hamiltonians: Topics by WorldWideScience.org

Hamiltonian formulation of the N=1 D=10 supergravity coupled to super Yang-Mills theory

The systems for which the algebra of gauge transformations in the lagrangian formalism is closed, are considered. The hamiltonian BRST charge and the BRST-invariant hamiltonian are found explicitly. Their expansions in powers of the ghost variables contain, in general, an infinite number of terms. (orig.).

1991-11-01

Vacuum structures in Hamiltonian light-front dynamics

The authors derive in full details the Hamiltonian formulation of the N = 1D = 10 supergravity coupled to super Yang-Mills theory. In particular, they present the explicit form of the first class constraints and compute the constraints gauge algebra.

1988-01-01

Rotational band-structures in transitional odd-A nuclei

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic nonperturbative approximations to quantum field theories. The authors investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meets all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. Relations are exhibited of the Hamiltonian to the nontrivial vacuum structure. 30 refs.

1994-03-01

Minimal Polynomials of Some Matrices Via Quaternions

... deformed nuclei eigenvalues even-odd nuclei gold 195 hamiltonians iridium

Collective model for the odd-mass transitional nucleus "1"8"7Ir

This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete determination of the Jordan structure of skew-Hamiltonian matrices and the computation of the Cayley transform are given. Some new classes of matrices are uncovered, whose behaviour insofar as minimal polynomials are concerned, is remarkably similar to those of skew-Hamiltonian and Hamiltonian matrices. The main technique is the invocation of the associative algebra isomorphism between the tensor product of the quaternions with themselves and the algebra of real $4\\times 4$ matrices.

2010-01-01

A new algebraic technique for polynomial-time computing the number modulo 2 of Hamiltonian decompositions and similar partitions of a graph's edge set

... collective model hamiltonians iridium 187 matrix elements nuclear cores

1976-06-15

The canonical form of the Rabi hamiltonian

In Graph Theory a number of results were devoted to studying the computational complexity of the number modulo 2 of a graph's edge set decompositions of various kinds, first of all including its Hamiltonian decompositions, as well as the number modulo 2 of, say, Hamiltonian cycles/paths etc. While the problems of finding a Hamiltonian decomposition and Hamiltonian cycle are NP-complete, counting these objects modulo 2 in polynomial time is yet possible for certain types of regular undirected graphs. Some of the most known examples are the theorems about the existence of an even number of Hamiltonian decompositions in a 4-regular graph and an even number of such decompositions where two given edges e and g belong to different cycles (Thomason, 1978), as well as an even number of Hamiltonian cycles passing through any given edge in a regular odd-degreed graph ...

2010-01-01

The quasimolecular model in transitional nuclei

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.

1996-01-01

Solution of Bohr's collective Hamiltonian for transitional odd-mass nuclei

A review is made of some recent developments in the application of the Bohr Hamiltonian to transitional nulcei. The primary concern is to understand the advantages and limitations inherent to the basic model and its many variants. (author).

Conformal field theories via Hamiltonian reduction

A numerically feasible method, based on the use of deformed phonons, is developed for the diagonalization of the collective quadrupole Hamiltonian for a system with an odd particle coupled to an anharmonic even core. Examples: the transition from prolate to oblate via #gamma#-unstable shapes and furthermore the hsub(9/2) spectra of the nuclei "1"8"7Ir and "1"9"7Tl. (Auth.).

Bender-Dunne Orthogonal Polynomials, Quasi-Exact Solvability and Asymptotic Iteration Method for Rabi Hamiltonian

Constraining the SL(3) WZW-model we construct a reduced theory which is invariant with respect to the new chiral algebra W_3"2. This symmetry is generated by the stress-energy tensor, two bosonic currents with spins 3/2 and the U(1) current. We conjecture a Kac formula that describes the highly reducible representation for this algebra. We also discuss the quantum Hamiltonian reduction for the general type of constraints that leads to the new extended conformal algebras. (orig.).

1991-01-01

Isomorphisms of quantizations via quantization of resolutions

We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method (AIM). The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. We show (i) that orthogonal polynomials are generated from the upper limit (i.e., truncation limit) of polynomial solutions deduced from AIM, and (ii) prove to have nonpositive norm. (authors)

2011-08-01

Asymptotics and Hamiltonians in a First order formalism

In this paper we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations of Kleinian resolutions obtained by three different constructions are isomorphic to each other. The constructions are via symplectic reflection algebras, quantum Hamiltonian reduction, and W-algebras. Next, we prove that parabolic W-algebras in type A are isomorphic to quantum Hamiltonian reductions associated to quivers of type A. Finally, we show that the symplectic reflection algebras for wreath-products of the symmetric group and a Kleinian group are isomorphic to certain quantum Hamiltonian reductions. Our results involving W-algebras are new, while for those dealing with symplectic reflection algebras we just give new proofs. A key ingredient in our proofs is the study of ...

2010-01-01

Spin operator matrix elements in the quantum Ising chain: fermion approach

We consider 4-dimensional space-times which are asymptotically flat at spatial infinity and show that, in the first order framework, action principle is well-defined \\emph{without the need of infinite counter terms.} It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy-momentum and angular momentum of the space-time. We address the subtle but important problems that arise because of logarithmic translations and super-translations both in the Langrangian and Hamiltonian frameworks. As a forthcoming paper will show, the treatment of higher dimensions is considerably simpler. Our first order framework also suggests a new direction for generalizing the spectral action of non-commutative geometry.

2008-01-01

Quantum theory of the interaction of Josephson junctions with non-classical microwaves

Using some modification of the standard fermion technique we derive factorized formula for spin operator matrix elements (form-factors) between general eigenstates of the Hamiltonian of quantum Ising chain in a transverse field of finite length. The derivation is based on the approach recently used to derive factorized formula for Z_N-spin operator matrix elements between ground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrable chiral Potts quantum chain. The obtained factorized formulas for the matrix elements of Ising chain coincide with the corresponding expressions obtained by the Separation of Variables Method.

