $\\alpha$ $\\Omega$ type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force t...
Time-odd mean fields in covariant density functional theory: Rotating systems
Afanasjev, A V; 10.1103/PhysRev.82.034329
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 dependences of their impact on the moments of inertia have been analysed 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 ...
EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO
Energy Technology Data Exchange (ETDEWEB)
Pipin, V. V. [Institute of Solar-Terrestrial Physics, Russian Academy of Sciences (Russian Federation); Kosovichev, A. G. [W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)
2015-11-10
We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.
Nonrelativistic mean-field description of the deformation of Λ hypernuclei
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.
Can realistic interaction be useful for nuclear mean-field approaches?
Energy Technology Data Exchange (ETDEWEB)
Nakada, H.; Sugiura, K. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Inakura, T. [Chiba University, Department of Physics, Graduate School of Science, Inage, Chiba (Japan); Kyoto University, Yukawa Institute of Theoretical Physics, Sakyo, Kyoto (Japan); Niigata University, Department of Physics, Niigata (Japan); Margueron, J. [Universite de Lyon 1, CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2016-07-15
Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: (i) Prediction of magic numbers and (ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that the realistic interaction, which is derived from the bare 2N and 3N interaction, furnishes a new theoretical instrument for advancing nuclear mean-field approaches. (orig.)
Crowd-Averse Cyber-Physical Systems: The Paradigm of Robust Mean Field Games
Bauso, D.; Tembine, H.
2015-01-01
For a networked controlled system we illustrate the paradigm of robust mean-field games. This is a modeling framework at the interface of differential game theory, mathematical physics, and H1-optimal control that tries to capture the mutual influence between a crowd and its individuals. First, we establish a mean-field system for such games including the effects of adversarial disturbances. Second, we identify the optimal response of the individuals for a given population behavior. Third, we...
On the mean-field theory of the Karlsruhe Dynamo Experiment
Directory of Open Access Journals (Sweden)
K.-H. Rädler
2002-01-01
Full Text Available In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as is expected to exist in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. The main predictions of this theory are explained and compared with the experimental results. Key words. Dynamo, geodynamo, dynamo experiment, mean-field dynamo theory, a-effect
Rädler, K.-H.
This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.
Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows
Rädler, Karl-Heinz; Del Sordo, Fabio; Rheinhardt, Matthias
2011-01-01
Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the P\\'eclet or magnetic Reynolds numbers are not too large and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic case several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented as well as numerical results obtained by the test-field method, which applies independently of this a...
Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field
Institute of Scientific and Technical Information of China (English)
LI Yan-Song; LONG Gui-Lu
2004-01-01
We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shellmodel (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method.In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF)theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained.This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei 16O and 208Pb,the deformed nucleus 20Ne. Good agreement is obtained.
Nuclear Matter in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S
1997-01-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the delta-meson [a_0(980)] is studied. While the delta-meson mean 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_s=30 MeV, a stronger rho-meson coupling is required than in the absence of the delta-field. The energy per particle of neutron matter is then 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.
Lin, Nan; Gull, Emanuel; Millis, Andrew J
2012-09-07
A method is presented for the unbiased numerical computation of two-particle response functions of correlated electron materials via a solution of the dynamical mean-field equations in the presence of a perturbing field. The power of the method is demonstrated via a computation of the Raman B(1g) and B(2g) scattering intensities of the two-dimensional Hubbard model in parameter regimes believed to be relevant to high-temperature superconductivity. The theory reproduces the "two-magnon" peak characteristic of the Raman intensity of insulating parent compounds of high-T(c) copper oxide superconductors, and shows how it evolves to a quasiparticle response, as carriers are added. The method can be applied in any situation where a solution of equilibrium dynamical mean-field equations is feasible.
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.)
Excitation dynamics in a lattice Bose gas within the time-dependent Gutzwiller mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Krutitsky, Konstantin V. [Fakultaet fuer Physik der Universitaet Duisburg-Essen, Campus Duisburg, Lotharstrasse 1, D-47048 Duisburg (Germany); Navez, Patrick [Fakultaet fuer Physik der Universitaet Duisburg-Essen, Campus Duisburg, Lotharstrasse 1, D-47048 Duisburg (Germany); Institut fuer Theoretische Physik, TU Dresden, D-01062 Dresden (Germany)
2011-09-15
The dynamics of the collective excitations of a lattice Bose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework of the linear-response theory as solutions of the generalized Bogoliubov-de Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary values of parameters. The expression for the sound velocity derived in this approach coincides with the hydrodynamic relation. We calculate the transition amplitudes for the excitations in the Bragg scattering process and show that the higher excitation modes make significant contributions. We simulate the dynamics of the density perturbations and show that their propagation velocity in the limit of week perturbation is satisfactorily described by the predictions of the linear-response analysis.
Dynamical mean field theory-based electronic structure calculations for correlated materials.
Biermann, Silke
2014-01-01
We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.
Skyrme mean-field studies of nuclei far from the stability line
Heenen, P H; Cwiok, S; Nazarewicz, W; Valor, A
1999-01-01
Two applications of mean-field calculations based on 3D coordinate-space techniques are presented. The first concerns the structure of odd-N superheavy elements that have been recently observed experimentally and shows the ability of the method to describe, in a self-consistent way, very heavy odd-mass nuclei. Our results are consistent with the experimental data. The second application concerns the introduction of correlations beyond a mean-field approach by means of projection techniques and configuration mixing. Results for Mg isotopes demonstrate that the restoration of rotational symmetry plays a crucial role in the description of 32Mg.
Another mean field treatment in the strong coupling limit of lattice QCD
Ohnishi, Akira; Miura, Kohtaroh; Nakano, Takashi Z.
2011-01-01
We discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresp...
Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.
Lee, Cathy Yuen Yi; Wand, Matt P
2016-07-01
Streamlined mean field variational Bayes algorithms for efficient fitting and inference in large models for longitudinal and multilevel data analysis are obtained. The number of operations is linear in the number of groups at each level, which represents a two orders of magnitude improvement over the naïve approach. Storage requirements are also lessened considerably. We treat models for the Gaussian and binary response situations. Our algorithms allow the fastest ever approximate Bayesian analyses of arbitrarily large longitudinal and multilevel datasets, with little degradation in accuracy compared with Markov chain Monte Carlo. The modularity of mean field variational Bayes allows relatively simple extension to more complicated scenarios.
Non-mean-field effects in systems with long-range forces in competition.
Bachelard, R; Staniscia, F
2012-11-01
We investigate the canonical equilibrium of systems with long-range forces in competition. These forces create a modulation in the interaction potential and modulated phases appear at the system scale. The structure of these phases differentiate this system from monotonic potentials, where only the mean-field and disordered phases exist. With increasing temperature, the system switches from one ordered phase to another through a first-order phase transition. Both mean-field and modulated phases may be stable, even at zero temperature, and the long-range nature of the interaction will lead to metastability characterized by extremely long time scales.
Gandolfo, Daniel; Rodriguez, Roger; Tuckwell, Henry C.
2017-03-01
We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh-Nagumo model neurons, which are often used to approximate Hodgkin-Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.
Gandolfo, Daniel; Rodriguez, Roger; Tuckwell, Henry C.
2017-01-01
We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh-Nagumo model neurons, which are often used to approximate Hodgkin-Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.
Multiple chiral doublet candidate nucleus $^{105}$Rh in a relativistic mean-field approach
Li, Jian; Meng, J; 10.1103/PhysRevC.83.037301
2011-01-01
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\\chi$D) phenomenon. The existence of M$\\chi$D phenomenon in $^{105}$Rh is highly expected.
A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet
Directory of Open Access Journals (Sweden)
Boualem Djehiche
2014-01-01
a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.
Ground state correlations and mean field using the exp(S) method
Heisenberg, J H; Heisenberg, Jochen H.; Mihaila, Bogdan
1999-01-01
This document gives a detailed account of the terms used in the computation of the ground state mean field and the ground state correlations. While the general approach to this description is given in a separate paper (nucl-th/9802029) we give here the explicite expressions used.
Automating the mean-field method for large dynamic gossip networks
Bakhshi, Rena; Endrullis, Jörg; Endrullis, Stefan; Fokkink, Wan; Haverkort, Boudewijn
2010-01-01
We investigate an abstraction method, called mean- field method, for the performance evaluation of dynamic net- works with pairwise communication between nodes. It allows us to evaluate systems with very large numbers of nodes, that is, systems of a size where traditional performance evaluation meth
Analytically Solvable Mean-Field Potential for Stable and Exotic Nuclei
Stoitsov, M. V.; S. S. Dimitrova(INRNE, Sofia); Pittel, S.; Van Isacker, P.(GANIL, CEA/DSM–CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France); Frank, A
1997-01-01
Slater determinants built from the single-particle wave functions of the analytically solvable Ginocchio potential are used to approximate the self-consistent Hartree-Fock solutions for the ground states of nuclei. The results indicate that the Ginocchio potential provides a good parametrization of the nuclear mean field for a wide range of nuclei, including those at the limit of particle stability.
Van Mieghem, P.F.A.; Van de Bovenkamp, R.
2015-01-01
Mean-field approximations (MFAs) are frequently used in physics. When a process (such as an epidemic or a synchronization) on a network is approximated by MFA, a major hurdle is the determination of those graphs for which MFA is reasonably accurate. Here, we present an accuracy criterion for Markovi
Mott-Hubbard and Anderson transitions in dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Byczuk, Krzysztof [Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, PL-00-681 Warsaw (Poland)]. E-mail: byczuk@fuw.edu.pl; Hofstetter, Walter [Condensed Matter Theory Group, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Vollhardt, Dieter [Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, D-86135 Augsburg (Germany)
2005-04-30
The Anderson-Hubbard Hamiltonian at half-filling is investigated within dynamical mean-field theory at zero temperature. The local density of states is calculated by taking the geometric and arithmetic mean, respectively. The non-magnetic ground state phase diagrams obtained within the different averaging schemes are compared.
Shape Coexistence for 179Hg in Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
WANG Nan; MENG Jie; ZHAO En-Guang
2005-01-01
The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.
Phase behaviour of colloids suspended in a near-critical solvent : A mean-field approach
Edison, John R.; Belli, Simone; Evans, Robert; Van Roij, René; Dijkstra, Marjolein
2015-01-01
Colloids suspended in a binary solvent may, under suitable thermodynamic conditions, experience a wide variety of solvent-mediated interactions that can lead to colloidal phase transitions and aggregation phenomena. We present a simple mean-field theory, based on free-volume arguments, that describe
Mean-field description of the structure and tension of curved fluid interfaces
Kuipers, Joris
2009-01-01
This thesis described the interfacial properties of curved fluid interfaces mainly employing mean-field models. Investigations of Tolman's length in simple systems and systems in contact with a hard wall are presented. Both the interfacial properties as well as the wetting behavior of phase-separate
Mean field limit for bosons and infinite dimensional phase-space analysis
Zied, Ammari
2007-01-01
This article proposes the construction of Wigner measures in the infinite dimensional bosonic quantum field theory, with applications to the derivation of the mean field dynamics. Once these asymptotic objects are well defined, it is shown how they can be used to make connections between different kinds of results or to prove new ones.
A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Lacroix, Denis; Tanimura, Yusuke [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France); Ayik, Sakir [Tennessee Technological University, Physics Department, Cookeville, TN (United States); Yilmaz, Bulent [Ankara University, Physics Department, Faculty of Sciences, Ankara (Turkey)
2016-04-15
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-,.., N -body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results. (orig.)
A simplified BBGKY hierarchy for correlated fermionic systems from a Stochastic Mean-Field approach
Lacroix, Denis; Ayik, Sakir; Yilmaz, Bulent
2015-01-01
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here, that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-, ..., N-body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for sho...
Another mean field treatment in the strong coupling limit of lattice QCD
Ohnishi, Akira; Nakano, Takashi Z
2010-01-01
We discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresponds to the point-splitting mesonic composite. Fermion determinant with this mean field under the anti-periodic boundary condition gives rise to a term which interpolates the effective potentials in the previously proposed zero and finite temperature mean field treatments. While the shift of the transition temperature at zero chemical potential is in the desirable direction and the phase boundary shape is improved, we find that the effects are too large to be compatible with the MDP simulation results.
Mean field dynamics of networks of delay-coupled noisy excitable units
Franović, Igor; Todorović, Kristina; Vasović, Nebojša; Burić, Nikola
2016-06-01
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.
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...
Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion
Gomes, Diogo A.
2017-01-05
Here, we consider one-dimensional first-order stationary mean-field games with congestion. These games arise when crowds face difficulty moving in high-density regions. We look at both monotone decreasing and increasing interactions and construct explicit solutions using the current formulation. We observe new phenomena such as discontinuities, unhappiness traps and the non-existence of solutions.
Beyond the mean field in the particle-vibration coupling scheme
Baldo, M; Colo', G; Rizzo, D; Sciacchitano, L
2015-01-01
The Energy Density Functional theory is one of the most used methods developed in nuclear structure. It is based on the assumption that the energy of the ground state is a functional only of the density profile. The method is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other bulk properties along the whole mass table. Although the Density Functional is in this case represented formally as the Hartree-Fock mean field of an effective force, the corresponding single-particle states in general do not reproduce the phenomenology particularly well. To overcome this difficulty, a strategy has been developed where the effective force is adjusted to reproduce directly the single particle energies, trying to keep the ground state energy sufficiently well reproduced. An alternative route, that has been developed along several years, for solving this problem is to introduce the mean field fluctuations, as represented by t...
Systematic nuclear structure studies using relativistic mean field theory in mass region A ˜ 130
Shukla, A.; Åberg, Sven; Bajpeyi, Awanish
2017-02-01
Nuclear structure studies for even-even nuclei in the mass region \\backsim 130, have been performed, with a special focus around N or Z = 64. On the onset of deformation and lying between two closed shell, these nuclei have attracted attention in a number of studies. A revisit to these experimentally accessible nuclei has been made via the relativistic mean field. The role of pairing and density depletion in the interior has been specially investigated. Qualitative analysis between two versions of relativistic mean field suggests that there is no significant difference between the two approaches. Moreover, the role of the filling {{{s}}}1/2 orbital in density depletion towards the centre has been found to be consistent with our earlier work on the subject Shukla and Åberg (2014 Phys. Rev. C 89 014329).
State-of-the-art of beyond mean field theories with nuclear density functionals
Egido, J Luis
2016-01-01
We present an overview of beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in nuclear physics with effective forces. After a reminder of the Hartree-Fock-Bogoliubov (HFB) theory a discussion of the shortcomings of any mean field approximation (MFA) is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. The lack of fluctuations around the average values of the MFA is a shortcoming of this approach. To build in correlations in BMFT one selects the relevant degrees of freedom: quadrupole, octupole and the pairing vibrations as well as the single particle ones. In the GCM the operators representing these degrees of f...
Mean field theory for Lyapunov exponents and KS entropy in Lorentz lattice gases
Ernst, M H; Nix, R; Jacobs, D; Ernst, M H; Dorfman, J R; Nix, R; Jacobs, D
1994-01-01
automata lattice gases are useful systems for systematically exploring the connections between non-equilibrium statistical mechanics and dynamical systems theory. Here the chaotic properties of a Lorentz lattice gas are studied analytically and by means of computer simulations. The escape-rates, Lyapunov exponents, and KS entropies are estimated for a one- dimensional example using a mean field theory. The results are compared with simulations for a range of densities and scattering parameters of the lattice gas. The computer results show a distribution of values for the dynamical quantities with average values that are in good agreement with the mean field theory and consistent with the escape-rate formalism for the coefficient of diffusion.
Mean-field analysis of phase transitions in the emergence of hierarchical society
Okubo, Tsuyoshi; Odagaki, Takashi
2007-09-01
Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau [Physica A 217, 373 (1995)] to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings. We apply this mean-field analysis to the pacifist society model recently investigated by use of Monte Carlo simulation [Physica A 367, 435 (2006)]. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased and there are three phases: one egalitarian and two hierarchical states. We also highlight that the transition from the egalitarian phase to the first hierarchical phase is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.
Spectral properties of the one-dimensional Hubbard model: cluster dynamical mean-field approaches
Go, Ara; Jeon, Gun Sang
2011-03-01
We investigate static and dynamic properties of the one-dimensional Hubbard model using cluster extensions of the dynamical mean-field theory. It is shown that the two different extensions, the cellular dynamical mean-field theory and the dynamic cluster approximation, yield the ground-state properties which are qualitatively in good agreement with each other. We compare the results with the Bethe ansatz results to check the accuracy of the calculation with finite sizes of clusters. We also analyze the spectral properties of the model with the focus on the spin-charge separation and discuss the dependency on the cluster size in the two approaches. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2010-0010937).
Beyond-mean-field approach to low-lying spectra of $\\Lambda$ hypernuclei
Hagino, K; Yao, J M; Motoba, T
2015-01-01
Taking the hypernucleus $^{13}_{~\\Lambda}$C as an example, we illustrate the miscroscopic particle-rotor model for low-lying spectra of hypernuclei. This approach is based on the beyond-mean-field method, with the particle number and angular momentum projections. The quantum fluctuation of the mean-field is also taken into account for the core nucleus using the generator coordinate method. We show that the impurity effect of $\\Lambda$ hyperon, such as a change in $B(E2)$, is well described with this model. Our calculation indicates that the most important impurity effect in $sd$-shell hypernuclei is a change in a deformation parameter rather than in a nuclear size.