2010-01-01

Description of odd-A nuclei in the Pt region in the interacting boson-fermion model

We present a study of the interaction between Josephson junctions in circular superconducting rings and non-classical microwaves, treating both quantum mechanically. A Hamiltonian that describes both inductive and capacitive coupling between the two systems is derived within the external field approximation. Other Hamiltonians which go beyond the external field approximation, and describe explicitly the interaction of the quantum circuit that produces the non-classical microwaves with the Josephson junction circuit, are also presented. A comparison between current experiments which use classical electromagnetic fields and the proposed experiments that use non-classical microwaves, is made. (orig.) With 6 figs., 32 refs.

1997-01-01

Description of odd-A nuclei in the Pt region in the interacting boson-fermion model

Properties of unique parity states in odd-proton (/sub 77/Ir, /sub 79/Au) and odd-neutron nuclei (/sub 78/Pt) are investigated in the framework of the interacting boson-fermion approximation model. The core (boson)-particle (fermion) interaction is represented by a quadrupole-quadrupole interaction and an exchange term, which takes into account the effects of the Pauli exclusion principle. The even-even core nucleus is described in terms of the IBA-1 hamiltonian. The change in the properties of the corresponding odd-A nuclei can be interpreted in terms of a transition of the core hamiltonian between the O(6) and SU(3) limiting cases.

1982-05-03

A Hamiltonian Formulation of the BKL Conjecture

Properties of unique parity states in odd-proton (_7_7Ir, _7_9Au) and odd-neutron nuclei (_7_8Pt) are investigated in the framework of the interacting boson-fermion approximation model. The core (boson)-particle (fermion) interaction is represented by a quadrupole-quadrupole interaction and an exchange term, which takes into account the effects of the Pauli exclusion principle. The even-even core nucleus is described in terms of the IBA-1 hamiltonian. The change in the properties of the corresponding odd-A nuclei can be interpreted in terms of a transition of the core hamiltonian between the O(6) and SU(3) limiting cases. (orig.).

Relativistic corrections to the spectra and radiative transitions in quarkonia

The Belinskii, Khalatnikov and Lifshitz conjecture \\cite{bkl1} posits that on approach to a space-like singularity in general relativity the dynamics are well approximated by `ignoring spatial derivatives in favor of time derivatives.' In \\cite{ahs1} we examined this idea from within a Hamiltonian framework and provided a new formulation of the conjecture in terms of variables well suited to loop quantum gravity. We now present the details of the analytical part of that investigation. While our motivation came from quantum considerations, thanks to some of its new features, our formulation should be useful also for future analytical and numerical investigations within general relativity.

2011-01-01

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An Algebraic Approach to the Evolution of Emittances upon Crossing the Linear Coupling Difference Resonance

The author calculated the wavefunctions and the energy-spectra of c bar c and b bar b bound systems using the Hamiltonian proposed by Gupta, Radford and Repko (GRR). He writes the GRR Hamiltonian as H = H_o + H', where H_o includes the kinetic energy terms and the most dominant terms in the Hamiltonian. H' includes among other things the spin-spin, spin-orbit and the tensor terms in the Hamiltonian. The eigenvalue problem of H_o is solved by the variational method which makes use of a trial wave-function with eleven parameters. H' is then treated in the first order perturbation theory. The energy-spectra agree very well with experimental data. He also calculated the E1 and the M1 decay rates of these quarkonia. With relativistic corrections, the E1 transitions agree better with experiment. The dominant relativistic correction comes from the relativistic modification of the wave-function. The M1 ...

Gauge invariant perturbation theory in spatially homogeneous cosmology

One of the hallmarks of linear coupling is the resonant exchange of oscillation amplitude between the horizontal and vertical planes when the difference between the unperturbed tunes is close to an integer. The standard derivation of this phenomenon (known as the difference resonance) can be found, for example, in the classic papers of Guignard [1, 2]. One starts with an uncoupled lattice and adds a linear perturbation that couples the two planes. The equations of motion are expressed in hamiltonian form. As the difference between the unperturbed tunes approaches an integer, one finds that the perturbing terms in the hamiltonian can be divided into terms that oscillate slowly and ones that oscillate rapidly. The rapidly oscillating terms are discarded or transformed to higher order with an appropriate canonical transformation. The resulting approximate hamiltonian gives equations of motion that clearly exhibit the exchange ...

Dissipation and entropy production in open quantum systems

The perturbations of the L.R.S. class A spatially homogeneous spacetimes are treated using Hamiltonian methods in conjunction with techniques from the theory of Lie group harmonic analysis. These latter techniques lead to a simple way of handling any set of tensor equations on these background spacetimes which has the same symmetry group as the space-time metric. Once this approach is developed, the Hamiltonian formulation is used to recover in a clean way the Bonanos equations for the perturbations of the perfect fluid models of the class of spacetimes under consideration. The conserved quantities associated with the four-dimensional symmetry group are evaluated and their role in the linearized Hamiltonian dynamics is discussed. The time-dependent linear canonical transformation of the linearized vacuum gravitational phase space adapted to Moncrief's gauge invariant decomposition is described in general for these models ...

Two-boson algebra and quantum computing with Josephson-like systems

A microscopic description of an open system is generally expressed by the Hamiltonian of the form: H{sub tot} = H{sub sys} + H{sub environ} + H{sub sys-environ}. We developed a microscopic theory of entropy and derived a general formula, so-called 'entropy-Hamiltonian relation' (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by H{sub sys-environ} for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space L := H x H-tilde, where H denotes the ordinary Hilbert space while H-tilde the tilde Hilbert space conjugates to H. We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained ...