Nonuniversal behavior for aperiodic interactions within a mean-field approximation.
Faria, Maicon S; Branco, N S; Tragtenberg, M H R
2008-04-01
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.
Macroscopic and large scale phenomena coarse graining, mean field limits and ergodicity
Rademacher, Jens; Zagaris, Antonios
2016-01-01
This book is the offspring of a summer school school “Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins. Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions. Francois Golse delivers a chapter on the dynamics of large particle systems in the mean field limit and surveys the most significant tools and methods to establish such limits with mathematical rigor. Golse discusses in depth a variety of examples, including Vlasov--Poisson and Vlasov--Maxwell systems. Lucia Scardia focuses on the rigorous derivation of macroscopic models using $\\Gamma$-convergence, a more recent variational method, which has proved very powerful for problems in material science. Scardia illustrates this by various basic examples and a mor...
Three-dimensional angular momentum projection in relativistic mean-field theory
Yao, J M; Ring, P; Arteaga, D Pena
2009-01-01
Based on a relativistic mean-field theory with an effective point coupling between the nucleons, three-dimensional angular momentum projection is implemented for the first time to project out states with designed angular momentum from deformed intrinsic states generated by triaxial quadrupole constraints. The same effective parameter set PC-F1 of the effective interaction is used for deriving the mean field and the collective Hamiltonian. Pairing correlations are taken into account by the BCS method using both monopole forces and zero range d-forces with strength parameters adjusted to experimental even-odd mass differences. The method is applied successfully to the isotopes 24Mg, 30Mg, and 32Mg.
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 d......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...... 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....
Heterogeneous mean field for neural networks with short-term plasticity
di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro
2014-08-01
We report about the main dynamical features of a model of leaky integrate-and-fire excitatory neurons with short-term plasticity defined on random massive networks. We investigate the dynamics by use of a heterogeneous mean-field formulation of the model that is able to reproduce dynamical phases characterized by the presence of quasisynchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks with a sufficiently large average in-degree.
Institute of Scientific and Technical Information of China (English)
XueJianjun; YouXiaohu
1997-01-01
Channel equalization is essential in the Pan-European GSM mobile communication system.The maximum likelihood sequence estimation(MLSE) using the Viterbi algorithm(VA)iscommonly recommended for the dqualization,which can only accommodate the channels with limited time delay spread.In[1],we presented a mean field annealing(MFA)partially connected neural equalizer for the GSM system,in which the complexity is linearly proportional to the time delay spread and therefore relatively fast convergence speed is achieved.But the annealing coefficient of the MFA equalizer is fixed,which is not flexible in timing-varying circumstance such as mobile communications.To decrease the computation of MFA approach so as to make it more easy for practical use,the MFA approach is reated as a homotopy problem.The ordinary equations which the MFA approach should obey are derived.These equations can be used to reflect the deviation of the iteration result from the track of MFA approach.Based on this tesult,an adaptive annealing control algorithm is proposed,which can dynamically control the annealing coefficient according to the iteration deviation.Computer simulations show that our approach can provide a much higher convergence speed and performance improvement over 16-state and 32-state VA's which are usually suggested for practical applications.
Mean field and collisional dynamics of interacting fermion-boson systems the Jaynes-Cummings model
Takano-Natti, E R
1996-01-01
A general time-dependent projection technique is applied to the study of the dynamics of quantum correlations in a system consisting of interacting fermionic and bosonic subsystems, described by the Jaynes-Cummings Hamiltonian. The amplitude modulation of the Rabi oscillations which occur for a strong, coherent initial bosonic field is obtained from the spin intrinsic depolarization resulting from collisional corrections to the mean-field approximation.
Existence for stationary mean-field games with congestion and quadratic Hamiltonians
Gomes, Diogo A.
2015-09-03
Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel
Finite Size Corrected Relativistic Mean-Field Model and QCD Critical End Point
Uddin, Saeed; Ahmad, Jan Shabir
2012-01-01
The effect of finite size of hadrons on the QCD phase diagram is analyzed using relativistic mean field model for the hadronic phase and the Bag model for the QGP phase. The corrections to the EOS for hadronic phase are incorporated in a thermodynamic consistent manner for Van der Waals like interaction. It is found that the effect of finite size of baryons is to shift CEP to higher chemical potential values.
Time-odd mean fields in the rotating frame microscopic nature of nuclear magnetism
Afanasiev, A V
2000-01-01
The microscopic role of nuclear magnetism in rotating frame is investigated for the first time in the framework of the cranked relativistic mean field theory. It is shown that nuclear magnetism modifies the expectation values of single-particle spin, orbital and total angular momenta along the rotational axis effectively creating additional angular momentum. This effect leads to the increase of kinematic and dynamic moments of inertia at given rotational frequency and has an impact on effective alignments.
Universal mean-field phase diagram for biaxial nematics obtained from a minimax principle.
Bisi, Fulvio; Virga, Epifanio G; Gartland, Eugene C; De Matteis, Giovanni; Sonnet, André M; Durand, Georges E
2006-05-01
We study a class of quadratic Hamiltonians which describe both fully attractive and partly repulsive molecular interactions, characteristic of biaxial liquid crystal molecules. To treat the partly repulsive interactions we establish a minimax principle for the associated mean-field free energy. We show that the phase diagram described by Sonnet [Phys. Rev. E 67, 061701 (2003)] is universal. Our predictions are in good agreement with the recent observations on both V-shaped and tetrapodal molecules.
Directory of Open Access Journals (Sweden)
A. Sadeghi
2007-03-01
Full Text Available Using both mean field renormalization group (MFRG and Surface-Bulk MFRG (SBMFRG, we study the critical behavior of the classical Heisenberg and XY models on a simple cubic lattice. Critical temperatures as well as critical exponents, characteristic the universality classes of these two models were calculated, analytically for1, 2, 3 and 4 spin clusters. The results are in good agreement with higher accurate methods such as Monte Carlo and High- temperature series.
The mean field study of phase transitions in two dimensional Kagome lattice under local anisotropy
Directory of Open Access Journals (Sweden)
S. Mortezapour
2007-06-01
Full Text Available In this work we investigated the critical properties of the anti-ferromagnetic XY model on a two dimensional Kagome lattice under single-ion easy-axes anisotropy. Employing the mean field theory, we found that this model shows a second order phase transition from disordered to all-in all-out state for any value of anisotropy.
Ammari, Zied
2011-01-01
We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our previous works with a slightly different strategy.
Mean-Field Calculations for the Three-Dimensional Holstein Model
Institute of Scientific and Technical Information of China (English)
罗强; 刘川
2002-01-01
The electron-phonon Holstein model is studied in three spatial dimensions. It is argued that this model can be used to account for major features of the high-To BaPb1-xBixO3 and BaxK1-xBiO3 systems. Mean-field calculations are performed via a path integral representation of the model. Charge-density-wave order parameters and transition temperatures are obtained.
Nonlinear Effects in Quantum Dynamics of Atom Laser: Mean-Field Approach
Institute of Scientific and Technical Information of China (English)
JING Hui
2002-01-01
Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.
Inverse Magnetic Catalysis in Nambu--Jona-Lasinio Model beyond Mean Field
Mao, Shijun
2016-01-01
We study inverse magnetic catalysis in the Nambu--Jona-Lasinio model beyond mean field approximation. The feed-down from mesons to quarks is embedded in an effective coupling constant at finite temperature and magnetic field. While the magnetic catalysis is still the dominant effect at low temperature, the meson dressed quark mass drops down with increasing magnetic field at high temperature due to the dimension reduction of the Goldstone mode in the Pauli-Villars regularization scheme.
A Mean Field Game Approach to Urban Drainage Systems Control: A Barcelona Case Study
Ramírez Jaime, Andrés Felipe
2016-01-01
Urban drainage systems (UDSs) are complex large-scale systems that carry stormwater and wastewater throughout urban areas. During heavy rain scenarios, UDSs are not able to handle the amount of extra water that enters the network and flooding occurs. Usually, this might happen because the network is not being used efficiently, i.e., some structures remain underused while many others are overused. This thesis proposes a control methology based on mean field game theory and model...
Description of $^{178}$Hf$^{m2}$ in the constrained relativistic mean field theory
Wei, Zhang; Shuang-Quan, Zhang
2009-01-01
The properties of the ground state of $^{178}$Hf and the isomeric state $^{178}$Hf$^{m2}$ are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of $^{178}$Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with $K^\\pi=16^+$ is found to be $\
Restoration of rotational symmetry in deformed relativistic mean-field theory
Institute of Scientific and Technical Information of China (English)
YAO Jiang-Ming; MENG Jie; Pena Arteaga Daniel; Ring Peter
2009-01-01
We report on a very recently developed three-dimensional angular momentum projected relativistic mean-field theory with point-coupling interaction (3DAMP+RMF-PC). Using this approach the same effective nucleon-nucleon interaction is adopted to describe both the single-particle and collective motions in nuclei.Collective states with good quantum angular momentum are built projecting out the intrinsic deformed meanfield states. Results for 24Mg are shown as an illustrative application.
Particle-number projection in the finite-temperature mean-field approximation
Fanto, P; Bertsch, G F
2016-01-01
Calculation of statistical properties of nuclei in a finite-temperature mean-field theory requires projection onto good particle number, since the theory is formulated in the grand canonical ensemble. This projection is usually carried out in a saddle-point approximation. Here we derive formulas for an exact particle-number projection of the finite-temperature mean-field solution. We consider both deformed nuclei, in which the pairing condensate is weak and the Hartree-Fock (HF) approximation is the appropriate mean-field theory, and nuclei with strong pairing condensates, in which the appropriate theory is the Hartree-Fock-Bogoliubov (HFB) approximation, a method that explicitly violates particle-number conservation. For the HFB approximation, we present a general projection formula for a condensate that is time-reversal invariant and a simpler formula for the Bardeen-Cooper-Schrieffer (BCS) limit, which is realized in nuclei with spherical condensates. We apply the method to three heavy nuclei: a typical de...
Mean field study of a propagation-turnover lattice model for the dynamics of histone marking
Yao, Fan; Li, FangTing; Li, TieJun
2017-02-01
We present a mean field study of a propagation-turnover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 (2012)] for understanding how posttranslational histone marks modulate gene expression in mammalian cells. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter κ = k +/ k -, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.
Mean-Field Approximation to the Hydrophobic Hydration in the Liquid-Vapor Interface of Water.
Abe, Kiharu; Sumi, Tomonari; Koga, Kenichiro
2016-03-03
A mean-field approximation to the solvation of nonpolar solutes in the liquid-vapor interface of aqueous solutions is proposed. It is first remarked with a numerical illustration that the solvation of a methane-like solute in bulk liquid water is accurately described by the mean-field theory of liquids, the main idea of which is that the probability (Pcav) of finding a cavity in the solvent that can accommodate the solute molecule and the attractive interaction energy (uatt) that the solute would feel if it is inserted in such a cavity are both functions of the solvent density alone. It is then assumed that the basic idea is still valid in the liquid-vapor interface, but Pcav and uatt are separately functions of different coarse-grained local densities, not functions of a common local density. Validity of the assumptions is confirmed for the solvation of the methane-like particle in the interface of model water at temperatures between 253 and 613 K. With the mean-field approximation extended to the inhomogeneous system the local solubility profiles across the interface at various temperatures are calculated from Pcav and uatt obtained at a single temperature. The predicted profiles are in excellent agreement with those obtained by the direct calculation of the excess chemical potential over an interfacial region where the solvent local density varies most rapidly.
Rios, Arnau; Buchler, Mark; Danielewicz, Pawel
2010-01-01
Nonequilibrium Green's function methods allow for an intrinsically consistent description of the evolution of quantal many-body body systems, with inclusion of different types of correlations. In this paper, we focus on the practical developments needed to build a Green's function methodology for nuclear reactions. We start out by considering symmetric collisions of slabs in one dimension within the mean-field approximation. We concentrate on two issues of importance for actual reaction simulations. First, the preparation of the initial state within the same methodology as for the reaction dynamics is demonstrated by an adiabatic switching on of the mean-field interaction, which leads to the mean-field ground state. Second, the importance of the Green's function matrix-elements far away from the spatial diagonal is analyzed by a suitable suppression process that does not significantly affect the evolution of the elements close to the diagonal. The relative lack of importance of the far-away elements is tied t...
Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models
Institute of Scientific and Technical Information of China (English)
RENZhong-Zhou; TAIFei; XUChang; CHENDing-Han; ZHANGHu-Yong; CAIXiang-Zhou; SHENWen-Qing
2004-01-01
We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupysignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of vaJence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ，ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.
Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach
Sun, Wu-Ji; Xu, Hai-Dan; Li, Jian; Liu, Yong-Hao; Ma, Ke-Yan; Yang, Dong; Lu, Jing-Bing; Ma, Ying-Jun
2016-08-01
Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown. Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)
Self-consistent chaotic transport in a high-dimensional mean-field Hamiltonian map model
Martínez-del-Río, D; Olvera, A; Calleja, R
2016-01-01
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of $N$ coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of th...
Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation
Goldstein, Raymond E.; Cherayil, Binny J.
1989-06-01
A theoretical description of the critical point of a polymer solution is formulated directly from the Edwards continuum model of polymers with two- and three-body excluded-volume interactions. A Hubbard-Stratonovich transformation analogous to that used in recent work on the liquid-vapor critical point of simple fluids is used to recast the grand partition function of the polymer solution as a functional integral over continuous fields. The resulting Landau-Ginzburg-Wilson (LGW) Hamiltonian is of the form of a generalized nonsymmetric n=1 component vector model, with operators directly related to certain connected correlation functions of a reference system. The latter is taken to be an ensemble of Gaussian chains with three-body excluded-volume repulsions, and the operators are computed in three dimensions by means of a perturbation theory that is rapidly convergent for long chains. A mean field theory of the functional integral yields a description of the critical point in which the power-law variations of the critical polymer volume fraction φc, critical temperature Tc, and critical amplitudes on polymerization index N are essentially identical to those found in the Flory-Huggins theory. In particular, we find φc ˜N-1/2, Tθ-Tc˜N-1/2 with (Tθ the theta temperature), and that the composition difference between coexisting phases varies with reduced temperature t as N-1/4t1/2. The mean field theory of the interfacial tension σ between coexisting phases near the critical point, developed by considering the LGW Hamiltonian for a weakly inhomogeneous solution, yields σ˜N-1/4t3/2, with the correlation length diverging as ξ˜N1/4t-1/2 within the same approximation, consistent with the mean field limit of de Gennes' scaling form. Generalizations to polydisperse systems are discussed.
Baryon resonances in the mean field approach and a simple explanation of the Theta+ pentaquark
Diakonov, Dmitri
2008-01-01
We suggest to classify baryon resonances as single-quark states in a mean field, and/or as its collective excitations. Identifying the Roper resonance N(1440), the nucleon resonance N(1535), and the singlet hyperon Lambda(1405) as single-quark excitations, we find that there must be an exotic S=+1 baryon resonance Theta+ (the "pentaquark") with a mass about 1440+1535-1405=1570 MeV and spin-parity one-half-plus. We argue that Theta+ is an analog of the Gamov--Teller excitation long known in nuclear physics.
From energy-density functionals to mean field potentials: a systematic derivation
Energy Technology Data Exchange (ETDEWEB)
Chomaz, Ph.; Hasnaoui, K.H.O. [GANIL, DSM-CEA/IN2P3-CNRS, B.P.5027, F-14076 Caen cedex 5 (France); Gulminelli, F. [LPC, IN2P3-CNRS/Ensicaen et Universite, F-14050 Caen cedex (France)
2006-10-15
The density functional theory (DFT) is one of the most powerful theories to deal with the intractable quantum many body problem for interacting systems with an arbitrary number of constituents. In this paper we present a systematic method to solve the variational problem of the derivation of a self-consistent Kohn-Sham field from an arbitrary local energy functional. We illustrate this formalism with an application in nuclear physics and give the general mean field associated to the widely used Skyrme effective interaction. (authors)
Institute of Scientific and Technical Information of China (English)
舒崧; 李家荣
2012-01-01
We used the Cornwall, Jackiw and Tomboulis （CJT） resummation scheme to study nuclear matter. In the CJT formalism the meson propagators are treated as the bare propagators and the the higher order loop corrections of the thermodynamic potential are evaluated at the Hartree approximation, while the vacuum fluctuations are ignored. Under these treatments in the CJT formalism we derived exact mean-field theory （MFT） results for the nuclear matter. The results are thermodynamically consistent, and our study indicates that the MFT result is the lowest order resummation result in the CJT resummation scheme. The relation between CJT formalism and MFT is clearly presented through the calculations.
Coexistence of nuclear shapes: self-consistent mean-field and beyond
Li, Zhipan; Vretenar, Dario
2015-01-01
A quantitative analysis of the evolution of nuclear shapes and shape phase transitions, including regions of short-lived nuclei that are becoming accessible in experiments at radioactive-beam facilities, necessitate accurate modeling of the underlying nucleonic dynamics. Important theoretical advances have recently been made in studies of complex shapes and the corresponding excitation spectra and electromagnetic decay patterns, especially in the "beyond mean-field" framework based on nuclear density functionals. Interesting applications include studies of shape evolution and coexistence in N = 28 isotones, the structure of lowest $0^+$ excitations in deformed N $\\approx$ 90 rare-earth nuclei, and quadrupole and octupole shape transitions in thorium isotopes.
Topological Origin of the Phase Transition in a Mean-Field Model
Energy Technology Data Exchange (ETDEWEB)
Casetti, L. [Istituto Nazionale per la Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy); Cohen, E.G. [The Rockefeller University, 1230 York Avenue, New York, New York 10021-6399 (United States); Pettini, M.; Pettini, M. [Istituto Nazionale per la Fisica della Materia (INFM), Unita di Ricerca di Firenze, Firenze, Italy] [RAMAN SPECTRA, MICROSCOPY, IMAGES, BIOPHYSICS, MULTI-PHOTON PROCESSES, FLUORESCENCE, BACTERIA, VIBRATIONAL STATES
1999-05-01
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological change can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological change occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N . Furthermore, as in statistical mechanics, the way the thermodynamic limit is taken is crucial in topology. {copyright} {ital 1999} {ital The American Physical Society}
Phase transitions and topology in 2+k XY mean-field models.
Angelani, L; Ruocco, G
2007-11-01
The thermodynamics and topology of mean-field models with 2+k body interaction terms (generalizing XY model) are derived. Focusing on two particular cases (2+4 and 2+6 body interaction terms), a comparison between thermodynamic (phase transition energy, thermodynamically forbidden energy regions) and topological (singularity and curvature of saddle entropy) properties is performed. We find that (i) a topological change is present at the phase transition energy; however, (ii) only one topological change occurs, also for those models exhibiting two phase transitions; (iii) the order of a phase transition is not completely signaled by the curvature of topological quantities.
Transport in multilayered nanostructures the dynamical mean-field theory approach
Freericks, James K
2016-01-01
Over the last 25 years, dynamical mean-field theory (DMFT) has emerged as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, this book presents the first comprehensive treatment of this ever-developing topic. Transport in Mutlilayered Nanostructures is varied and modern in its scope, and: A series of over 50 problems help develop the skills to allow readers to reach the level of being able to contribute to research. This book is suitable for an advanced graduate course in DMFT, and for individualized study by graduate students, postdoctoral fellows and advanced researchers wishing to enter the field.
Delfino, A; Frederico, T
1996-01-01
The link between non-linear chiral effective Lagrangians and the Walecka model description of bulk nuclear matter [1] is questioned. This fact is by itself due to the Mean Field Approximation (MFA) which in nuclear mater makes the picture of a nucleon-nucleon interaction based on scalar(vector) meson exchange, equivalent to the description of a nuclear matter based on attractive and repulsive contact interactions. We present a linear chiral model where this link between the Walecka model and an underlying to chiral symmetry realization still holds, due to MFA.
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....
Doping Induced Spin State Transition in LaCoO3: Dynamical Mean-Field Study
Augustinský, P.; Křápek, V.; Kuneš, J.
2013-06-01
Hole and electron doped LaCoO3 is studied using dynamical mean-field theory. The one-particle spectra are analyzed and compared to the available experimental data, in particular the x-ray absorption spectra. Analyzing the temporal spin-spin correlation functions we find the atomic intermediate spin state is not important for the observed Curie-Weiss susceptibility. Contrary to the commonly held view about the roles played by the t2g and eg electrons we find narrow quasiparticle bands of t2g character crossing the Fermi level accompanied by strongly damped eg excitations.
One-Proton Halo in 31Cl with Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
蔡翔舟; 沈文庆; 任中洲; 蒋维洲; 方德清; 张虎勇; 钟晨; 魏义彬; 郭威; 马余刚; 朱志远
2002-01-01
We investigate proton-rich isotopes s1,32Cl using the nonlinear relativistic mean-field model. It is shown that this model can reproduce the properties of these nuclei well. A long tail appears in the calculated proton density distribution of 31 Cl. The results of relativistic density-dependent Hartree theory show a similar trend of tail density distribution. It is strongly suggested that there is a proton halo in 31Cl and it is indicated that there may be a proton skin in 32 Cl. The relation between the proton halo in 31Cl and the new proton magic number is discussed.
Magnetic material in mean-field dynamos driven by small scale helical flows
Giesecke, A.; Stefani, F.; Gerbeth, G.
2014-07-01
We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G O Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-Kármán-sodium dynamo. For both examined flow configurations the consideration of magnetic material within the fluid flow causes a reduction of the critical magnetic Reynolds number of up to 25%. The development of the growth-rate in the limit of the largest achievable permeabilities suggests no further significant reduction for even larger values of the permeability. In order to study the dynamo behavior of systems that consist of tens of thousands of helical cells we resort to the mean-field dynamo theory (Krause and Rädler 1980 Mean-field Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon)) in which the action of the small scale flow is parameterized in terms of an α- and β-effect. We compute the relevant elements of the α- and the β-tensor using the so called testfield method. We find a reasonable agreement between the fully resolved models and the corresponding mean-field models for wall or rod materials in the considered range 1\\leqslant {{\\mu }_{r}}\\leqslant 20. Our results may be used for the development of global large scale models with recirculation
Application of Mean-Field Jordan-Wigner Transformation to Antiferromagnet System
Institute of Scientific and Technical Information of China (English)
LI Jia-Liang; LEI Shu-Guo; JIANG Yu-Chi
2008-01-01
By using the mean-field Jordan-Wigner transformation analysis,this paper studies the one-dimensional spin-1/2 XYZ antiferromagnetic chain in the transverse field with uniform long-range interactions among the z-components of the spins.The thermodynamic quantities,such as Helmholtz free energy,the internal energy,the specific heat,and the isothermal susceptibility,are obtained.Under degenerating condition,our results agree with numerical results of the other literatures.
I. M. Sokolov; Yuste, S. B.; Ruiz-Lorenzo, J. J.; Lindenberg, Katja
2008-01-01
We present a mean field model for coagulation ($A+A\\to A$) and annihilation ($A+A\\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is exponentially distributed about the mean for that trap, and the distribution of mean escape times is a power law. Even in the absence of reactions, the distribution of particles over sites changes with time as particles are caught in ever deeper traps, that is, t...
Shell evolution at N=20 in the constrained relativistic mean field approach
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field(RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82.It is also found that the octupole deformations may exist in the La isotopes with mass number A ～ 145-155.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
Institute of Scientific and Technical Information of China (English)
WANG Nan; GUO Lu
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field (RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A=139 where the neutron number is the magic number N=82.It is also found that the octupole deformations may exist in the La isotopes with mass number A～ 145-155.
Energy Technology Data Exchange (ETDEWEB)
Stancu, A. E-mail: alstancu@uaic.ro; Stoleriu, Laurentiu; Cerchez, Mihai
2001-07-01
Samples with Stoner-Wohlfarth ferromagnetic particles interacting only through dipolar magnetostatic fields were computer generated and the effects of the interactions on the magnetisation processes have been analysed. In some geometrical configurations of the particles, magnetostatic mean-field interaction field was also obtained, in agreement with the usual assumption in the moving Preisach model. A micromagnetic analysis of the magnetostatic mean interaction field is made. Classical {delta}M and integral generalised {delta}M curves have been calculated and the results have been analysed.
Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
Ammari, Zied
2010-01-01
Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the Wick calculus defined for polynomials are preserved by the action of a nonlinear flow. Nevertheless taking advantage carefully of the information brought by these two calculuses in the mean field asymptotics, the propagation of Wigner measures for general states can be proved, extending to the infinite dimensional case a standard result of semiclassical analysis.
Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
Niksic, T; Vretenar, D; Prochniak, L; Meng, J; Ring, P
2008-01-01
The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A model is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.
Cluster Monte Carlo and numerical mean field analysis for the water liquid-liquid phase transition
Mazza, Marco G.; Stokely, Kevin; Strekalova, Elena G.; Stanley, H. Eugene; Franzese, Giancarlo
2009-04-01
Using Wolff's cluster Monte Carlo simulations and numerical minimization within a mean field approach, we study the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases. Both methods allow us to study the thermodynamic behavior of water at temperatures, where other numerical approaches - both Monte Carlo and molecular dynamics - are seriously hampered by the large increase of the correlation times. The cluster algorithm also allows us to emphasize that the liquid-liquid phase transition corresponds to the percolation transition of tetrahedrally ordered water molecules.
Fission Barrier for 240Pu in the Quadrupole Constrained Relativistic Mean Field Approach
Institute of Scientific and Technical Information of China (English)
L(U) Hong-Feng; GENG Li-Sheng; MENG Jie
2006-01-01
@@ The fission barrier for 240Pu is investigated beyond the second saddle point in the potential energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essential to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.
A Bayesian mean field game approach to supply demand analysis of the smart grid
Kamgarpour, Maryam
2013-07-01
We explore a game theoretic framework for multiple energy producers competing in energy market. Each producer, referred to as a player, optimizes its own objective function given the demand utility. The equilibrium strategy of each player depends on the production cost, referred to as type, of the other players. We show that as the number of players increases, the mean of the types is sufficient for finding the equilibrium. For finite number of players, we design a mean field distributed learning algorithm that converges to equilibrium. We discuss extensions of our model to include several realistic aspects of the energy market. © 2013 IEEE.
Queueing Analysis of a Large-Scale Bike Sharing System through Mean-Field Theory
Li, Quan-Lin; Chen, Chang; Fan, Rui-Na; Xu, Liang; Ma, Jing-Yu
2016-01-01
The bike sharing systems are fast increasing as a public transport mode in urban short trips, and have been developed in many major cities around the world. A major challenge in the study of bike sharing systems is that large-scale and complex queueing networks have to be applied through multi-dimensional Markov processes, while their discussion always suffers a common difficulty: State space explosion. For this reason, this paper provides a mean-field computational method to study such a lar...
The cumulative overlap distribution function in spin glasses: mean field vs. three dimensions
Yllanes, David; Billoire, Alain; Maiorano, Andrea; Marinari, Enzo; Martin-Mayor, Victor
2015-03-01
We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution in spin glasses. Using analytical and numerical mean-field results for the Sherrington-Kirkpatrick model, as well as data from toy models, we show that this approach is an effective tool to distinguish the low-temperature behavior of replica symmmetry breaking systems from that expected in the droplet picture. An application of the method to the three-dimensional Edwards-Anderson models shows agreement with the replica symmetry breaking predictions. Supported by ERC Grant No. 247328 and from MINECO (Spain), Contract No. FIS2012-35719-C02.
Analytical results on the magnetization of the Hamiltonian Mean-Field model
Energy Technology Data Exchange (ETDEWEB)
Bachelard, R., E-mail: romain.bachelard@synchrotron-soleil.f [Synchrotron Soleil, L' Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette cedex (France); Chandre, C. [Centre de Physique Theorique, CNRS - Aix-Marseille Universites, Campus de Luminy, case 907, F-13288 Marseille cedex 09 (France); Ciani, A.; Fanelli, D. [Dipartimento di Energetica ' Sergio Stecco' , Universita di Firenze, via s. Marta 3, 50139 Firenze (Italy)] [Centro interdipartimentale per lo Studio delle Dinamiche Complesse - CSDC (Italy)] [INFN (Italy); Yamaguchi, Y.Y. [Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 606-8501 Kyoto (Japan)
2009-11-09
The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high- and low-energy limits are investigated and the analytical predictions are compared with direct N-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.
Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean field Theory
Institute of Scientific and Technical Information of China (English)
MENG Jie; GUO Jian-you; LIU Lang; ZHANG Shuang-quan
2006-01-01
A Shell-model-like approach suggested to treat the pairing correlations in relativistic mean field theory is introduced,in which the occupancies thus obtained have been iterated back into the densities.The formalism and numerical techniques are given in detail.As examples,the ground state properties and low-lying excited states for Ne isotopes are studied.The results thus obtained are compared with the data available.The binding energies,the odd-even staggering,as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.
Characteristic Feature of Self-Consistent Mean-Field in Level Crossing Region
Guo, L; Zhao, E G; Guo, Lu; Sakata, Fumihiko; Zhao, En-Guang
2004-01-01
A shape change of the self-consistent mean-field induced by a configuration change is discussed within the conventional constrained Hartree-Fock (CHF) theory. It is stressed that a single-particle level crossing dynamics should be treated carefully, because the shape of the mean-field in such a finite many-body system as the nucleus strongly changes depending on its configuration. This situation is clearly shown by applying an adiabatic assumption, where the most energetically favorable single-particle states are assumed to be occupied. The excited HF states and the continuously-connected potential energy curves are given by applying the configuration dictated CHF method. The effect of pairing correlation is discussed in the level crossing region. Triaxial deformed results in our Hartree-Fock-Bogoliubov (HFB) calculation with Gogny force nicely reproduce the available experimental data of Ge isotopes. From our numerical calculation, it is concluded that the CHFB state is more fragile than the CHF state in the...
Hadron resonance gas and mean-field nuclear matter for baryon number fluctuations
Fukushima, Kenji
2014-01-01
We give an estimate for the skewness and the kurtosis of the baryon number distribution in two representative models; i.e., models for a hadron resonance gas and relativistic mean-field nuclear matter. We emphasize formal similarity between these two descriptions. The hadron resonance gas leads to a deviation from the Skellam distribution if quantum statistical correlation is taken into account at high baryon density, but this effect is not strong enough to explain fluctuation data seen in the beam-energy scan at RHIC/STAR. In the calculation of mean-field nuclear matter the density correlation with the vector \\omega-field rather than the effective mass with the scalar \\sigma-field renders the kurtosis suppressed at higher baryon density so as to account for the observed behavior of the kurtosis. We finally discuss the difference between the baryon number and the proton number fluctuations from correlation effects in isospin space. Our numerical results suggest that such effects are only minor even in the cas...
On a mean field game optimal control approach modeling fast exit scenarios in human crowds
Burger, Martin
2013-12-01
The understanding of fast exit and evacuation situations in crowd motion research has received a lot of scientific interest in the last decades. Security issues in larger facilities, like shopping malls, sports centers, or festivals necessitate a better understanding of the major driving forces in crowd dynamics. In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. The model is formulated in the framework of mean field games and based on a parabolic optimal control problem. We consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position and velocity, the overall density of people, and the time to exit. This microscopic setup leads in a mean-field formulation to a nonlinear macroscopic optimal control problem, which raises challenging questions for the analysis and numerical simulations.We discuss different aspects of the mathematical modeling and illustrate them with various computational results. ©2013 IEEE.
Effects of anisotropy of turbulent convection in mean-field solar dynamo models
Pipin, V V
2013-01-01
We study how anisotropy of turbulent convection affects diffusion of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magneto-hydrodynamics framework using the minimal $\\tau$-approximation. We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model, and a distributed-dynamo model with the subsurface rotational shear layer. For both models we investigate effects of the double-cell meridional circulation, recently suggested by helioseismology. We introduce a parameter of anisotropy as a ratio of the radial and horizontal intensity of turbulent mixing, to characterize the anisotropy effects. It is found that the anisotropy of turbulent convection affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the d...
Mean field game theoretic approach for security in mobile ad-hoc networks
Wang, Yanwei; Tang, Helen; Yu, F. Richard; Huang, Minyi
2013-05-01
Game theory can provide a useful tool to study the security problem in mobile ad hoc networks (MANETs). Most existing work on applying game theories to security only considers two players in the security game model: an attacker and a defender. While this assumption is valid for a network with centralized administration, it may not be realistic in MANETs, where centralized administration is not available. Consequently, each individual node in a MANET should be treated separately in the security game model. In this paper, using recent advances in mean field game theory, we propose a novel game theoretic approach for security in MANETs. Mean field game theory provides a powerful mathematical tool for problems with a large number of players. Since security defence mechanisms consume precious system resources (e.g., energy), the proposed scheme considers not only the security requirement of MANETs but also the system resources. In addition, each node only needs to know its own state information and the aggregate effect of the other nodes in the MANET. Therefore, the proposed scheme is a fully distributed scheme. Simulation results are presented to illustrate the effectiveness of the proposed scheme.
Implementing the density matrix embedding theory with the hierarchical mean-field approach
Qin, Jingbo; Jie, Quanlin; Fan, Zhuo
2016-07-01
We show an implementation of density matrix embedding theory (DMET) for the spin lattice of infinite size. It is indeed a special form of hierarchical mean-field (HMF) theory. In the method, we divide the lattice into a small part and a large part. View the small part as an impurity, embedding in the large part, which is viewed as the environment. We deal the impurity with a high accuracy method. But treat the environment with a low-level method: the states of the environment nearby the impurity are expressed by a set of multiple block product states, while the distant parts are treated by mean-field consideration. Our method allows for the computation of the ground state of the infinite two-dimensional quantum spin systems. In the text, we take the frustrated Heisenberg model as an example to test our method. The ground state energy we calculated can reach a high accuracy. We also calculate the magnetization, and the fidelity to study the quantum phase transitions.
$\\sigma$-SCF: A Direct Energy-targeting Method To Mean-field Excited States
Ye, Hong-Zhou; Ricke, Nathan D; Van Voorhis, Troy
2016-01-01
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g.\\ Hartree-Fock) solutions. Energy-based optimization methods for excited states, like $\\Delta$-scf, tend to fall into the lowest solution consistent with a given symmetry -- a problem known as "variational collapse". In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, $\\sigma$-scf, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find \\emph{all} excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states -- ground or excited -- are treated on an equal footing. Third, it provides an alternate approach to locate $\\Delta$-scf solutions that are otherwise inaccessible by the...