2010-11-01

Quantum adiabatic theorem for chemical reactions and systems with time-dependent orthogonalization

Our investigation concerns the class of Josephson-like systems, sharing the same nonlinear Hamiltonian. Among the latter a Josephson junction with an external biasing circuit is considered. We diagonalize the fully nonlinear Hamiltonian (in the superconductive regime of the junction) in the Fock space of the TBHA (two-boson Heisenberg algebra) and prove that such algebra leads quite naturally to the theoretical realization of codewords and logical operators: the codewords are defined as the even and odd coherent states of the TBHA, while the logical operators are expressed in terms of operators in the same algebra. Our theoretical construction corresponds to a continuous variable quantum computation scheme; the continuous variables are identified in terms of the physical operators of the junction. The link between this scheme and the technique of fermionization of bosonic systems is also discussed.

2005-12-01

Field theory description of neutrino oscillations

A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the oscillating Schwinger Hamiltonian to establish the relationship between the internal (due to time-dependent eigenfunctions) and external (due to time-dependent Hamiltonian) time scales. We prove that this relationship needs to be taken as an independent quantum adiabatic approximation criterion. We give four examples, including logical expositions based on the spin-1/2 two-level system to address the gapped and gapless (due to energy level crossings) systems, as well as to understand how does this theorem allows one to study dynamical systems such as chemical reactions.

2011-01-01

Bianchi type-IX electromagnetic universes

We review various field theory approaches to the description of neutrino oscillations in vacuum and external fields. First we discuss a relativistic quantum mechanics based approach which involves the temporal evolution of massive neutrinos. To describe the dynamics of the neutrinos system we use exact solutions of wave equations in presence of an external field. It allows one to exactly take into account both the characteristics of neutrinos and the properties of an external field. In particular, we examine flavor oscillations an vacuum and in background matter as well as spin flavor oscillations in matter under the influence of an external electromagnetic field. Moreover we consider the situation of hypothetical nonstandard neutrino interactions with background fermions. In the case of ultrarelativistic particles we reproduce an effective Hamiltonian which is used in the standard quantum mechanical approach for the description of neutrino oscillations. The ...

2010-01-01

Bianchi type-IX electromagnetic universes

The dynamical effects of spatially homogeneous electromagnetic fields on anisotropic Bianchi type-IX models are studied. The Lagrangians and Hamiltonians affecting the evolution of anisotropy (including the gravitational and electromagnetic potentials) are obtained for very general spatially homogeneous metrics by means of the Arnowitt-Deser-Misner Hamiltonian formalism. For models having diagonal metrics an exact solution for the electromagnetic fields is obtained. This solution allows a qualitative solution for the gravitational variables. The total solution is similar to that of Brill. For Bianchi type-IX models having symmetric and general metrics, a discussion of the qualitative behavior of the universe point under the influence of the above potentials is given. In particular, it is shown that in some cases the presence of the electromagnetic potential inhibits some types of singularities.

1984-01-15

Marsden-Ratiu reduction and W_3"2 algebra

Loop quantum cosmology of Bianchi type IX models

The W_3"2 algebra is deduced by the Marsden-Ratiu reduction in the bi-Hamiltonian framework proposed by Magri et al and compared with the usual derivations via the Drinfeld-Sokolov formalism. It is observed that the choice of A in the first Poisson tensor must be different for W_3"2 algebra. (orig.).

1997-01-01

Landau-Ginzburg method applied to finite fermion systems: Pairing in nuclei

The loop quantum cosmology 'improved dynamics' of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.

2010-08-15

Integrability and symmetric spaces

Given the spectrum of a Hamiltonian, a methodology is developed which employs the Landau-Ginsburg theory for characterizing phase transitions in infinite systems to identify phase transition remnants in finite fermion systems. As a first application of our approach we discuss pairing in finite nuclei. (orig.)

2005-09-01

Energy flux operator, current conservation and the formal Fourier's law

It is shown that a sufficient condition for a model describing the motion of a particle on a coset space to possess a Fundamental Poisson bracket Relation, and consequently charges in involution, is that it must be a symmetric space. The conditions, a Hamiltonian, or any functions of the canonical variables, has to satisfy in order to commute with these charges, are studied. It is show that, for the case of the noncompact symmetric spaces, these conditions lead to an algebraic structure which lays an important role in the construction of conserved quantities.

1989-01-01

Electron impact excitation of lithium-like iron

By revisiting previous definitions, we show that one can define an energy current operator that satisfies the continuity equation for a general Hamiltonian in one dimension. This expression is useful for studying electronic, phononic and photonic energy flow in linear systems and in hybrid structures. The definition allows us to deduce the necessary conditions that result in current conservation for general-statistics systems. The discrete form of the Fourier's law of heat conduction naturally emerges in the present definition.

2009-01-16

Computing quantum eigenvalues made easy

Calculations of total and angle-differential excitation cross sections for the electron impact excitation of lithium-like iron were performed with the R-matrix formulation. The alignments of the excited states 1s{sup 2}np {sup 2}P{sub 3/2} are also presented for n=3 and 4 along with the angular photon distribution from these states to the ground state. Relativistic effects were included in the present calculations by the Breit-Pauli Hamiltonian.

1996-05-01

Chaotic behaviour in higher-order gravity theories

An extremely simple and convenient method is presented for computing eigenvalues in quantum mechanics by representing position and momentum operators in matrix form. The simplicity and success of the method is illustrated by numerical results concerning eigenvalues of bound systems and resonances for Hermitian and non-Hermitian Hamiltonians as well as driven quantum systems. Various MATLAB program codes are listed. (author)

2002-07-01

Chaotic behaviour in higher-order gravity theories

We show that the chaotic dynamical behaviour displayed by diagonal Bianchi type IX metrics in general relativity does not occur on approach to the singularity in higher-order lagrangian theories of gravity. However, chaotic behaviour does occur in the more general non-diagonal type IX models in these theories. An interpretation of these results in terms of the hamiltonian potential picture of the type IX evolution is given. (orig.).