GENERAL: Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
Yang, Xu-Hua; Sun, Bao; Wang, Bo; Sun, You-Xian
2010-04-01
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.
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.
Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems
Jin, Jiasen; Biella, Alberto; Viyuela, Oscar; Mazza, Leonardo; Keeling, Jonathan; Fazio, Rosario; Rossini, Davide
2016-07-01
We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1 /2 on a lattice interacting through an X Y Z Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.
Mean field approximation for biased diffusion on Japanese inter-firm trading network.
Watanabe, Hayafumi
2014-01-01
By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7.
Engl, Thomas; Richter, Klaus
2015-01-01
We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number $N$. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, non-perturbative solutions of the, typically non-linear, wave equation of the classical (mean-field) limit. To this end we construct the semiclassical approximation for both the smooth and oscillatory part of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects like vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence brea...
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Zia, R. K. P.
2012-02-01
Population dynamics is a venerable subject, dating back two centuries to Malthus, Verhulst, Lotka, Volterra, and many others. Nonetheless, new and interesting phenomena are continually being discovered. For example, the recent discovery of ``Survival of the Weakest'' in cyclic competition between 3 species with no spatial structure (Berr, Reichenbach, Schottenloher, and Frey, Phys. Rev. Lett. 102, 048102 (2009)) attracted considerable attention, e.g., http://www.sciencedaily.com/releases/2009/02/090213115127.htm. Considering a similar system with 4 or more species, we find a more intuitively understandable principle which appears to underpin all systems with cyclically competing species. We will present several interesting aspects of the 4 species system -- from non-linear dynamical phenomena in a deterministic mean-field approach to remarkable extinction probabilities in the stochastic evolution of a finite system. Some insights into the deterministic dynamics, gained from generalizing this system to one with any number of species with arbitrary pairwise interactions, will also be discussed.
Rhythmic behavior in a two-population mean field Ising model
Collet, Francesca; Tovazzi, Daniele
2016-01-01
Many real systems comprised of a large number of interacting components, as for instance neural networks , may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean field Ising model with the scope of investigating simple mechanisms capable to generate rhythm in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intra-population interactions of different strengths suffices for the emergence of a robust periodic behavior.
Mean-field dynamic criticality and geometric transition in the Gaussian core model
Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa
2016-04-01
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.
Mean-Field Theory of Intra-Molecular Charge Ordering in (TTM--TTP)I3
Omori, Yukiko; Tsuchiizu, Masahisa; Suzumura, Yoshikazu
2011-02-01
We examine an intra-molecular charge-ordered (ICO) state in the multi-orbital molecular compound (TTM--TTP)I3 on the basis of an effective two-orbital model derived from ab initio calculations. Representing the model in terms of the fragment molecular-orbital (MO) picture, the ICO state is described as the charge disproportionation on the left and right fragment MOs. By applying the mean-field theory, the phase diagram of the ground state is obtained as a function of the inter-molecular Coulomb repulsion and the intra-molecular transfer integral. The ICO state is stabilized by large inter-fragment Coulomb interactions, and the small intra-molecular transfer energy between two fragment MOs. Furthermore, we examine the finite-temperature phase diagram. The relevance to the experimental observations in the molecular compound of (TTM--TTP)I3 is also discussed.
Ground-State Properties of Z = 59 Nuclei in the Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
ZHOU Yong; MA Zhong-Yu; CHEN Bao-Qiu; LI Jun-Qing
2000-01-01
Ground-state properties of Pr isotopes are studied in a framework of the relativistic mean-field (RMF) theory using the recently proposed parameter set TM1. Bardeen-Cooper-Schrieffer (BCS) pproximation and blocking method is adopted to deal with pairing interaction and the odd nucleon, respectively. The pairing forces are taken to be isospin dependent. The domain of the validity of the BCS theory and the positions of neutron and proton drip lines are studied. It is shown that RMF theory has provided a good description of the binding energy,isotope shifts and deformation of nuclei over a large range of Pr isotopes, which are in good agreement with those obtained in the finite-range droplet model.
Estimating the relevance of predictions from nuclear mean-field models
Reinhard, P -G
2015-01-01
This contribution reviews the present status of the Skyrme-Hartree-Fock (SHF) approach as one of the leading self-consistent mean-field models in the physics of atomic nuclei. It starts with a brief summary of the formalism and strategy for proper calibration of the SHF functional. The main emphasis lies on an exploration of the reliability of predictions, particularly in the regime of extrapolations. Various strategies are discussed to explore the statistical and systematic errors of SHF. The strategies are illustrated on examples from actual applications. Variations of model and fit data are used to get an idea about systematic errors. The statistical error is evaluated in straightforward manner by statistical analysis based on $\\chi^2$ fits. This also allows also to evaluate the correlations (covariances) between observables which provides useful insights into the structure of the model and of the fitting strategy.
Mean-field state population study for iron-based superconductors
Wang, Zhigang; Fu, Zhen-Guo; Zheng, Fa-Wei; Zhang, Ping
2017-02-01
The occupation number distribution in momentum space are theoretically studied within a two-orbital model, which can be unified describing the low-energy physics of the iron pnictides and iron chalcogenides. The mean-field approximation of Hubbard interaction is employed. By tuning the hopping parameters, the difference between the iron pnictides and iron chalcogenides in their occupation number distribution behavior can be clearly observed. The results show that when the pairing interaction tends to zero, the occupation number n (k) ≈ 0 at Γ point for iron chalcogenides while n (k) ≈ 2 at Γ point for iron pnictides. By increasing the strength of the pairing interaction to a large value, the change of n (k) at Γ point for iron chalcogenides (pnictides) is remarkable (unremarkable). In addition, we find that the effect of the nearest-neighbor coupling between the two layers, contained in the S4 model [Hu and Hao, (2012) [33
Magnetic moments of 33Mg in the time-odd relativistic mean field approach
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.
Cluster decay in very heavy nuclei in a relativistic mean field model
Bhattacharya, Madhubrata; Gangopadhyay, G.
2008-02-01
Exotic cluster decay of very heavy nuclei was studied in the microscopic Super-Asymmetric Fission Model. The Relativistic Mean Field model with the force FSU Gold was employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction were used in the double folding model to obtain the potential between the cluster and the daughter. Half-life values were calculated in the WKB approximation and the spectroscopic factors were extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions were made for some possible decays.
Study of reaction and decay using densities from relativistic mean field theory
Gangopadhyay, G
2012-01-01
Relativistic mean field calculations have been performed to obtain nuclear density pro- file. Microscopic interactions have been folded with the calculated densities of finite nuclei to obtain a semi-microscopic potential. Life time values for the emission of proton, alpha particles and complex clusters have been calculated in the WKB approach assum- ing a tunneling process through the potential barrier. Elastic scattering cross sections have been estimated for proton-nucleus scattering in light neutron rich nuclei. Low en- ergy proton reactions have been studied and their astrophysical implications have been discussed. The success of the semi-microscopic potentials obtained in the folding model with RMF densities in explaining nuclear decays and reactions has been emphasized.
Enhancement of Noisy Planar Nuclear Medicine Images using Mean Field Annealing
Falk, D L; Rubin, D M
2007-01-01
Nuclear medicine (NM) images inherently suffer from large amounts of noise and blur. The purpose of this research is to reduce the noise and blur while maintaining image integrity for improved diagnosis. The proposed solution is to increase image quality after the standard pre- and post-processing undertaken by a gamma camera system. Mean Field Annealing (MFA) is the image processing technique used in this research. It is a computational iterative technique that makes use of the Point Spread Function (PSF) and the noise associated with the NM image. MFA is applied to NM images with the objective of reducing noise while not compromising edge integrity. Using a sharpening filter as a post-processing technique (after MFA) yields image enhancement of planar NM images.
Investigation of A＋c- and Ab-Hypernuclei in Relativistic Mean-Field Model
Institute of Scientific and Technical Information of China (English)
TANYu-Hong; CAIChong-Hai; LILei; NINGPing-Zhi
2003-01-01
We investigate the properties of A+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A+c bound states can exist if the A+c potential well depth |UA+c| in nuclear matter is less than 10 MeV. If |UA+c|is less than 20 MeV, A+c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A+c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A+c in hypernuclei is a/so observed, and for the Ab it is nearly zero.
Beyond mean-field boson-fermion model for odd-mass nuclei
Nomura, K; Vretenar, D
2016-01-01
A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.
Oscillation quenching in third order phase locked loop coupled by mean field diffusive coupling
Chakraborty, S.; Dandapathak, M.; Sarkar, B. C.
2016-11-01
We explored analytically the oscillation quenching phenomena (amplitude death and parameter dependent inhomogeneous steady state) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops were coupled through mean field diffusive coupling. The lower and upper limits of the quenched state were identified in the parameter space of the coupled PLL using the Routh-Hurwitz technique. We further observed that the ability of convergence to the quenched state of coupled PLLs depends on the design parameters. For identical systems, both the systems converge to the homogeneous steady state, whereas for non-identical parameter values they converge to an inhomogeneous steady state. It was also observed that for identical systems, the quenched state is wider than the non-identical case. When the system parameters are so chosen that each isolated loop is chaotic in nature, we observe narrowing down of the quenched state. All these phenomena were also demonstrated through numerical simulations.
Beyond-mean-field boson-fermion model for odd-mass nuclei
Nomura, K.; Nikšić, T.; Vretenar, D.
2016-05-01
A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
Burger, Martin
2016-11-18
In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas and Moll [15] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We prove existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.
Magnetic helicity in non-axisymmetric mean-field solar dynamo
Pipin, V V
2016-01-01
The paper address the effects of magnetic helicity conservation in a non-linear nonaxisymmetric mean-field solar dynamo model. We study the evolution of the shallow non-axisymmetric magnetic field perturbation with the strength about 10G in the solar convection zone. The dynamo evolves from the pure axisymmetric stage through the short (about 2 years) transient phase when the non-axisymmetric m=1 dynamo mode is dominant to the final stage where the axisymmetry of the dynamo is almost restored. It is found that magnetic helicity is transferred forth and back over the spectral space during the transient phase. Also our simulations shows that the non-axisymmetric distributions of magnetic helicity tend to follows the regions of the Hale polarity rule.
Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Petrovici, A.; Andrei, O. [National Institute for Physics and Nuclear Engineering, R-077125 Bucharest (Romania)
2015-02-24
Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.
Mean-field energy-level shifts and dielectric properties of strongly polarized Rydberg gases
Zhelyazkova, V; Hogan, S D
2016-01-01
Mean-field energy-level shifts arising as a result of strong electrostatic dipole interactions within dilute gases of polarized helium Rydberg atoms have been probed by microwave spectroscopy. The Rydberg states studied had principal quantum numbers $n=70$ and 72, and electric dipole moments of up to 14050 D, and were prepared in pulsed supersonic beams at particle number densities on the order of $10^{8}$ cm$^{-3}$. Comparisons of the experimental data with the results of Monte Carlo calculations highlight effects of the distribution of nearest-neighbor spacings in the pulsed supersonic beams, and the dielectric properties of the strongly polarized Rydberg gases, on the microwave spectra. These observations reflect the emergence of macroscopic electrical properties of the atomic samples when strongly polarized.
Ground State Properties of Ds Isotopes Within the Relativistic Mean Field Theory
Institute of Scientific and Technical Information of China (English)
张海飞; 张鸿飞; 李君清
2012-01-01
The ground state properties of Ds (Z=110) isotopes (N=151-195) are studied in the framework of the relativistic mean field (RMF) theory with the effective interaction NL-Z2.The pairing correlation is treated within the conventional BCS approximation.The calculated binding energies are consistent with the results from finite-range droplet model (FRDM) and Macroscopic-microscopic method (MMM).The quadrupole deformation,α-decay energy,α-decay half-live,charge radius,two-neutron separation energy and single-particle spectra are analyzed for Ds isotopes to find new characteristics of superheavy nuclei (SHN).Among the calculated results it is rather distinct that the isotopic shift appears evidently at neutron number N=184.
Cluster Mean-Field Signature of Entanglement Entropy in Bosonic Superfluid-Insulator Transitions
Zhang, Li; Ke, Yongguan; Lee, Chaohong
2016-01-01
Entanglement entropy (EE), a fundamental conception in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, for the first time, in the framework of a cluster MF treatment, we extract the signature of EE in the bosonic superfluid-insulator transitions. We consider a trimerized Kagome lattice of interacting bosons, in which each trimer is treated as a cluster, and implement the cluster MF treatment by decoupling all inter-trimer hopping. In addition to superfluid and integer insulator phases, we find that fractional insulator phases appear when the tunneling is dominated by the intra-trimer part. To quantify the residual bipartite entanglement in a cluster, we calculate the second-order Renyi entropy, which can be experimentally measured by quantum interference of many-body twins. The sec...
The glass crossover from mean-field Spin-Glasses to supercooled liquids
Rizzo, Tommaso
2016-03-01
Stochastic-Beta-Relaxation provides a characterisation of the glass crossover in discontinuous Spin-Glasses and supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper, I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landau theory can be associated to supercooled liquid described by Mode-Coupling Theory invoking a physical principle of time-scale invariance.
Nonlocal energy density functionals for pairing and beyond-mean-field calculations
Bennaceur, K; Dobaczewski, J; Dobaczewski, P; Kortelainen, M; Raimondi, F
2016-01-01
We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order (NLO) and next-to-next-to-leading order (N2LO), which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future implementations, which will include, e.g., EDF terms generated by three-body pseudopotentials.
Description of 178 Hfm2 in the Constrained Relativistic Mean Field Theory
Institute of Scientific and Technical Information of China (English)
ZHANG Wei; PENG Jing; ZHANG Shuang-Quan
2009-01-01
Properties of the ground state of 178 Hf and the isomeric state 178Hfn2 are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of 178Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with Kπ = 16+ is found to be v(7/2- [514])-1 (9/2+ [624])1 π(7/2+ [404])-1 (9/2-[514])1. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the 178 Hfm2 experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.
Influence of Chiral Mean Field on Kaon In-plane Flow in Heavy Ion Collisions
Institute of Scientific and Technical Information of China (English)
ZHENG Yu-Ming; FUCHS Christian; FAESSLER Amand; SHEKHTER Kirril; SRISAWAD Pornrad; KOBDAJ Chinorat; YAN Yu-Peng
2004-01-01
The influence of the chiral mean field on the K+ in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the inmedium kaon dynamics and strongly counterbalances the influence of the vector potential on the K+ in-plane flow. The calculated results show that the new FOPI data can be reasonably described using the Brown & Rho parametrization,which partly takes into account the correction of higher order contributions in the chiral expansion. This indicates that one can abstract the information on the kaon potential in a nuclear medium from the analysis of the K+ in-plane flow.
Rhythmic behavior in a two-population mean-field Ising model
Collet, Francesca; Formentin, Marco; Tovazzi, Daniele
2016-10-01
Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.
An exact solution of spherical mean-field plus a special separable pairing model
Dai, Lianrong; Pan, Feng; Draayer, J. P.
2017-01-01
An exact solution of nuclear spherical mean-field plus a special orbit-dependent separable pairing model is studied, of which the separable pairing interaction parameters are obtained by a linear fitting in terms of the single-particle energies considered. The advantage of the model is that, similar to the standard pairing case, it can be solved easily by using the extended Heine-Stieltjes polynomial approach. With the analysis of the model in the ds- and pf-shell subspace, it is shown that this special separable pairing model indeed provides similar pair structures of the model with the original separable pairing interaction, and is obviously better than the standard pairing model in many aspects.
The role of disorder in the dynamics of critical fluctuations of mean field models
Collet, Francesca
2011-01-01
The purpose of this paper is to analyze how the disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result concern the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).
Deterministic Methods for Filtering, part I: Mean-field Ensemble Kalman Filtering
Law, Kody J H; Tempone, Raul
2014-01-01
This paper provides a proof of convergence of the standard EnKF generalized to non-Gaussian state space models, based on the indistinguishability property of the joint distribution on the ensemble. A density-based deterministic approximation of the mean-field EnKF (MFEnKF) 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 d<2k. 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.
Modeling of coherent ultrafast magneto-optical experiments: Light-induced molecular mean-field model
Energy Technology Data Exchange (ETDEWEB)
Hinschberger, Y. [Instituto de Física dos Materiais da Universidade do Porto, Departamento de Física et Astronomia, Rua do campo Alegre, 687, 4169-007 Porto (Portugal); Hervieux, P.-A. [Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504 BP 43 - F-67034 Strasbourg Cedex 2 (France)
2015-12-28
We present calculations which aim to describe coherent ultrafast magneto-optical effects observed in time-resolved pump-probe experiments. Our approach is based on a nonlinear semi-classical Drude-Voigt model and is used to interpret experiments performed on nickel ferromagnetic thin film. Within this framework, a phenomenological light-induced coherent molecular mean-field depending on the polarizations of the pump and probe pulses is proposed whose microscopic origin is related to a spin-orbit coupling involving the electron spins of the material sample and the electric field of the laser pulses. Theoretical predictions are compared to available experimental data. The model successfully reproduces the observed experimental trends and gives meaningful insight into the understanding of magneto-optical rotation behavior in the ultrafast regime. Theoretical predictions for further experimental studies are also proposed.
Faster is More Different: Mean-Field Dynamics of Innovation Diffusion
Baek, Seung Ki; Kim, Mina
2013-01-01
Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally skewed in such a way that the fraction of innovators is substantially smaller than has been believed in conventional innovation-diffusion theory based on normality. Thus, the typical adoption pattern is predicted to be asymmetric with slow saturation in the ideal situation, which is compared with empirical data sets.
Mean-field energy-level shifts and dielectric properties of strongly polarized Rydberg gases
Zhelyazkova, V.; Jirschik, R.; Hogan, S. D.
2016-11-01
Mean-field energy-level shifts arising as a result of strong electrostatic dipole interactions within dilute gases of polarized helium Rydberg atoms have been probed by microwave spectroscopy. The Rydberg states studied had principal quantum numbers n =70 and 72, and electric dipole moments of up to 14 050 D, and were prepared in pulsed supersonic beams at particle number densities on the order of 108 cm-3. Comparisons of the experimental data with the results of Monte Carlo calculations highlight effects of the distribution of nearest-neighbor spacings in the pulsed supersonic beams, and the dielectric properties of the strongly polarized Rydberg gases, on the microwave spectra. These observations reflect the emergence of macroscopic electrical properties of the atomic samples when strongly polarized.
Hyperons in neutron star matter within relativistic mean-field models
Oertel, M; Gulminelli, F; Raduta, A R
2014-01-01
Since the discovery of neutron stars with masses around 2 solar masses the composition of matter in the central part of these massive stars has been intensively discussed. Within this paper we will (re)investigate the question of the appearance of hyperons. To that end we will perform an extensive parameter study within relativistic mean field models. We will show that it is possible to obtain high mass neutron stars (i) with a substantial amount of hyperons, (ii) radii of 12-13 km for the canonical mass of 1.4 solar masses, and (iii) a spinodal instability at the onset of hyperons. The results depend strongly on the interaction in the hyperon-hyperon channels, on which only very little information is available from terrestrial experiments up to now.
Nonequilibrium dynamical mean-field study of the nonthermal fixed point in the Hubbard model
Tsuji, Naoto; Eckstein, Martin; Werner, Philipp
2014-03-01
A fundamental question of whether and how an isolated quantum many-body system thermalizes has been posed and attracted broad interest since its ideal realization using cold atomic gases. In particular, it has been indicated by various theoretical studies that the system does not immediately thermalize but often shows ``prethermalization'' as a quasi-stationary state, where local observables quickly arrive at the thermal values while the full momentum distribution stays nonthermal for long time. Here we study the thermalization process for the fermionic Hubbard model in the presence of the antiferromagnetic long-range order. Time evolution is obtained by the nonequilibrium dynamical mean-field theory. Due to classical fluctuations, prethermalization is prevented, and the transient dynamics is governed by a nonthermal fixed point, which we discuss belongs to a universality class distinct from the conventional Ginzburg-Landau theory.
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
Institute of Scientific and Technical Information of China (English)
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-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 ah 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 116Sn. It is shown that
High-conductance states in a mean-field cortical network model
DEFF Research Database (Denmark)
Lerchner, Alexander; Ahmadi, Mandana; Hertz, John
2004-01-01
cortical network model with random connectivity and conductance-based synapses. We employ mean-field theory with correctly colored noise to describe temporal correlations in the neuronal activity. Our results illuminate the connection between two independent experimental findings: high-conductance states......Measured responses from visual cortical neurons show that spike times tend to be correlated rather than exactly Poisson distributed. Fano factors vary and are usually greater than 1, indicating a tendency toward spikes being clustered. We show that this behavior emerges naturally in a balanced...... of cortical neurons in their natural environment, and variable non-Poissonian spike statistics with Fano factors greater than 1. (C) 2004 Elsevier B.V. All rights reserved....
Angular momentum projection for a Nilsson mean-field plus pairing model
Wang, Yin; Pan, Feng; Launey, Kristina D.; Luo, Yan-An; Draayer, J. P.
2016-06-01
The angular momentum projection for the axially deformed Nilsson mean-field plus a modified standard pairing (MSP) or the nearest-level pairing (NLP) model is proposed. Both the exact projection, in which all intrinsic states are taken into consideration, and the approximate projection, in which only intrinsic states with K = 0 are taken in the projection, are considered. The analysis shows that the approximate projection with only K = 0 intrinsic states seems reasonable, of which the configuration subspace considered is greatly reduced. As simple examples for the model application, low-lying spectra and electromagnetic properties of 18O and 18Ne are described by using both the exact and approximate angular momentum projection of the MSP or the NLP, while those of 20Ne and 24Mg are described by using the approximate angular momentum projection of the MSP or NLP.
Shimizu, Y R; Shimizu, Yoshifumi R.; Matsuyanagi, Kenichi
2000-01-01
Diabatic description of rotational bands provides a clear-cut picture for understanding the back-bending phenomena, where the internal structure of the yrast band changes dramatically as a function of angular momentum. A microscopic framework to obtain the diabatic bands within the mean-field approximation is presented by making use of the selfconsistent collective coordinate method. Applying the framework, both the ground state rotational bands and the Stockholm bands are studied systematically for the rare-earth deformed nuclei. An overall agreement has been achieved between the calculated and observed rotational spectra. It is also shown that the inclusion of the double-stretched quadrupole-pairing interaction is crucial to obtain an overall agreement for the even-odd mass differences and the rotational spectra simultaneously.
Predicting the mean fields of compressible turbulent boundary layer via a symmetry approach
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su
2016-11-01
A symmetry approach for canonical wall turbulence is extended to develop mean-field predictions for compressible turbulent boundary layer (CTBL). A stress length and a weighted heat flux length are identified to obey the multilayer dilation symmetry of canonical flows, giving rise to predictions of the mean velocity and temperature profiles for a range of Reynolds number (Re), Mach number (Ma) and wall temperature (Tw). Also predicted are the streamwise developments of the shape factor, the boundary layer edge velocity and the boundary layer thicknesses, etc. Only three parameters are involved in the predictions, which have sound physics and organized behaviors with respect to the Re, Ma and Tw effects. The predictions are extensively validated by direct numerical simulation and experimental data, showing better accuracies than the previous theories. The results provide new quantifications that can be used to assess computations, measurements and turbulence models of CTBL, as well as to provide new insights for the CTBL physics.
Double-Cell Type Solar Meridional Circulation Based on Mean-Field Hydrodynamic Model
Bekki, Yuto
2016-01-01
The main object of the paper is to present the condition of the non-diffusive part of the Reynolds stress for driving the double-cell structure of the solar meridional circulation, which has been revealed by recent helioseismic observations. By conducting a set of mean-field hydrodynamic simulations, we confirm for the first time that the double-cell meridional circulation can be achieved along with the solar-like differential rotation when the Reynolds stress transports the angular momentum upward in the lower part and downward in the upper part of the convection zone. It is concluded that, in a stationary state, the accumulated angular momentum via the Reynolds stress in the middle layer is advected to both the upper and lower parts of the convection zone by each of the two meridional circulation cells, respectively.
K--nucleus relativistic mean field potentials consistent with kaonic atoms
Friedman, E.; Gal, A.; Mareš, J.; Cieplý, A.
1999-08-01
K- atomic data are used to test several models of the K- nucleus interaction. The t(ρ)ρ optical potential, due to coupled channel models incorporating the Λ(1405) dynamics, fails to reproduce these data. A standard relativistic mean field (RMF) potential, disregarding the Λ(1405) dynamics at low densities, also fails. The only successful model is a hybrid of a theoretically motivated RMF approach in the nuclear interior and a completely phenomenological density dependent potential, which respects the low density theorem in the nuclear surface region. This best-fit K- optical potential is found to be strongly attractive, with a depth of 180+/-20 MeV at the nuclear interior, in agreement with previous phenomenological analyses.
β-decay of magic nuclei: Beyond mean-field description
Energy Technology Data Exchange (ETDEWEB)
Niu, Yifei, E-mail: nyfster@gmail.com [Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900 (China); INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy); Niu, Zhongming [School of Physics and Material Science, Anhui University, Hefei 230601 (China); Colò, Gianluca [Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano (Italy); INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy); Vigezzi, Enrico [INFN, Sezione di Milano, via Celoria 16, I-20133 Milano (Italy)
2015-10-15
Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of {sup 34}Si, {sup 68}Ni, {sup 78}Ni, and {sup 132}Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.
Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution
Lynn, Christopher
2016-01-01
The problem of influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes. In this paper, we consider an alternate model that treats individual opinions as spins in an Ising network at dynamic equilibrium. We formalize the Ising influence maximization (IIM) problem, which has a physical interpretation as the maximization of the magnetization given a budget of external magnetic field. Under the mean-field (MF) approximation, we develop a number of sufficient conditions for when the problem is convex and exactly solvable, and we provide a gradient ascent algorithm that efficiently achieves an $\\epsilon$-approximation to the optimal solution. We show that optimal strategies exhibit a phase transition from focusing influence on high-degree individuals at high interaction strengths to spreading influence among low-degree individuals at low interaction strengths. We also establish a number of novel results about the structure of steady-states i...
Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction
de Buyl, Pierre; Bachelard, Romain; De Ninno, Giovanni
2009-01-01
The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration and free-electron lasers. The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent relaxation theory. In this context, the transition is explained as a dynamical switch between two metastable regimes, and related to the change of nature of a stationary point of an entropic functional.
Faster is more different: mean-field dynamics of innovation diffusion.
Directory of Open Access Journals (Sweden)
Seung Ki Baek
Full Text Available Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally skewed in such a way that the fraction of innovators is substantially smaller than has been believed in conventional innovation-diffusion theory based on normality. Thus, the typical adoption pattern is predicted to be asymmetric with slow saturation in the ideal situation, which is compared with empirical data sets.
Large-scale dynamo growth rates from numerical simulations and implications for mean-field theories.
Park, Kiwan; Blackman, Eric G; Subramanian, Kandaswamy
2013-05-01
Understanding large-scale magnetic field growth in turbulent plasmas in the magnetohydrodynamic limit is a goal of magnetic dynamo theory. In particular, assessing how well large-scale helical field growth and saturation in simulations match those predicted by existing theories is important for progress. Using numerical simulations of isotropically forced turbulence without large-scale shear with its implications, we focus on several additional aspects of this comparison: (1) Leading mean-field dynamo theories which break the field into large and small scales predict that large-scale helical field growth rates are determined by the difference between kinetic helicity and current helicity with no dependence on the nonhelical energy in small-scale magnetic fields. Our simulations show that the growth rate of the large-scale field from fully helical forcing is indeed unaffected by the presence or absence of small-scale magnetic fields amplified in a precursor nonhelical dynamo. However, because the precursor nonhelical dynamo in our simulations produced fields that were strongly subequipartition with respect to the kinetic energy, we cannot yet rule out the potential influence of stronger nonhelical small-scale fields. (2) We have identified two features in our simulations which cannot be explained by the most minimalist versions of two-scale mean-field theory: (i) fully helical small-scale forcing produces significant nonhelical large-scale magnetic energy and (ii) the saturation of the large-scale field growth is time delayed with respect to what minimalist theory predicts. We comment on desirable generalizations to the theory in this context and future desired work.
Magnetic Field Line Random Walk in Isotropic Turbulence with Varying Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.; Rowlands, G.; Vyas, S.
2016-08-01
In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R=(b/{B}0)({{\\ell }}\\parallel /{{\\ell }}\\perp ) for rms magnetic fluctuation b, large-scale mean field {{\\boldsymbol{B}}}0, and coherence scales parallel ({{\\ell }}\\parallel ) and perpendicular ({{\\ell }}\\perp ) to {{\\boldsymbol{B}}}0. Here we use a nonperturbative analytic framework based on Corrsin’s hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B 0 with finite b and isotropic fluctuations with {{\\ell }}\\parallel /{{\\ell }}\\perp =1, instead of the well-studied route of varying {{\\ell }}\\parallel /{{\\ell }}\\perp for b \\ll {B}0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with b z = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B 0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with b z = 0, when different routes to R\\to ∞ are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.
Saggar, Manish; Zanesco, Anthony P; King, Brandon G; Bridwell, David A; MacLean, Katherine A; Aichele, Stephen R; Jacobs, Tonya L; Wallace, B Alan; Saron, Clifford D; Miikkulainen, Risto
2015-07-01
Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and
DEFF Research Database (Denmark)
Sakellariou, Jason; Roudi, Yasser; Mezard, Marc;
2012-01-01
. The three theories include the first and second order Plefka expansions, referred to as naive mean field (nMF) and TAP, respectively, and a mean field theory which is exact for fully asymmetric couplings. We call the last of these simply MF theory. We show that for the direct problem, nMF performs worse......We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem is predicting the potentially time-varying magnetizations...
The crossover from mean-field to 3D-Ising critical behaviour in a 3-component microemulsion
DEFF Research Database (Denmark)
Seto, H.; Schwahn, D.; Yokoi, E.
1995-01-01
Density fluctuations and associated critical phenomena of water droplets in a water-in-oil microemulsion system have been studied, We have recently found a mean-field behavior in the ''near-critical region'', and this evidence suggested that a crossover from mean-field to non-mean-field behavior...... should be observed. Therefore, a measurement of small-angle neutron scattering was carried out at JAERI with more precise temperature steps. Indeed, the crossover from mean-held to 3D-Ising behavior was observed, and the result could be interpreted by the asymptotic crossover theory proposed by Belyakov...
Biopolymers under large external forces and mean-field RNA virus evolutionary dynamics
Ahsan, Syed Amir
The modeling of the mechanical response of single-molecules of DNA and RNA under large external forces through statistical mechanical methods is central to this thesis with a small portion devoted to modeling the evolutionary dynamics of positive-sense single-stranded RNA viruses. In order to develop and test models of biopolymer mechanics and illuminate the mechanisms underlying biological processes where biopolymers undergo changes in energy on the order of the thermal energy, , entails measuring forces and lengths on the scale of piconewtons (pN) and nanometers (nm), respectively. A capacity achieved in the past two decades at the single-molecule level through the development of micromanipulation techniques such as magnetic and optical tweezers, atomic force microscopy, coupled with advances in micro- and nanofabrication. The statistical mechanical models of biopolymers developed in this dissertation are dependent upon and the outcome of these advancements and resulting experiments. The dissertation begins in chapter 1 with an introduction to the structure and thermodynamics of DNA and RNA, highlighting the importance and effectiveness of simple, two-state models in their description as a prelude to the emergence of two-state models in the research manuscripts. In chapter 2 the standard models of the elasticity of polymers and of a polymer gel are reviewed, characterizing the continuum and mean-field models, including the scaling behavior of DNA in confined spaces. The research manuscript presented in the last section of chapter 2 (section 2.5), subsequent to a review of a Flory gel and in contrast to it, is a model of the elasticity of RNA as a gel, with viral RNA illustrating an instance of such a network, and shown to exhibit anomalous elastic behavior, a negative Poisson ratio, and capable of facilitating viral RNA encapsidation with further context provided in section 5.1. In chapter 3 the experimental methods and behavior of DNA and RNA under mechanical
Brenna, M; Roca-Maza, X; Bortignon, P F; Moghrabi, K; Grasso, M
2013-01-01
A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of single-particle states (e.g. spectroscopic factors), as well as of collective states (e.g. their damping width and their gamma decay to the ground state or to low lying states). Since commonly used effective interactions are fitted at the mean-field level, one should aim at refitting them including the desired beyond mean-field contributions in the refitting procedure. If zero-range interactions are used, divergences arise. We present some steps towards the refitting of Skyrme interactions, for its application in finite nuclei.