1989-11-30

Adiabatic quantum computing with phase modulated laser pulses

The superspin approach to a disordered quantum wire in the chiral-unitary symmetry class with an arbitrary number of channels

Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language. (letter to the editor)

2005-09-23

The quantum Zeno paradox revisited: the time evolution for a two-level system interacting with a reservoir

We use a superspin Hamiltonian defined on an infinite-dimensional Fock space with positive definite scalar product to study localization and delocalization of noninteracting spinless quasiparticles in quasi-one-dimensional quantum wires perturbed by weak quenched disorder. Past works using this approach have considered a single chain. Here, we extend the formalism to treat a quasi-one-dimensional system: a quantum wire with an arbitrary number of channels coupled by random hopping amplitudes. The computations are carried out explicitly for the case of a chiral quasi-one-dimensional wire with broken time-reversal symmetry (chiral-unitary symmetry class). By treating the space direction along the chains as imaginary time, the effects of the disorder are encoded in the time evolution induced by a single site superspin (non-Hermitian) Hamiltonian. We obtain the density of states near the band center of an infinitely long quantum wire. Our results ...

2009-01-01

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T=(5/2) "2"7Na from "1"4C+"1"4C, and the N=16 shell gap

We revisited the quantum Zeno paradox, which claims that a generic quantum system prepared in a state which is not an eigenstate of the Hamiltonian operator and is continuously observed never decays. Since any perfectly isolated quantum system always interact with a vacuum field, we analyze the possibility of using this fact to solve the above mentioned conceptual problem. Therefore we discuss a two-level system or qubit-Bose field interaction Hamiltonians. We consider the quantum dynamics of this two-level system, prepared in the excited state interacting with a Bose field prepared in the Poincare invariant vacuum state. Using a first-order approximation in time-dependent perturbation theory, we evaluate the probability of spontaneous decay of the two-level system driven by the vacuum field. This probability is evaluated for a finite time interval. Using the standard argument to obtain the quantum Zeno paradox, we consider N measurements where ...

2006-12-15

Shell-model predictions for electromagnetic properties of N = 50 nuclei

For the first time a comprehensive level and decay scheme has been obtained for a T=(5/2) nucleus in the s-d shell ("2"7Na) by using a radioactive beam and target. Particle-#gamma# and p-#gamma#-#gamma# coincidences were measured following the "1"4C("1"4C,p#gamma#)"2"7Na reaction at E_l_a_b=22 MeV. The results do not support an inversion of the 2s_1_/_2 and 1d_5_/_2 orbitals, as previously proposed for T_z#>=#3, but they do suggest an increased N=16 gap between the 2s_1_/_2 and 1d_3_/_2 orbitals due to the neutron excess. A consistent interpretation of the level scheme in terms of the s-d shell model using the USD Hamiltonian is possible below 4 MeV, but differences increase at higher excitation energies. Another interpretation is that the influences of both the p_1_/_2 and f_7_/_2 intruder orbitals increase simultaneously with increasing T, an effect not included in the USD Hamiltonian.

2002-05-01

Path integral of the hydrogen atom, Jacobi's principle of least action and one-dimensional quantum gravity

Predictions for E2, M1, and M4 transition rates and moments, together with examples of transition-charge densities, are presented for states of N = 50 nuclei. These predictions are based on one-body spectroscopic amplitudes obtained from the wave functions of a new N = 50 shell-model calculation which incorporates the 0f/sub 5/2/, 1p/sub 3/2/, 1p/sub 1/2/, and 0g/sub 9/2/ single-particle orbits and an empirically determined effective Hamiltonian for this space. The predictions are compared with experimental data, first in order to evaluate how well the model space, as applied by this Hamiltonian, accounts for observations, and then to assess the importance of configurations excluded from the model space and to determine the values of the operator renormalizations (effective charges and effective g factors) which optimally map the theoretical results onto the corresponding experimental values.

1988-12-01

Noncommutative Bloch analysis of Bochner Laplacians with nonvanishing gauge fields

A path integral evaluation of the Green's function for the hydrogen atom initiated by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville type. The basic dynamical principle involved is identified as Jacobi's principle of least action for given energy which is reparametrization invariant, and thus the appearance of a gauge freedom is naturally understood. The separation of variables in the operator formalism corresponds to a choice of gauge in the path integral, and the Green's function is shown to be gauge independent if the operator ordering is properly taken into account. Unlike the conventional Feynman path integral, which deals with a space-time picture of particle motion, the path integral on the basis of Jacobi's principle sums over orbits in space. We illustrate these properties by evaluating an exact path integral of the Green's function for the hydrogen atom in parabolic ...

EPR, optical, infrared and Raman studies of VO"2"+ ions in polyvinylalcohol films

Given an invariant gauge potential and a periodic scalar potential \\tilde{V} on a Riemannian manifold \\tilde{M} with a discrete symmetry group \\Gamma, consider a \\Gamma-periodic quantum Hamiltonian \\tilde{H}=-\\tilde{\\Delta}_{B}+\\tilde{V} where \\tilde{\\Delta}_{B} is the Bochner Laplacian. Both the gauge group and the symmetry group \\Gamma can be noncommutative, and the gauge field need not vanish. On the other hand, \\Gamma is supposed to be of type I. To any unitary representation \\Lambda of \\Gamma one relates a Hamiltonian H^{\\Lambda}=-\\Delta_{B}^{\\Lambda}+V on M=\\tilde{M}/\\Gamma where V is the projection of \\tilde{V} to M. We describe a construction of the Bloch decomposition of \\tilde{H} into a direct integral whose components are H^{\\Lambda}, with \\Lambda running over the dual space \\hat{\\Gamma}. The evolution operator and the resolvent decompose correspondingly. Conversely, given \\Lambda\\in\\hat{\\Gamma}, one can ...