Energy Technology Data Exchange (ETDEWEB)
Erler, Bastian
2012-07-18
Realistic nucleon-nucleon interactions transformed via the Unitary Correlation Operator Method (UCOM) or the Similarity Renormalization Group (SRG) have proven to be a suitable starting point for the description of closed-shell nuclei via mean-field methods like Hartree-Fock (HF). This allows the treatment of a number of heavy nuclei with realistic nucleon-nucleon interactions, which would otherwise only be possible with phenomenological interactions. To include three-nucleon forces in an approximate way, the UCOM or SRG transformed interactions can be augmented by a three-body contact interaction, which is necessary to reproduce measured charge radii. However, many interesting nuclei, including those near the neutron drip line, are far away from closed shells. These nuclei are of great importance for modeling nucleosynthesis processes in the universe, but experiments can only be performed at a few research facilities. In this work, the Hartree Fock (HF) approach with realistic interactions is extended to light deformed nuclei. Pairing correlations are not taken into account. A crucial step in this process is to allow deformed ground states on the mean-field level, as only nuclei with at least one closed shell can be described with spherical HF ground states. To restore the rotational symmetry in the lab frame, exact angular-momentum projection (AMP) is implemented. Constrained HF calculations are used for an approximate variation after projection approach. The AMP-HF description of open-shell nuclei is on par with the pure HF description of closed-shell nuclei. Charge-radii and systematics of binding energies agree well with experiment. However, missing correlations, lead to an underestimated absolute value of the binding energy. Projection on higher angular momenta approximately reproduces the energy systematics of rotational bands. To describe collective excitations, the Random Phase Approximation (RPA) constitutes a well tested approach, which can also be
Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example
Bouchet, Freddy; Gawȩdzki, Krzysztof; Nardini, Cesare
2016-06-01
In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory (Freidlin and Wentzell, Random perturbations of dynamical systems, 2012). In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory (Bertini et al., arXiv:1404.6466 URL"/> , 2014), which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to 1/√{N}, where N is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter λ , starting from a known quasi-potential for λ =0. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner (Stochastics 20:247-308, 1987; Stochastic differential systems, vol 96, pp 1-10, 1987). Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators (Prog Theoret Phys 75:1105-1110, [74
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)
A mean field approach to Coulomb blockade for a disordered assembly of quantum dots
Indian Academy of Sciences (India)
Akashdeep Kamra; Praveen Pathak; Vijay A Singh
2008-02-01
The Coulomb blockade (CB) in quantum dots (QDs) is by now well documented. It has been used to guide the fabrication of single electron transistors. Even the most sophisticated techniques for synthesizing QDs (e.g. MOCVD/MBE) result in an assembly in which a certain amount of disorder is inevitable. On the other hand, theoretical approaches to CB limit themselves to an analysis of a single QD. In the present work we consider two types of disorders: (i) size disorder; e.g. QDs have a distribution of sizes which could be unimodal or bimodal in nature. (ii) Potential disorder with the confining potential assuming a variety of shapes depending on growth condition and external fields. We assume a Gaussian distribution in disorder in both size and potential and employ a simplified mean field theory. To do this we rely on the scaling laws for the CB (also termed as Hubbard ) obtained for an isolated QD [1]. We analyze the distribution in the Hubbard as a consequence of disorder and observe that Coulomb blockade is partially suppressed by the disorder. Further, the distribution in is a skewed Gaussian with enhanced broadening.
Quantum Dynamics of Dark and Dark-Bright Solitons beyond the Mean-Field Approximation
Krönke, Sven; Schmelcher, Peter
2014-05-01
Dark solitons are well-known excitations in one-dimensional repulsively interacting Bose-Einstein condensates, which feature a characteristical phase-jump across a density dip and form stability in the course of their dynamics. While these objects are stable within the celebrated Gross-Pitaevskii mean-field theory, the situation changes dramatically in the full many-body description: The condensate being initially in a dark soliton state dynamically depletes and the density notch fills up with depleted atoms. We analyze this process in detail with a particular focus on two-body correlations and the fate of grey solitons (dark solitons with finite density in the notch) and thereby complement the existing results in the literature. Moreover, we extend these studies to mixtures of two repulsively interacting bosonic species with a dark-bright soliton (dark soliton in one component filled with localized atoms of the other component) as the initial state. All these many-body quantum dynamics simulations are carried out with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB).
Mean field theory of charge-density wave state in magnetic field
Grigoriev, Pavel; Lyubshin, Dmitrij
2005-03-01
We develop a mean field theory of charge-density wave (CDW) state in magnetic field and study properties of this state below the transition temperature. We show that the CDW state with shifted wave vector in high magnetic field (CDWx phase) has a double harmonic modulation on the most part of the phase diagram. At perfect nesting the single harmonic CDW state with shifted wave vector exists only in a very narrow region near the triple point. We show that the transition from CDW0 to CDWx state below the critical temperature is accompanied by a jump of the CDW order parameter and of the CDW wave vector rather than by their continuous increase. This implies a first order transition between these CDW states and explains a strong hysteresis accompanying this transition. The similarities between CDW in high magnetic field and nonuniform LOFF superconducting phase are pointed out. Our investigation provides a theoretical description for recent experiments on organic metal α-(BEDT-TTF)2KHg(SCN)4 and other compounds. In particular, we explain the higher value of the kink transition field and provide the calculation of the phase diagram in the case of perfect nesting.
Petocchi, Francesco; Capone, Massimo
2016-06-01
We study layered systems and heterostructures of s -wave superconductors by means of a suitable generalization of dynamical mean-field theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively small number of active layers is embedded in an effective potential accounting for the effect of the rest of the system. We introduce a feedback of the active layers on the embedding potential that improves on previous approaches and essentially eliminates the effects of the finiteness of the active slab allowing for cheap computation of very large systems. We extend the method to the superconducting state, and we benchmark the approach by means of simple paradigmatic examples showing some examples on how an interface affects the superconducting properties. As examples, we show that superconductivity can penetrate from an intermediate coupling superconductor into a weaker coupling one for around ten layers, and that the first two layers of a system with repulsive interaction can turn superconducting by proximity effects even when charge redistribution is inhibited.
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.
Treatment of Fluctuation Effects in Mean-field Models of Chain Stretching
Douglas, Jack; Mansfield, Marc
1997-03-01
Many recent studies of chain stretching in block copolymer materials, polymer brushes, and many-arm stars have been formulated in terms of mean- field models, leading generally to power-law potentials describing the chain stretching arising from interchain and intrachain excluded volume interactions. This type of model has been highly successful, but fluctuation effects associated with finite chain length are often neglected in model calculations. We investigate whether fluctuation effects can be accounted for by reintroducing these effective pseudo-potentials into a path-integral description to calculate the chain streching. Numerical treatment of chain swelling with repulsive power-law potentials leads to universal scaling curves which are similar to those found for chain swelling due to excluded volume in polymer solutions. Density profiles are also calculated and the parabolic potential led to a density profile having a "foot" for finite chain lengths, as in measurements on polymer "brushes". Analytic calculations indicate a general relation between the polymer size exponent nu and the power of the potential which also holds for Hamiltonian dynamical systems and thus the 2/3 power law describing the strong segregation scaling of block copolymer lamellae with chain mass corresponds to Kepler's third law of planetary motion relating the orbital scale to its period.
Mean-field dynamo in a turbulence with shear and kinetic helicity fluctuations.
Kleeorin, Nathan; Rogachevskii, Igor
2008-03-01
We study the effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau approximation and the second-order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause a large-scale dynamo. A mean-field dynamo is possible when the kinetic helicity fluctuations are inhomogeneous, which causes a nonzero mean alpha effect in a sheared turbulence. On the other hand, the shear-current effect can generate a large-scale magnetic field even in a homogeneous nonhelical turbulence with large-scale shear. This effect was investigated previously for large hydrodynamic and magnetic Reynolds numbers. In this study we examine the threshold required for the shear-current dynamo versus Reynolds number. We demonstrate that there is no need for a developed inertial range in order to maintain the shear-current dynamo (e.g., the threshold in the Reynolds number is of the order of 1).
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.)
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
In this contribution we present some results of potential energy surfaces of actinide and transfermium nuclei from multi-dimensional constrained relativistic mean field (MDC-RMF) models. Recently we developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) in which all shape degrees of freedom $\\beta_{\\lambda\\mu}$ with even $\\mu$ are allowed and the functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In MDC-RMF models, the pairing correlations are treated with the BCS method. With MDC-RMF models, the potential energy surfaces of even-even actinide nuclei were investigated and the effect of triaxiality on the fission barriers in these nuclei was discussed. The non-axial reflection-asymmetric $\\beta_{32}$ shape in some transfermium nuclei with $N=150$, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No were also studied.
Beyond-mean-field corrections within the second random-phase approximation
Grasso, M.; Gambacurta, D.; Engel, J.
2016-06-01
A subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, is used in the second random-phase approximation (SRPA). Doublecounting problems arise in the energy-density functional framework in all cases where effective interactions tailored at leading order are used for higher-order calculations, such as those done in the SRPA model. It was recently shown that this subtraction procedure also guarantees that the stability condition related to the Thouless theorem is verified in extended RPA models. We discuss applications of the subtraction procedure, introduced within the SRPA model, to the nucleus 16O. The application of the subtraction procedure leads to: (i) stable results that are weakly cutoff dependent; (ii) a considerable upwards correction of the SRPA spectra (which were systematically shifted downwards by several MeV with respect to RPA spectra, in all previous calculations). With this important implementation of the model, many applications may be foreseen to analyze the genuine impact of 2 particle-2 hole configurations (without any cutoff dependences and anomalous shifts) on the excitation spectra of medium-mass and heavy nuclei.
Magnetic material in mean-field dynamos driven by small scale helical flows
Giesecke, Andre; Gerbeth, Gunter
2014-01-01
We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G.O. Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-K\\'arm\\'an-Sodium (VKS) dynamo. For both examined flow configurations the consideration of magnetic material within...
Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Tome, Tania; Carvalho, Kelly C de [Instituto de FIsica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970 Sao Paulo (Brazil)
2007-10-26
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model.
Allen, James T; Richardson, Chris T; Ferland, Gary J; Baldwin, Jack A
2013-01-01
We present an analysis of the optical spectra of narrow emission-line galaxies, based on mean field independent component analysis (MFICA). Samples of galaxies were drawn from the Sloan Digital Sky Survey (SDSS) and used to generate compact sets of `continuum' and `emission-line' component spectra. These components can be linearly combined to reconstruct the observed spectra of a wider sample of galaxies. Only 10 components - five continuum and five emission line - are required to produce accurate reconstructions of essentially all narrow emission-line galaxies; the median absolute deviations of the reconstructed emission-line fluxes, given the signal-to-noise ratio (S/N) of the observed spectra, are 1.2-1.8 sigma for the strong lines. After applying the MFICA components to a large sample of SDSS galaxies we identify the regions of parameter space that correspond to pure star formation and pure active galactic nucleus (AGN) emission-line spectra, and produce high S/N reconstructions of these spectra. The phys...
Tumaneng, Paul W.; Pandit, Sagar A.; Zhao, Guijun; Scott, H. L.
2011-03-01
The connection between membrane inhomogeneity and the structural basis of lipid rafts has sparked interest in the lateral organization of model lipid bilayers of two and three components. In an effort to investigate anisotropic lipid distribution in mixed bilayers, a self-consistent mean-field theoretical model is applied to palmitoyloleoylphosphatidylcholine (POPC)-palmitoyl sphingomyelin (PSM)-cholesterol mixtures. The compositional dependence of lateral organization in these mixtures is mapped onto a ternary plot. The model utilizes molecular dynamics simulations to estimate interaction parameters and to construct chain conformation libraries. We find that at some concentration ratios the bilayers separate spatially into regions of higher and lower chain order coinciding with areas enriched with PSM and POPC, respectively. To examine the effect of the asymmetric chain structure of POPC on bilayer lateral inhomogeneity, we consider POPC-lipid interactions with and without angular dependence. Results are compared with experimental data and with results from a similar model for mixtures of dioleoylphosphatidylcholine, steroyl sphingomyelin, and cholesterol.
Site-disorder driven superconductor-insulator transition: a dynamical mean field study.
Kamar, Naushad Ahmad; Vidhyadhiraja, N S
2014-03-05
We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap.
Properties and structure of N=Z nuclei within relativistic mean field theory
Institute of Scientific and Technical Information of China (English)
GAO Yuan; DONG Jian-Min; ZHANG Hong-Fei; ZUO Wei; LI Jun-Qing
2009-01-01
The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.
Dynamical mean field theory of the repulsive BCS+U model
Energy Technology Data Exchange (ETDEWEB)
Park, Kwon [School of Physics, Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of)], E-mail: kpark@kias.re.kr
2009-07-15
The Gutzwiller-projected BCS Hamiltonian is a useful model for high-temperature superconductivity due to its equivalence to the Heisenberg model at half filling and a close connection to the t-J model at moderate doping. In this work, a dynamical mean field theory (DMFT) is developed for the BCS Hamiltonian with d-wave pairing subject to on-site repulsive interaction, U, which we call the BCS+U model. The large-U limit corresponds to the Gutzwiller-projected BCS Hamiltonian. It is shown that the equivalence between the Heisenberg and the Gutzwiller-projected BCS model is a manifestation of a broader duality in the BCS+U model: for any finite U, the local dynamics of the BCS+U model is dual at half filling with respect to the exchange between the hopping parameter, t, and the pairing amplitude, {delta}. It is explicitly demonstrated in our DMFT analysis that the real superconducting gap, determined from the sharp coherence peaks in the local density of states, shows strong renormalization from its bare value as a function of U.
Mukherjee, Shantanu; Lee, Wei-Cheng
2015-12-01
The quasiparticle interferences (QPIs) of the featureless Mott insulators are investigated by a T -matrix formalism implemented with the dynamical mean field theory (T -DMFT). In the Mott insulating state, due to the singularity at zero frequency in the real part of the electron self-energy [Re Σ (ω )˜η /ω ] predicted by DMFT, where η can be considered as the "order parameter" for the Mott insulating state, QPIs are completely washed out at small bias voltages. However, a further analysis shows that Re Σ (ω ) serves as an energy-dependent chemical potential shift. As a result, the effective bias voltage seen by the system is e V'=e V -Re Σ (e V ) , which leads to a critical bias voltage e Vc˜√{η } satisfying e V'=0 if and only if η is nonzero. Consequently, the same QPI patterns produced by the noninteracting Fermi surfaces appear at this critical bias voltage e Vc in the Mott insulating state. We propose that this reentry of noninteracting QPI patterns at e Vc could serve as an experimental signature of the Mott insulating state, and the order parameter can be experimentally measured as η ˜(eVc) 2 .
Nuclear mean field and double-folding model of the nucleus-nucleus optical potential
Khoa, Dao T; Loan, Doan Thi; Loc, Bui Minh
2016-01-01
Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density- and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies, wher...
Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
Hewson, A. C.
2016-11-01
We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.
Numerical evidence against both mean field and droplet scenarios of the Edwards-Anderson model
Fernandez, Julio F.; Alonso, Juan J.
2013-03-01
From tempered Monte Carlo simulations, we have obtained accurate probability distributions p (q) of the spin-overlap parameter q for finite Edwards-Anderson (EA) and Sherrington-Kirkpatrick (SK) spin-glass systems at low temperatures. Our results for p (q) follow from averages over 105 disordered samples of linear sizes L = 4 - 8 and over 15 000 samples for L = 10 . In both the SK and EA models, at temperatures as low as 0 . 2Tsg , where Tsg is the transition temperature, p (q) varies insignificantly with L. This does not fit the trend that the droplet model predicts for large L. We have also calculated correlation functions, F (q1 ,q2) , from which rms deviations, δp , over different realizations of quenched disorder, as well as thermal fluctuations, w, of q values, follow. Our numerical results for δp and w scale as √{ L} and 1 / L , respectively, in the SK model. This fits in well with mean field predictions. On the other hand, our data for w and δp vary little, if at all, for the EA model.
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.
van Albada, S J; Gray, R T; Drysdale, P M; Robinson, P A
2009-04-21
Neuronal correlates of Parkinson's disease (PD) include a shift to lower frequencies in the electroencephalogram (EEG) and enhanced synchronized oscillations at 3-7 and 7-30 Hz in the basal ganglia, thalamus, and cortex. This study describes the dynamics of a recent physiologically based mean-field model of the basal ganglia-thalamocortical system, and shows how it accounts for many key electrophysiological correlates of PD. Its detailed functional connectivity comprises partially segregated direct and indirect pathways through two populations of striatal neurons, a hyperdirect pathway involving a corticosubthalamic projection, thalamostriatal feedback, and local inhibition in striatum and external pallidum (GPe). In a companion paper, realistic steady-state firing rates were obtained for the healthy state, and after dopamine loss modeled by weaker direct and stronger indirect pathways, reduced intrapallidal inhibition, lower firing thresholds of the GPe and subthalamic nucleus (STN), a stronger projection from striatum to GPe, and weaker cortical interactions. Here it is shown that oscillations around 5 and 20 Hz can arise with a strong indirect pathway, which also causes increased synchronization throughout the basal ganglia. Furthermore, increased theta power with progressive nigrostriatal degeneration is correlated with reduced alpha power and peak frequency, in agreement with empirical results. Unlike the hyperdirect pathway, the indirect pathway sustains oscillations with phase relationships that coincide with those found experimentally. Alterations in the responses of basal ganglia to transient stimuli accord with experimental observations. Reduced cortical gains due to both nigrostriatal and mesocortical dopamine loss lead to slower changes in cortical activity and may be related to bradykinesia. Finally, increased EEG power found in some studies may be partly explained by a lower effective GPe firing threshold, reduced GPe-GPe inhibition, and/or weaker
Real-space, mean-field algorithm to numerically calculate long-range interactions
Cadilhe, A.; Costa, B. V.
2016-02-01
Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.
Magnetic Field Line Random Walk in Isotropic Turbulence with Zero Mean Field
Sonsrettee, W.; Subedi, P.; Ruffolo, D.; Matthaeus, W. H.; Snodin, A. P.; Wongpan, P.; Chuychai, P.