2010-01-01

Crystal-field excitations in the visible spectrum of Nd{sub 2}CuO{sub 4}

Electron paramagnetic resonance (EPR), optical, infrared and Raman spectral studies have been carried out on vanadyl ions doped in polyvinylalcohol (PVA) films. The spin-Hamiltonian parameters (g and A) and the molecular orbital coefficients (#beta#_2"*"2 and k) have been evaluated. The values of spin-Hamiltonian parameters confirm that the vanadyl ions are present in PVA films as VO"2"+ molecular ions in an octahedral site with a tetragonal compression (C_4_v). The temperature variation EPR studies reveal that the variation of number of spins with temperature is in accordance with Boltzmann law. It is interesting to observe that the variation of susceptibility with temperature obeys Curie-Weiss law. The FT-IR and FT-Raman spectrum exhibits few bands, which are attributed to O-H, C-H, C-C and C-O groups of stretching and bending vibrations. The optical absorption spectrum exhibits two bands, which are assigned to "2B_2_g->"2B_1_g and ...

2007-01-15

Crystal-field excitations in the visible spectrum of Nd_2CuO_4

A phenomenological simulation was carried out for 41 experimental crystal-field (CF) levels within the {sup 4}I{sub 9/2-15/2}, {sup 4}F{sub 3/2-9/2}, {sup 4}S{sub 3/2} and {sup 2}H{sub 9/2} J manifolds, including the available infrared (IR) data up to {approx}15 000 cm{sup -1} for the Nd{sup 3+} ions in the Nd{sub 2}CuO{sub 4} single crystals. The CF Hamiltonian for the tetragonal C{sub 4v} symmetry was diagonalized together with the free-ion Hamiltonian in a basis that spans the entire 4f{sup 3} configuration. A rms error of 9 cm{sup -1} between the calculated and experimental energy level schemes was obtained. A comparison of the spectra in the visible region between the insulating Nd{sub 2}CuO{sub 4} and the metallic Nd{sub 2-x}Ce{sub x}CuO{sub 4}, allowed identifying the absorption bands associated with the development of the charge-doping induced local structural distortions in the superconducting regime.

2004-07-14

Continuous and Discrete (Classical) Heisenberg Spin Chain revised

A phenomenological simulation was carried out for 41 experimental crystal-field (CF) levels within the "4I_9_/_2_-_1_5_/_2, "4F_3_/_2_-_9_/_2, "4S_3_/_2 and "2H_9_/_2 J manifolds, including the available infrared (IR) data up to #approx#15 000 cm"-"1 for the Nd"3"+ ions in the Nd_2CuO_4 single crystals. The CF Hamiltonian for the tetragonal C_4_v symmetry was diagonalized together with the free-ion Hamiltonian in a basis that spans the entire 4f"3 configuration. A rms error of 9 cm"-"1 between the calculated and experimental energy level schemes was obtained. A comparison of the spectra in the visible region between the insulating Nd_2CuO_4 and the metallic Nd_2_-_xCe_xCuO_4, allowed identifying the absorption bands associated with the development of the charge-doping induced local structural distortions in the superconducting regime.

2004-07-14

Weyl gauge, Schwinger terms and bosonization in light-front field theory

The Hamiltonian structure of the Classical Heisenberg Spin Chain (CHSC) has been extensively studied by a number of authors. First of all, we mention Faddeev and Thaktadjan that, in their fundamental monograph "Hamiltonian Methods in the Theory of Soliton", elucidate the main properties of both continuous and (semi-)discrete models. An analysis of the su(2) continuous model in the context of the reduction theory for Poisson Nijenhuis manifolds was performed by Magri et al in1985, while through a similar approach a few years later Ragnisco and Santini analyzed the discrete case. In the meantime, among the condensed matter community there was some renewed interest on Potts models, sort of generalized spin chains where the relevant field variable is allowed to take values at the $N^{th}$ roots of unity. The proper theoretical setting for such models, at least at the classical level, would have been the extension to NxN matrices of the approach ...

2006-01-01

The full order weak schemes of the Langevin simulations

A systematic study of non-perturbative quantum structure of the massive light-front Schwinger model and QED(3+1) in the continuum formulation is outlined. The light-front Hamiltonian and field algebra are derived in the Weyl gauge using the Dirac-Bergmann constrained quantization. Unitary transformation to the light-cone gauge representation is performed and the gauge-invariant fermi field is constructed. The importance of the Schwinger term in the current-current commutation relations for the derivation of the fermionic vacuum structure and bosonization in two dimensions is indicated.

2002-04-01

The electronic structure of organometallic complexes of the f elements XXV. Crystal field splitting pattern of the anionic complex [Cp_3Pr. NCS]"-

New partial differential equations (PDEs) for the full order weak schemes of the Langevin simulations are formulated. They are solved recursively in full order series solutions with respect to {radical}(t) (the full order weak Taylor schemes). Arbitrariness involved in the solutions is analyzed and clarified in detail. Specific solutions within some orders are presented as examples of the weak Taylor schemes. These PDEs and their solutions will serve for further developments of efficient higher order Runge-Kutta-like schemes. The similar formulation is possible for the imaginary time Hamiltonian evolution kernels as well. (orig.). 9 refs.

1998-04-01

Optimal oscillation-center transformations

The absorption, emission and magnetic circular dichroism spectra of the anionic complex (Cp_3Pr. NCS)"- were measured at room and low temperatures. On the basis of these spectra the electronic structure in the f-f range could be derived. The parameters of an empirical Hamiltonian were fitted to the experimentally determined crystal field splitting pattern. Compared with the previously examined neutral Cp_3 Pr.X complexes the quadratic crystal field parameter B_0"2 is considerably reduced.

Optimal generation planning for a thermal system with pumped-storage based on analytical production costing model

A variational principle is proposed for defining that canonical transformation, continuously connected with the identity transformation, which minimizes the residual, coordinate-dependent part of the new Hamiltonian. The principle is based on minimization of the mean-square generalized force. The transformation reduces to the action-angle transformation in that part of the phase space of an integrable system where the orbit topology is that of the unperturbed system, or on primary KAM surfaces. General arguments in favor of this definition are given, based on Galilean invariance, decay of the Fourier spectrum, and its ability to include external fields or inhomogeneous systems. The optimal oscillation-center transformation for the physical pendulum, or particle in a sinusoidal potential, is constructed.

1984-08-01

Optimal generation planning for a thermal system with pumped-storage based on analytical production costing model

This paper presents a new algorithm for the optimal long-range generation planning for a thermal system with pumped-storage plants. The algorithm is based upon the analytical production costing model developed under the assumption of Gaussian probabilistic distribution of random load fluctuations and plant outages. The optimization problem consists of the master problem to determine the annual investment, and the pumped-storage subproblem to determine the optimal pumped-storage operation. The master problem is formulated as a Hamiltonian minimization problem, and the pumped-storage subproblem is solved using the concept of peak-shaving operation on the original load curve.

1986-01-01

Magnetic properties of CeRh_2Si_2 and CePd_2Si_2 single crystals

1987-05-01

Higher spin symmetries and w_#infinity# algebra in the conformal affine Toda model

Single-crystalline CeRh_2Si_2 and CePd_2Si_2 were grown by the Czochralsky pulling method and the temperature dependence of magnetic susceptibility was investigated. The crystalline electric field (CEF) states in each compound were determined by considering the tetragonal CEF Hamiltonian with mean-field approximation. Interactions between Ce"3"+ ion and the surrounding ligands in CeRh_2Si_2 turned out to be strong and highly anisotropic in comparison to CePd_2Si_2. (orig.)

1998-01-01

Determination of Scaling Parameter and Dynamical Resonances in Complex-Rotated Hamiltonian II: Numerical Analysis

As recently shown the conformal affine Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (w_#infinity# algebra) is established. (orig.).

1992-05-01

Computer simulation of interface potentials: Towards a first principle description of complex interfaces?

This paper is concerned with the determination of a unique scaling parameter in complex scaling analysis and with accurate calculation of dynamics resonances. In the preceding paper we have presented a theoretical analysis and provided a formalism for dynamical resonance calculations. In this paper we present accurate numerical results for two non-trivial dynamical processes, namely, models of diatomic molecular predissociation and of barrier potential scattering for resonances. The results presented in this paper confirm our theoretical analysis, remove a theoretical ambiguity on determination of the complex scaling parameter, and provide an improved understanding for dynamical resonance calculations in rigged Hilbert space.

2008-03-15

British Library Electronic Table of Contents (United Kingdom)

We discuss the feasibility of a hierarchical protocol whereby the description and prediction of adsorbed fluids in confined systems at the mesoscopic scale is achieved by use of interface potentials that are obtained from raw molecular simulation data. Starting from a microscopic description of a fluid?s interface on a flat substrate, we attempt to extract the minimum information that is required in order to predict the behavior of that fluid at larger length scales from coarse grained surface Hamiltonians. A critical assessment of this procedure hinges on controversial aspects of wetting behavior and more generally on the meaning of metastability and instability of thermodynamic systems.

2011-01-01

Cocycles, the descent equations, and the Virasoro algebra

Bianchi type IX cosmological models with homogeneous spinor fields

A generalization of Faddeev's group cohomology applicable to diffeomorphism groups is presented. This cohomology is used to calculate the two cocycles associated with a projective representation of the diffeomorphism group on the circle. The group version of the n"3 term descends from a three dimensional Chern-Simons action based on the diffeomorphism group. The group version of the n term arises from an ambiguity in the descent equations of adding closed but not exact forms and is trivial only if its appropriately normalized coefficient is quantized to be an integer. Finally, a hamiltonian interpretation of global anomalies is suggested in the language of group cohomology. (orig.).

1990-05-01

1 2 3 4 5 6 7

Bianchi type IX cosmological models with homogeneous spinor fields

The diagonal and symmetric Bianchi type IX models are coupled to a homogeneous spinor field. An action for the combined fields is constructed, where the orthonormal basis used is given explicitly in terms of the metric. This allows one to vary the action with respect to the metric and the spinor fields only. Next, a Hamiltonian formulation is given, and a qualitative solution for the problem is presented. We also show that the k = +1 FRW (Friedmann--Robertson--Walker) model is not compatible with a homogeneous spinor field, while the more complicated models are.

1981-03-01

On foundation of the generalized Nambu mechanics

cap alpha. decay of fission isomers

We outline basic principles of a canonical formalism for the Nambu mechanics - a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of a Nambu bracket, which generalizes the Poisson bracket - a 'binary'' operation on classical observables on the phase space - to the 'multiple' operation of higher order n#>=#3. Nambu dynamics is described by the phase flow given by Nambu-Hamilton equations of motion - a system of ODE's which involves n-1 'Hamiltonians'. We introduce the fundamental identity for the Nambu bracket - a generalization of the Jacobi identity - as a consistency condition for the dynamics. We show that Nambu bracket structure defines a hierarchy of infinite families of 'subordinated' structures of lower order, including Poisson bracket structure, which satisfy certain matching conditions. The notion of Nambu bracket enables us to define Nambu-Poisson manifolds - phase spaces for the ...

Variational derivation of improved KP-type of equations

The theory of ..cap alpha.. decay in first-order perturbation theory is presented. The theory is designed for a strongly deformed nucleus in an isomeric state which changes its deformation dynamically through decay from a very deformed to an almost spherical shape. It is shown that other channels are not coupled to the ..cap alpha.. channel in first-order perturbation theory. The collective degrees of freedom of the daughter nucleus are described by shape vibrational states, eigenstates of a Hamiltonian whose potential has two minima. The parent nucleus is described by dynamically coupling the vibrational degrees of freedom to the ..cap alpha..-particle motion and also taking rotations into account. The ..cap alpha.. particle is taken to be a point-like particle. The theory is applied to the ..cap alpha.. decay of the isomeric state of /sub 95//sup 242/Am.