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B 0)(l∥/l) for rms magnetic fluctuation b, large-scale mean field B 0, and parallel and perpendicular coherence scales l∥ and l, respectively. Here we examine the FLRW when R → ∞ by taking B 0 → 0 for finite bz (fluctuation component along B 0), which differs from the well-studied route with bz = 0 or bz Lt B 0 as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B 0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k -1 or k -2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B 0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
MAGNETIC FIELD LINE RANDOM WALK IN ISOTROPIC TURBULENCE WITH ZERO MEAN FIELD
Energy Technology Data Exchange (ETDEWEB)
Sonsrettee, W.; Ruffolo, D.; Snodin, A. P.; Wongpan, P. [Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400 (Thailand); Subedi, P.; Matthaeus, W. H. [Bartol Research Institute, University of Delaware, Newark, DE 19716 (United States); Chuychai, P., E-mail: bturbulence@gmail.com, E-mail: david.ruf@mahidol.ac.th, E-mail: andrew.snodin@gmail.com, E-mail: pat.wongpan@postgrad.otago.ac.nz, E-mail: piyanate@gmail.com, E-mail: prasub@udel.edu, E-mail: whm@udel.edu [Thailand Center of Excellence in Physics, CHE, Ministry of Education, Bangkok 10400 (Thailand)
2015-01-01
In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B {sub 0})(ℓ{sub ∥}/ℓ ) for rms magnetic fluctuation b, large-scale mean field B {sub 0}, and parallel and perpendicular coherence scales ℓ{sub ∥} and ℓ , respectively. Here we examine the FLRW when R → ∞ by taking B {sub 0} → 0 for finite b{sub z} (fluctuation component along B {sub 0}), which differs from the well-studied route with b{sub z} = 0 or b{sub z} << B {sub 0} as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B {sub 0} = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k {sup –1} or k {sup –2} moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B {sub 0} → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.
Single-chain-in-mean-field simulations of weak polyelectrolyte brushes
Léonforte, F.; Welling, U.; Müller, M.
2016-12-01
Structural properties of brushes which are composed of weak acidic and basic polyelectrolytes are studied in the framework of a particle-based approach that implicitly accounts for the solvent quality. Using a semi-grandcanonical partition function in the framework of the Single-Chain-in-Mean-Field (SCMF) algorithm, the weak polyelectrolyte is conceived as a supramolecular mixture of polymers in different dissociation states, which are explicitly treated in the partition function and sampled by the SCMF procedure. One obtains a local expression for the equilibrium acid-base reaction responsible for the regulation of the charged groups that is also incorporated to the SCMF sampling. Coupled to a simultaneous treatment of the electrostatics, the approach is shown to capture the main features of weak polyelectrolyte brushes as a function of the bulk pH in the solution, the salt concentration, and the grafting density. Results are compared to experimental and theoretical works from the literature using coarse-grained representations of poly(acrylic acid) (PAA) and poly(2-vinyl pyridine) (P2VP) polymer-based brushes. As the Born self-energy of ions can be straightforwardly included in the numerical approach, we also study its effect on the local charge regulation mechanism of the brush. We find that its effect becomes significant when the brush is dense and exposed to high salt concentrations. The numerical methodology is then applied (1) to the study of the kinetics of collapse/swelling of a P2VP brush and (2) to the ability of an applied voltage to induce collapse/swelling of a PAA brush in a pH range close to the pKa value of the polymer.
The ground state energy of the mean field spin glass model
Koukiou, Flora
2008-01-01
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the ground state energy $\\epsilon_0$ \\[\\epsilon_0\\geq -0.7833...,\\] close to the replica symmetry breaking and numerical simulations values.
Kleeorin, N; Sokoloff, D D
2002-01-01
Magnetic fluctuations with a zero mean field in a random flow with a finite correlation time and a small yet finite magnetic diffusion are studied. Equation for the second-order correlation function of a magnetic field is derived. This equation comprises spatial derivatives of high orders due to a non-local nature of magnetic field transport in a random velocity field with a finite correlation time. For a random Gaussian velocity field with a small correlation time the equation for the second-order correlation function of the magnetic field is a third-order partial differential equation. For this velocity field and a small magnetic diffusion with large magnetic Prandtl numbers the growth rate of the second moment of magnetic field is estimated. The finite correlation time of a turbulent velocity field causes an increase of the growth rate of magnetic fluctuations. It is demonstrated that the results obtained for the cases of a small yet finite magnetic diffusion and a zero magnetic diffusion are different. As...
Cattes, Stefanie M; Gubbins, Keith E; Schoen, Martin
2016-05-21
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.
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.
Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides
Zhao, Jie; Lu, Bing-Nan; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui
2015-01-01
Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of 226,228,230,232Th and 232,235,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U . The third minima in 230 ,232Th are very shallow, whereas those in 226 ,228Th and 238U are quite prominent. With the functional PC-PK1 a third barrier is found only in 226 ,228 ,230Th . Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z =90 proton energy gap at β20≈1.5 and β30≈0.7 . Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases
Hartree-Fock mean-field theory for trapped dirty bosons
Khellil, Tama; Pelster, Axel
2016-06-01
Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree-Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose-Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.
Deformed neutron stars due to strong magnetic field in terms of relativistic mean field theories
Yanase, Kota; Yoshinaga, Naotaka
2014-09-01
Some observations suggest that magnetic field intensity of neutron stars that have particularly strong magnetic field, magnetars, reaches values up to 1014-15G. It is expected that there exists more strong magnetic field of several orders of magnitude in the interior of such stars. Neutron star matter is so affected by magnetic fields caused by intrinsic magnetic moments and electric charges of baryons that masses of neutron stars calculated by using Tolman-Oppenheimer-Volkoff equation is therefore modified. We calculate equation of state (EOS) in density-dependent magnetic field by using sigma-omega-rho model that can reproduce properties of stable nuclear matter in laboratory Furthermore we calculate modified masses of deformed neutron stars.
How to do mean field theory in Feynman gauge and doing it for U(1) with corrections to fourth order
Energy Technology Data Exchange (ETDEWEB)
Flyvbjerg, H.
1984-07-02
It is demonstrated how mean field theory with corrections from fluctuations may be applied to lattice gauge theories in covariant gauges. By fixing the gauge at tree level, the importance of fluctuations is decreased. This is understood as inclusion of terms of next-to-leading-order in d in the definition of the mean field tree approximation, d being the dimension of the lattice. The gauge group U(1) and Wilson's action are used as testing ground. Tree and one-loop results comparable to those previously obtained in axial gauge are obtained in for d=4. The next three correction terms to the free and plaquette energies are evaluated in Feynmann gauge. The truncated asympotic series thus obtained is compared to that of the ordinary weak coupling expansion. The mean field series gives, to those orders studied, a much better approximation. The location of phase transitions in 4d and 5d are predicted with 1% error bars.
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Li, Sen; Zhang, Wei; Lian, Jianming; Kalsi, Karanjit
2016-07-08
This paper studies a multi-stage pricing problem for a large population of thermostatically controlled loads. The problem is formulated as a reverse Stackelberg game that involves a mean field game in the hierarchy of decision making. In particular, in the higher level, a coordinator needs to design a pricing function to motivate individual agents to maximize the social welfare. In the lower level, the individual utility maximization problem of each agent forms a mean field game coupled through the pricing function that depends on the average of the population control/state. We derive the solution to the reverse Stackelberg game by connecting it to a team problem and the competitive equilibrium, and we show that this solution corresponds to the optimal mean field control that maximizes the social welfare. Realistic simulations are presented to validate the proposed methods.
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, Serafim [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom); Terry, John R. [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom)]. E-mail: j.r.terry@lboro.ac.uk; Breakspear, Michael [Black Dog Institute, Randwick, NSW 2031 (Australia); School of Psychiatry, UNSW, NSW 2030 (Australia)
2006-07-10
In this Letter, the genesis of spike-wave activity-a hallmark of many generalized epileptic seizures-is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling.
Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states
Decelle, Aurélien; Ricci-Tersenghi, Federico
2016-07-01
In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and spiking regimes in neural networks). Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may lead to very poor inference (e.g., in the low-temperature phase of the Curie-Weiss model). In this work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of our method on different clustered structures (low-temperature phases of Curie-Weiss and Hopfield models).
Energy Technology Data Exchange (ETDEWEB)
Hazra, Soumitra; Nandy, Dibyendu [Department of Physical Sciences, Indian Institute of Science Education and Research, Kolkata, West Bengal (India); Passos, Dário, E-mail: s.hazra@iiserkol.ac.in, E-mail: dariopassos@ist.utl.pt, E-mail: dnandi@iiserkol.ac.in [CENTRA-IST, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
2014-07-01
Fluctuations in the Sun's magnetic activity, including episodes of grand minima such as the Maunder minimum have important consequences for space and planetary environments. However, the underlying dynamics of such extreme fluctuations remain ill-understood. Here, we use a novel mathematical model based on stochastically forced, non-linear delay differential equations to study solar cycle fluctuations in which time delays capture the physics of magnetic flux transport between spatially segregated dynamo source regions in the solar interior. Using this model, we explicitly demonstrate that the Babcock-Leighton poloidal field source based on dispersal of tilted bipolar sunspot flux, alone, cannot recover the sunspot cycle from a grand minimum. We find that an additional poloidal field source effective on weak fields—e.g., the mean-field α effect driven by helical turbulence—is necessary for self-consistent recovery of the sunspot cycle from grand minima episodes.
Energy Technology Data Exchange (ETDEWEB)
Snoek, M; Titvinidze, I; Toeke, C; Hofstetter, W [Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, 60438 Frankfurt/Main (Germany); Byczuk, K [Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute for Physics, University of Augsburg, 86135 Augsburg (Germany)], E-mail: snoek@itp.uni-frankfurt.de
2008-09-15
We apply dynamical mean-field theory to strongly interacting fermions in an inhomogeneous environment. With the help of this real-space dynamical mean-field theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting fermions with spin1/2 in a harmonic potential. Within R-DMFT, antiferromagnetic order is found to be stable in spatial regions with total particle density close to one, but persists also in parts of the system where the local density significantly deviates from half filling. In systems with spin imbalance, we find that antiferromagnetism is gradually suppressed and phase separation emerges beyond a critical value of the spin imbalance.
Mean field theory, topological field theory, and multi-matrix models
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Dijkgraaf, R. (Princeton Univ., NJ (USA). Joseph Henry Labs.); Witten, E. (Institute for Advanced Study, Princeton, NJ (USA). School of Natural Sciences)
1990-10-08
We show that the genus zero correlation functions of an arbitrary topological field theory coupled to two-dimensional topological gravity are determined by an appropriate Landau-Ginzburg potential. We determine the potentials that arise for topological sigma models with CP{sup 1} or a Calabi-Yau manifold for target space. We present substantial evidence that the multi-matrix models that have been studied recently are equivalent to certain topological field theories coupled to topological gravity. We also describe a topological version of the general 'string equation'. (orig.).
Mean field theory, topological field theory, and multi-matrix models
Dijkgraaf, Robbert; Witten, Edward
1990-10-01
We show that the genus zero correlation functions of an arbitrary topological field theory coupled to two-dimensional topological gravity are determined by an appropriate Landau-Ginzburg potential. We determine the potentials that arise for topological sigma models with CP 1 or a Calabi-Yau manifold for target space. We present substantial evidence that the multi-matrix models that have been studied recently are equivalent to certain topological field theories coupled to topological gravity. We also describe a topological version of the general "string equation".
Waldorp, Lourens J
2016-01-01
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To analyse changes over time and characterise possible future behaviour is rather difficult for large graphs. We describe the dynamics of networks using one-dimensional discrete time dynamical systems theory obtained from a mean field approach to (elementary) probabilistic cellular automata (PCA). Often the mean field approach is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We show that we can use variations of the mean field of the grid to describe the dynamics of the PCA on a random and small-world graph. Bifurcation diagrams for the mean field of the grid, random, and small-world graphs indicate possible phase transitions for certain parameter settings. Extensive simulations indicate for di...
Mean field analysis of a spatial stochastic model of a gene regulatory network.
Sturrock, M; Murray, P J; Matzavinos, A; Chaplain, M A J
2015-10-01
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia; Piekarewicz, J.
2014-10-01
Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, "FSUGold2," is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.
Mendoza-Arenas, J. J.; Clark, S. R.; Felicetti, S.; Romero, G.; Solano, E.; Angelakis, D. G.; Jaksch, D.
2016-02-01
In the present work we investigate the existence of multiple nonequilibrium steady states in a coherently driven X Y lattice of dissipative two-level systems. A commonly used mean-field ansatz, in which spatial correlations are neglected, predicts a bistable behavior with a sharp shift between low- and high-density states. In contrast one-dimensional matrix product methods reveal these effects to be artifacts of the mean-field approach, with both disappearing once correlations are taken fully into account. Instead, a bunching-antibunching transition emerges. This indicates that alternative approaches should be considered for higher spatial dimensions, where classical simulations are currently infeasible. Thus we propose a circuit QED quantum simulator implementable with current technology to enable an experimental investigation of the model considered.
Valor, A; Bonche, P
2000-01-01
We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.
Energy Technology Data Exchange (ETDEWEB)
García Daza, Fabián A.; Mackie, Allan D., E-mail: allan.mackie@urv.cat [Department d’Enginyeria Química, ETSEQ, Universitat Rovira i Virgili, Avinguda dels Països Catalans 26, 43007 Tarragona (Spain); Colville, Alexander J. [Department of Chemical Engineering, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115-5000 (United States)
2015-03-21
Microscopic modeling of surfactant systems is expected to be an important tool to describe, understand, and take full advantage of the micellization process for different molecular architectures. Here, we implement a single chain mean field theory to study the relevant equilibrium properties such as the critical micelle concentration (CMC) and aggregation number for three sets of surfactants with different geometries maintaining constant the number of hydrophobic and hydrophilic monomers. The results demonstrate the direct effect of the block organization for the surfactants under study by means of an analysis of the excess energy and entropy which can be accurately determined from the mean-field scheme. Our analysis reveals that the CMC values are sensitive to branching in the hydrophilic head part of the surfactant and can be observed in the entropy-enthalpy balance, while aggregation numbers are also affected by splitting the hydrophobic tail of the surfactant and are manifested by slight changes in the packing entropy.
Study of the Alpha-Decay Chain for7753 194Rn with Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
SHENG Zong-Qiang; GUO Jian-You
2008-01-01
The structures of the nuclei on the alpha-decay chain of 194Rn are investigated in the deformed relativistic mean-field theory with the effective interaction TMA. We put an emphasis on the ground state properties of 194Rn. The calculated alpha-decay energies and lifetimes are both very close to the experimental data for 186pb and 190po. For 194 Rn, the deviations are a little large on both the alpha-decay energy and the lifetime. We also calculate the alpha-decay energies for the isotopes 192～208Rn. The tendency for the change of the alpha-decay energies with neutron number is correctly reproduced in the relativistic mean-field theory (RMF). In general, the RMF theory can give a good description of the alpha decay chain of 194Rn.
Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model
Ribeiro, Bruno V; Elskens, Yves
2016-01-01
We study the dynamics of the N-particle system evolving in the XY hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent brownian noises over a time scale diverging not slower than $N^{2/5}$ as $N \\to \\infty$, which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
Brownian regime of finite-N corrections to particle motion in the XY Hamiltonian mean field model
Ribeiro, Bruno V.; Amato, Marco A.; Elskens, Yves
2016-08-01
We study the dynamics of the N-particle system evolving in the XY Hamiltonian mean field (HMF) model for a repulsive potential, when no phase transition occurs. Starting from a homogeneous distribution, particles evolve in a mean field created by the interaction with all others. This interaction does not change the homogeneous state of the system, and particle motion is approximately ballistic with small corrections. For initial particle data approaching a waterbag, it is explicitly proved that corrections to the ballistic velocities are in the form of independent Brownian noises over a time scale diverging not slower than {N}2/5 as N\\to ∞ , which proves the propagation of molecular chaos. Molecular dynamics simulations of the XY-HMF model confirm our analytical findings.
Yang, Min-Fong; Sun, Shih-Jye; Hong, Tzay-Ming
1993-12-01
We show that a special kind of slave-boson mean-field approximation, which allows for the symmetry-broken states appropriate for a bipartite lattice, can give essentially the same results as those by the variational-wave-function approach proposed by Gula´csi, Strack, and Vollhardt [Phys. Rev. B 47, 8594 (1993)]. The advantages of our approach are briefly discussed.
He, Yi; Maciejczyk, Maciej; Ołdziej, Stanisław; Scheraga, Harold A.; Liwo, Adam
2013-01-01
A proposed coarse-grained model of nucleic acids demonstrates that average interactions between base dipoles, together with chain connectivity and excluded-volume interactions, are sufficient to form double-helical structures of DNA and RNA molecules. Additionally, local interactions determine helix handedness and direction of strand packing. This result, and earlier research on reduced protein models, suggest that mean-field multipole-multipole interactions are the principal factors responsible for the formation of regular structure of biomolecules. PMID:23496746
Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav
2015-05-01
One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems.
Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1D optical lattices.
Morsch, O; Müller, J H; Cristiani, M; Ciampini, D; Arimondo, E
2001-10-01
We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well depth, Bloch oscillations were observed. Reducing the potential depth further, Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied and used as a probe for the effective potential resulting from mean-field interactions as predicted by Choi and Niu [Phys. Rev. Lett. 82, 2022 (1999)]. The effective potential was measured for various condensate densities and trap geometries, yielding good qualitative agreement with theoretical calculations.