1984-10-01

The program HAMILTON for the analytic solution of the equations of motion through fifth order

The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg-de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 ) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.

2010-01-04

The planetary N-body problem: symplectic?foliation, reductions and invariant tori

HAMILTON is a computer code performing all algebraic operations necessary for an analytic determination of the power series of the Hamiltonian equations of motion in the electromagnetic fields with at least one plane of symmetry. It is written entirely in FORTRAN in order to achieve fast machine performance, a requirement which is essential due to the complexity of the equations of motion in higher orders. HAMILTON is considerably faster than common more versatile formula manipulators and uses noticeably less storage. Besides the mere solution of the equations of motion, HAMILTON also produces FORTRAN code compatible with the program COSY 5.0 allowing the computation of matrix elements of individual optical elements and their concatenation. The produced FORTRAN code is highly optimized and on average requires only 30% of the execution time of a handwritten comparable code. (orig.).

British Library Electronic Table of Contents (United Kingdom)

The 6n-dimensional phase space of the planetary (1+n)-body problem (after the classical reduction of the total linear momentum) is shown to be foliated by symplectic leaves of dimension (6n?2) invariant for the planetary Hamiltonian Formula Not Shown . Such foliation is described by means of a new global set of Darboux coordinates related to a symplectic (partial) reduction of rotations. On each symplectic leaf Formula Not Shown has the same form and it is shown to preserve classical symmetries. Further sets of Darboux coordinates may be introduced on the symplectic leaves so as to achieve a complete (total) reduction of rotations. Next, by explicit computations, it is shown that, in the reduced settings, certain degeneracies are removed. In particular, full torsion is checked both in the ...

2011-01-01

The kernel polynomial method for non-orthogonal electronic structure calculations

The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for \\hat gl(m|n)

The Kernel Polynomial Method (KPM) has been successfully applied to tight-binding electronic structure calculations as an O(N) method. Here the authors extend this method to nonorthogonal basis sets with a sparse overlap matrix S and a sparse Hamiltonian H. Since the KPM method utilizes matrix vector multiplications it is necessary to apply S{sup {minus}1}H onto a vector. The multiplication of S{sup {minus}1} is performed using a preconditioned conjugate gradient method and does not involve the explicit inversion of S. Hence the method scales the same way as the original KPM method, i.e. O(N), although there is an overhead due to the additional conjugate gradient part. The authors show an application of this method to defects in a titanate/platinum interface and to a large scale electronic structure calculation of amorphous diamond.

1996-11-01

Tensor network states and geometry

We prove an analogue of the MacMahon Master Theorem for the right quantum superalgebras. In particular, we obtain a new and simple proof of this theorem for the right quantum algebras. In the super case the theorem is then used to construct higher order Sugawara operators for the affine Lie superalgebra \\hat gl(m|n) in an explicit form. The operators are elements of a completed universal enveloping algebra of \\hat gl(m|n) at the critical level. They occur as the coefficients in the expansion of a noncommutative Berezinian and as the traces of powers of generator matrices. The same construction yields higher Hamiltonians for the Gaudin model associated with the Lie superalgebra gl(m|n).

2009-01-01

Strong coupled organic microcavities

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure ...

2011-01-01

Pseudospin symmetry and the relativistic harmonic oscillator

Strong coupled organic-inorganic microcavities device has been realized and studied. One of the two cavities contains an organic thin film of tetrakis(4-methoxyphenyl)porphyrin, whereas the other microcavity is a dielectric structure coupled to the organic one by means of a LiF/ZnS Bragg mirror. Reflectivity spectra show the presence of two well defined cavity dips. We observe an energy splitting of the two cavity-modes. Despite only one cavity contains the active layer, the photoluminescence spectra display two peaks at the same energy of the reflectivity dips. These observations indicate the strong coupling of the two cavities. The comparison of the diagonalized effective Hamiltonian with the observed resonances further confirms the strong coupling.

2010-02-01

Pinned fluxons in a Josephson junction with a finite-length inhomogeneity

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar, $S$, and a vector, $V$, quadratic potentials in the radial coordinate, as well as a tensor potential, $U$, linear in $r$. Setting either or both combinations $\\Sigma=S+V$ and $% \\Delta=V-S$ to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the non-relativistic limit and the case $\\Sigma=0$, for which pseudospin symmetry is exact. We also show that the case $U=\\Delta=0$ is the most natural generalization of the non-relativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the ...

2004-01-01

Optimized pulse sequences for the suppression of decoherence in quantum information

We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or - for instance by varying the length of the inhomogeneity - may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity - a relation we determine explicitly. In combination with continuation arguments and Sturm-Liouville theory, we determine the ...

2011-01-01

Neutrinos and long-range weak forces in cosmology

The dynamical decoupling (DD) aims at suppressing the decoherence by means of coherent control pulses. Even if devices exist where instantaneous pulses are an adequate approximation, experimentally a finite duration #tau#_p and a bounded amplitude are inevitable. They are the cause of additional errors which can be corrected by designing the pulse shape appropriately. The new pulse has the overall effect of an ideal, instantaneous pulse with the advantage of decoupling the spin (or qubit) from the bath up to the order O(#tau#_p"3). The limitation of the no-go theorem for #pi# pulses is avoided. Hence, the Uhrig sequence (UDD), originally thought for ideal #pi# pulses, works also for bounded control Hamiltonians. Numerical simulations show that concatenated sequences of real pulses are effective against general decoherence.