Modeling premartensitic effects in Ni2MnGa: A mean-field and Monte Carlo simulation study
DEFF Research Database (Denmark)
Castan, T.; Vives, E.; Lindgård, Per-Anker
1999-01-01
is constructed and justified based on the analysis of the experimentally observed strain variables and precursor phenomena. The description includes the (local) tetragonal distortion, the amplitude of the plane-modulating strain, and the magnetization. The model is solved by means of mean-field theory and Monte...... Carlo simulations. This last technique reveals the crucial importance of fluctuations in pretransitional effects. The results show that a variety of premartensitic effects may appear due to the magnetoelastic coupling. In the mean-held formulation this coupling is quadratic in both the modulation...
Kónya, G.; Szirmai, G.; Domokos, P.
2011-11-01
We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.
Konya, G; Domokos, P
2011-01-01
We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.
Okamoto, Satoshi
2009-09-02
The surface magnetic phase transition of a double-exchange model for metallic manganites is studied using a Schwinger-boson mean-field method. About three unit-cells wide surface layers are identified. The magnetic moment in these layers decreases more rapidly than that in the bulk when the temperature is increased. This behavior is consistent with experimental observations. We also discuss the implication of this behavior to the tunneling magnetoresistance effect using manganites and possible improvement of the magnetoresistance effect near the bulk Curie temperature.
Mean-field studies of time reversal breaking states in super-heavy nuclei with the Gogny force
Energy Technology Data Exchange (ETDEWEB)
Robledo, L. M., E-mail: luis.robledo@uam.es [Departamento Física Teórica, Facultad de Ciencias, Universidad Autónoma de Madrid, E-28049 Madrid (Spain)
2015-10-15
Recent progress on the description of time reversal breaking (odd mass and multi-quasiparticle excitation) states in super-heavy nuclei within a mean field framework and using several flavors of the Gogny interaction is reported. The study includes ground and excited states in selected odd mass isotopes of nobelium and mendelevium as well as high K isomeric states in {sup 254}No. These are two and four-quasiparticle excitations that are treated in the same self-consistent HFB plus blocking framework as the odd mass states.
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.
Institute of Scientific and Technical Information of China (English)
Erhan Albayrak
2013-01-01
The spin-1 Blume-Capel model with transverse Ω and longitudinal external magnetic fields h,in addition to a longitudinal random crystal field D,is studied in the mean-field approximation.It is assumed that the crystal field is either turned on with probability p or turned off with probability 1-p on the sites of a square lattice.Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ =-Ω/J and p at zero h.Thus,the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.
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.
Energy Technology Data Exchange (ETDEWEB)
Nakano, Hiroshi [Department of Molecular Engineering, Kyoto University, Kyoto Daigaku Katsura, Kyoto 615-8510 (Japan); Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Kyoto 615-8245 (Japan)
2015-12-31
Electronic polarization effects of a medium can have a significant impact on a chemical reaction in condensed phases. We discuss the effects on the charge transfer excitation of a chromophore, N,N-dimethyl-4-nitroaniline, in various solvents using the mean-field QM/MM method with a polarizable force field. The results show that the explicit consideration of the solvent electronic polarization effects is important especially for a solvent with a low dielectric constant when we study the solvatochromism of the chromophore.
Lu, K Q; Li, Z P; Yao, J M; Meng, J
2015-01-01
We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-ME$\\delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\\sim34\\%$ in comparison with cranking prescription.
Ortiz, Gerardo; Cobanera, Emilio
2016-09-01
We investigate Majorana modes of number-conserving fermionic superfluids from both basic physics principles, and concrete models perspectives. After reviewing a criterion for establishing topological superfluidity in interacting systems, based on many-body fermionic parity switches, we reveal the emergence of zero-energy modes anticommuting with fermionic parity. Those many-body Majorana modes are constructed as coherent superpositions of states with different number of fermions. While realization of Majorana modes beyond mean field is plausible, we show that the challenge to quantum-control them is compounded by particle-conservation, and more realistic protocols will have to balance engineering needs with astringent constraints coming from superselection rules. Majorana modes in number-conserving systems are the result of a peculiar interplay between quantum statistics, fermionic parity, and an unusual form of spontaneous symmetry breaking. We test these ideas on the Richardson-Gaudin-Kitaev chain, a number-conserving model solvable by way of the algebraic Bethe ansatz, and equivalent in mean field to a long-range Kitaev chain.
Balram, Ajit C.; Dhar, Deepak
2012-03-01
We consider the spherical model on a spider-web graph. This graph is effectively infinite dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of δ-functions, and all the modes are localized. The fractional number of modes with frequency less than ω varies as exp ( - C/ω) for ω tending to zero, where C is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time t varies as exp ( - C‧t1/3), for large t, where C‧ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free energy per site at temperature T, near and above the critical temperature Tc, also has an essential singularity of the type exp [ - K(T - Tc)-1/2].
Directory of Open Access Journals (Sweden)
Wilten eNicola
2016-02-01
Full Text Available A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF. The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks
On-site residence time in a driven diffusive system: violation and recovery of mean-field
Messelink, Joris J B; Vahabi, Mahsa; MacKintosh, Fred C; Sharma, Abhinav
2016-01-01
We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using Domain wall theory (DWT), we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics (TASEP + LK), and TASEP coupled to mutually interactive LK (TASEP + MILK). The high ...
Modeling MHD accretion-ejection: episodic ejections of jets triggered by a mean-field disk dynamo
Energy Technology Data Exchange (ETDEWEB)
Stepanovs, Deniss; Fendt, Christian; Sheikhnezami, Somayeh, E-mail: deniss@stepanovs.org, E-mail: fendt@mpia.de [Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg (Germany)
2014-11-20
We present MHD simulations exploring the launching, acceleration, and collimation of jets and disk winds. The evolution of the disk structure is consistently taken into account. Extending our earlier studies, we now consider the self-generation of the magnetic field by an α{sup 2}Ω mean-field dynamo. The disk magnetization remains on a rather low level, which helps to evolve the simulations for T > 10, 000 dynamical time steps on a domain extending 1500 inner disk radii. We find the magnetic field of the inner disk to be similar to the commonly found open field structure, favoring magneto-centrifugal launching. The outer disk field is highly inclined and predominantly radial. Here, differential rotation induces a strong toroidal component, which plays a key role in outflow launching. These outflows from the outer disk are slower, denser, and less collimated. If the dynamo action is not quenched, magnetic flux is continuously generated, diffuses outward through the disk, and fills the entire disk. We have invented a toy model triggering a time-dependent mean-field dynamo. The duty cycles of this dynamo lead to episodic ejections on similar timescales. When the dynamo is suppressed as the magnetization falls below a critical value, the generation of the outflows and also accretion is inhibited. The general result is that we can steer episodic ejection and large-scale jet knots by a disk-intrinsic dynamo that is time-dependent and regenerates the jet-launching magnetic field.
Grasso, Marcella
2014-01-01
We investigate the magicity of the isotopes $^{52}$Ca and $^{54}$Ca, that was recently confirmed by two experimental measurements, and relate it to like--particle and neutron--proton tensor effects within a mean--field description. By analyzing Ca isotopes, we show that the like--particle tensor contribution induces shell effects that render these nuclei more magic than they would be predicted by neglecting it. In particular, such induced shell effects are stronger in the nucleus $^{52}$Ca and the single--particle gaps are increased in both isotopes due to the tensor force. By studying $N=32$ and $N=34$ isotones, neutron--proton tensor effects may be isolated and their role analyzed. It is shown that neutron--proton tensor effects lead to increasing $N=32$ and $N=34$ gaps, when going along isotonic chains, from $^{58}$Fe to $^{52}$Ca, and from $^{60}$Fe to $^{54}$Ca, respectively. The mean--field calculations are perfomed by employing one Skyrme parameter set, that was introduced in a previous work by fitting...
Śliwa, Izabela; Zakharov, A V
2014-11-21
Using the extended McMillan's mean field approach with anisotropic forces a study of both the structural and thermodynamic properties of free-standing smectic film (FSSF) in water on heating to the isotropic temperature is carried out numerically. By solving the self-consistent nonlinear equations for the order parameters, we obtained that the smectic-A-isotropic (AI) transition occurs through the series of layer-thinning transitions causing the films to thin in the stepwise manner as the temperature is increased above the bulk smectic-A-isotropic temperature TAI(bulk). With enhanced pair interactions in the bounding layers, the smectic-isotropic transition corresponds to smectic melting of the central layers. The effects of surface "enhanced" pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy and entropy, as well as the temperature dependence of the heat capacity of FSSFs, have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained - by means of optical microscopy and ellipsometry techniques - data of the temperature when the thin decylcyanobiphenyl smectic film immersing in water ruptures has been obtained.
Edison, John R; Monson, Peter A
2014-07-14
Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.
Institute of Scientific and Technical Information of China (English)
WU Ying; YANG Xiao-Xue
2002-01-01
We present the analytical solutions to the two-mode mean-field model for a split Bose Einstein condensate.These explicit solutions completely determine the system's dynamics under the two-mode mean-field approximation for all possible initial conditions.
Zhao, Jie; Niksic, Tamara; Vretenar, Dario; Zhou, Shan-Gui
2016-01-01
Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm are explored. Fission paths, action integrals and corresponding half-lives computed in the three-dimensional collective space of shape and pa...
Applications of mean-field plus nearest-orbit pairing interaction model to well-deformed nuclei
Chen Yu Yan
2002-01-01
An exactly solvable mean-field plus nearest-orbit pairing model for describing the well-deformed nuclei is adopted for study of the nuclei in rare-earth and actinide regions. Binding energies and pairing excitation energies of sup 1 sup 5 sup 8 sup - sup 1 sup 7 sup 1 Er, sup 1 sup 6 sup 0 sup - sup 1 sup 7 sup 8 Yb, sup 1 sup 7 sup 0 sup - sup 1 sup 8 sup 3 Hf, sup 2 sup 2 sup 6 sup - sup 2 sup 3 sup 4 Th, sup 2 sup 3 sup 0 sup - sup 2 sup 4 sup 0 U and sup 2 sup 3 sup 6 sup - sup 2 sup 4 sup 3 Pu isotopes are calculated and compared with the corresponding experimental results
Cluster mean-field theory study of J1-J2 Heisenberg model on a square lattice.
Ren, Yong-Zhi; Tong, Ning-Hua; Xie, Xin-Cheng
2014-03-19
We study the spin-1/2 J1-J2 Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size L to infinity, we obtain accurate phase boundaries J(c1)(2) ≈ 0.42 (between the Néel antiferromagnetic phase and non-magnetic phase), and J(c2)(2) ≈ 0.59 (between non-magnetic phase and the collinear antiferromagnetic phase). Our results support the second-order phase transition at J(c1)(2) and the first-order one at J(c2)(2). For the spin-anisotropic J1-J2 model, we present its finite temperature phase diagram and demonstrate that the non-magnetic state is unstable towards the first-order phase transition under intermediate spin anisotropy.
Electronic structure of CeRu4Sn6: a density functional plus dynamical mean field theory study
Wissgott, Philipp; Held, Karsten
2016-01-01
The Kondo system CeRu4Sn6 shows a strong anisotropy in its electric, optic and magnetic properties. We employ density functional theory plus dynamical mean field theory and show that the predominant Ce-f state has total angular moment J = 5 / 2 and z-component mJ = ± 1 / 2 in agreement with recent X-ray absorption experiments. There is also an admixture of mJ = ± 3 / 2 which is reduced in favor of mJ = ± 1 / 2 with the onset of the Kondo effect. Even though CeRu4Sn6 has the direct gap of a Kondo insulator through most of the Brillouin zone it remains weakly metallic. This is because of (i) a band crossing in the z-direction and (ii) a negative indirect gap.
Gukelberger, Jan; Hafermann, Hartmut
2016-01-01
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). It can address the full range of interactions, the lowest order theory is asymptotically exact in both the weak- and strong-coupling limits, and the technique naturally incorporates long-range correlations beyond the reach of current cluster extensions to 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 Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We use benchmarking against numerically exact Diagrammatic Determin...
Bai, Hong-Bo; Zhang, Zhen-Hua; Li, Xiao-Wei
2016-11-01
Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations. Supported by NSFC (11465001,11275098, 11275248, 11505058,11165001) and Natural Science Foundation of Inner Mongolia of China (2016BS0102)
Li, Peng; Su, Haibin; Dong, Hui-Ning; Shen, Shun-Qing
2009-08-12
We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interactions J(1) and third-nearest-neighbor interactions J(3) by means of Schwinger-boson mean-field theory. By setting an antiferromagnetic J(3) and varying J(1) from positive to negative values, we disclose the low-temperature features of its interesting incommensurate phase. The gapless dispersion of quasiparticles leads to the intrinsic T(2) law of specific heat. The magnetic susceptibility is linear in temperature. The local magnetization is significantly reduced by quantum fluctuations. We address possible relevance of these results to the low-temperature properties of NiGa(2)S(4). From a careful analysis of the incommensurate spin wavevector, the interaction parameters are estimated as J(1)≈-3.8755 K and J(3)≈14.0628 K, in order to account for the experimental data.
Bensadiq, A.; Zaari, H.; Benyoussef, A.; El Kenz, A.
2016-09-01
Using the density functional theory, the electronic structure; density of states, band structure and exchange couplings of Tb Ni4 Si compound have been investigated. Magnetic and magnetocaloric properties of this material have been studied using Monte Carlo Simulation (MCS) and Mean Field Approximation (MFA) within a three dimensional Ising model. We calculated the isothermal magnetic entropy change, adiabatic temperature change and relative cooling power (RCP) for different external magnetic field and temperature. The highest obtained isothermal magnetic entropy change is of -14.52 J kg-1 K-1 for a magnetic field of H=4 T. The adiabatic temperature reaches a maximum value equal to 3.7 K and the RCP maximum value is found to be 125.12 J kg-1 for a field magnetic of 14 T.
Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi
2016-10-01
Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.
Institute of Scientific and Technical Information of China (English)
CHEN Jin-Gen; ZHOU Xing-Fei; WANG Kun; MA Guo-Liang; TIAN Wen-Dong; ZUO Jia-Xu; MA Chun-Wang; CHEN Jin-Hui; YAN Ting-Zhi; SHEN Wen-Qing; CAI Xiang-Zhou; WANG Ting-Tai; MA Yu-Gang; REN Zhong-Zhou; FANG De-Qing; ZHONG Chen; WEI Yi-Bin; GUO Wei
2004-01-01
@@ A candidate for proton halo nucleus 23Al is investigated based on the constrained calculations in the framework of the deformed relativistic mean field (RMF) model with the NL075 parameter set. It is shown by the constrained calculations that the ground state of 23Al has a large deformation that corresponds to the prolate shape. With that large deformation, the non-constrained RMF calculation predicts that there appears an inversion between the 2s1/2 [211] and 1d5/2 [202] shells. The valence proton of 23Al is weakly bound and occupies 2s1/2 [211] and 1d5/2 [202] with the weights of 56% and 29%, respectively. The calculated RMS radius for matter is in agreement with the experimental one. It is also predicted that the difference between the proton RMS radius and the neutron one is very large. This suggests that there exists a proton halo in 23Al.
Abaimov, Sergey G.; Akhatov, Iskander S.
2016-09-01
In this study, we apply the mean-field approach to the three-dimensional damage phenomena. The model approximates a solid as a polycrystalline material where grains are assumed isotropic. While the stiffness properties are considered homogeneous, the heterogeneous distribution of grains' strengths provides the quenched statistical variability generating non-thermal fluctuations in the ensemble. Studying the statistical properties of the fluctuations, we introduce the concept of susceptibility of damage. Its divergence in the vicinity of the point of material failure can be treated as a catastrophe predictor. In accordance with this criterion, we find that damage growth in reality is much faster than it could be expected from intuitive engineering considerations. Also, we consider avalanches of grain failures and find that due to the slowing down effect the characteristic time of the relaxation processes diverges in the vicinity of the point of material failure.
Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model
Yucesoy, Burcu; Katzgraber, Helmut G.; Machta, Jonathan
2013-03-01
The three and four-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states. J. M. and B. Y. are supported in part by the NSF (Grant No. DMR-0907235 and DMR-1208046).
Energy Technology Data Exchange (ETDEWEB)
Ku, Wai Lim; Girvan, Michelle; Ott, Edward [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742 (United States)
2015-12-15
In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.
Pietracaprina, Francesca; Ros, Valentina; Scardicchio, Antonello
2016-02-01
In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-body) or many-body localized phase. This approximation, which consists of summing over the amplitudes of only the shortest paths in the locator expansion, is known to overestimate the critical value of the disorder which determines the onset of the localized phase. Nevertheless, the results provided by the approximation become more and more accurate as the local coordination (dimensionality) of the graph, defined by the hopping matrix, is made larger. In this sense, the forward approximation can be regarded as a mean-field theory for the Anderson transition in infinite dimensions. The sum can be efficiently computed using transfer matrix techniques, and the results are compared with the most precise exact diagonalization results available. For the Anderson problem, we find a critical value of the disorder which is 0.9 % off the most precise available numerical value already in 5 spatial dimensions, while for the many-body localized phase of the Heisenberg model with random fields the critical disorder hc=4.0 ±0.3 is strikingly close to the most recent results obtained by exact diagonalization. In both cases we obtain a critical exponent ν =1 . In the Anderson case, the latter does not show dependence on the dimensionality, as it is common within mean-field approximations. We discuss the relevance of the correlations between the shortest paths for both the single- and many-body problems, and comment on the connections of our results with the problem of directed polymers in random medium.