2010-03-21

Mixmaster: fact and belief

The Lorentz and coordinate covariant calculus of spinors in Riemannian spacetime, which is the mathematical model for the description of the quantum mechanics of elementary particles with spin interacting with the classical gravitation field, is explored. The Dirac equation describing the interaction of neutrinos with the gravitational fields of the Robertson-Walker cosmological world models is separated, and the spectrum of eigenfunctions and eigenvalues for particular choices of the set of quantum numbers is given explicitly for the k = 0 and k = +1 models, although only the radial equations determining the final quantum number are given for the k = -1 model. The mathematical theory of the motion of a perfect fluid whose elements interact via long-range neutrino-exchange forces, as well as gravitationally, is developed. The formalism for calculating, by calculating the Bogoliubov transformation of the Fock space operators that instantaneously diagonalize their quantized field ...

Magnetic properties of CeRh{sub 2}Si{sub 2} and CePd{sub 2}Si{sub 2} single crystals

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. Surprisingly few facts are known about the 'Mixmaster' dynamics of these models, while at the same time most of the commonly held beliefs are rather vague. In this paper, we use Mixmaster facts as a base to build an infrastructure that makes it possible to sharpen the main Mixmaster beliefs. We formulate explicit conjectures concerning (i) the past asymptotic states of type IX solutions and (ii) the relevance of the Mixmaster/Kasner map for generic past asymptotic dynamics. The evidence for the conjectures is based on a study of the stochastic properties of this map in conjunction with dynamical systems techniques. We use a dynamical systems formulation, since this approach has so far been the only successful path to obtain theorems, but we also make comparisons with the 'metric' and ...

2009-04-07

Investigation of the electronic structure of base adducts derived from tris(#eta#"5-cyclopentadienyl)-lanthanide(III) and related compound types

Single-crystalline CeRh{sub 2}Si{sub 2} and CePd{sub 2}Si{sub 2} were grown by the Czochralsky pulling method and the temperature dependence of magnetic susceptibility was investigated. The crystalline electric field (CEF) states in each compound were determined by considering the tetragonal CEF Hamiltonian with mean-field approximation. Interactions between Ce{sup 3+} ion and the surrounding ligands in CeRh{sub 2}Si{sub 2} turned out to be strong and highly anisotropic in comparison to CePd{sub 2}Si{sub 2}. (orig.) 10 refs.

1998-01-01

Interplay between coherence and decoherence in LHCII photosynthetic complex

The purpose of this work is the elucidation of the f"n electronic structure of neutral mono base adducts derived from tris(#eta#"5-cyclopentadienyl)-lanthanide(III) (Cp_2Ln). The available data on related compounds like bis adducts and anionic mono adducts of the same moiety was also analyzed. The first aim was to derive the experimental crystal field splitting pattern from optical, magnetooptical and magnetochemical measurements and to reproduce it using an empirical Hamiltonian operator. The eigenvalues and eigenvectors obtained in this manner were used for a quantitative interpretation of the magnetochemical, EPR- and NMR-spectroscopic properties. For the latter subject it was necessary to develop an own procedure for the NMR analysis of paramagnetic compounds. This method is based on factor analysis and as demonstrated in the second part of this work, is clearly superior to all previous procedures. (orig.).

IBM-2 calculation of band mixing in "1"3"2Ba

This paper investigates the dynamics of excitonic transport in photocomplex LHCII, the primary component of the photosynthetic apparatus in green plants. The dynamics exhibits a strong interplay between coherent processes mediated by the excitonic Hamiltonian, and incoherent processes due to interactions with the environment. The spreading of the exciton over a single monomer is well described by a proper measure of delocalization that allows one to identify two relevant time scales. An exciton initially localized in one chromophore first spreads coherently to neighboring chromophores. During this initial coherent spreading, quantum effects such as entanglement play a role. As the effects of a decohering environment come into play, coherence and decoherence interact to give rise to efficient and robust excitonic transport, reaching a maximum efficiency at the levels of decoherence found in physiological conditions. We analyze the efficiency for different possible ...

2011-01-01

Free field resolution for nonunitary representations of N=2 SuperVirasoro

The band crossing in "1"3"2Ba has been investigated by using the interacting boson model. A broken neutron pair has been coupled to a collective boson core. The boson-fermion interaction hamiltonian contains terms which can transform a boson into a pair of quasiparticles and vice versa. The parameters were partly determined by fitting the collective states of "1"3"2","1"3"4Ba and the yrast states of "1"3"1Ba. The energy backbending has been satisfactorily reproduced. Good agreement of the electromagnetic moments has been reached. The structure of the wave functions has been discussed. (author)

1999-12-04

1 2 3 4 5 6 7

Fermion-fermion and boson-boson amplitudes: surprising similarities

We study N=2 SuperVirasoro SCFT for the generic value of the central charge. The main tool is the nonstandard bosonisation suggested in \\ref\\rRoz{L. Rozansky a letter to M. Bershadsky, 1989}, \\ref\\rSeBGR{B. Gato-Rivera, A. Semikhatov Phys. Letts. B293 (1992) 72},\\ref\\rBLNW{M. Bershadsky, W. Lerche, D. Nemeshansky, N. Warner N=2 Extended superconformal structure of Gravity and W Gravity coupled to Matter HUTP-A034/92}. The free field resolutions for the irreducible representations are obtained; the characters of these representations are computed. The quantum hamiltonian reduction from the Kac-Moody $\\hat{sl}_k(2|1)$ to N=2 $SVir$ is constructed.

1993-01-01

Electronic structures of organometallic complexes of f elements. XLIV. Parametrization of the crystal field splitting pattern of [(MeCp)_3PrCl]"-

Amplitudes for fermion-fermion, boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the model is the Weinberg's 2(2j+1)-component formalism for describing a particle of spin j. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the basis of the Hamiltonian formulation of quantum field theory on the mass hyperboloid, p_0^2 - p^2=M^2, proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of T-matrices for the fermion case and the boson case. However, certain differences are found. Possible physical applications are discussed.

2007-01-01

Electronic structures of highly symmetrical compounds of f elements. XXXI. Simulation of the crystal field splitting pattern of (THF)_3Li(#mu#-Cl)Nd[N(SiMe_3)_2]_3

The absorption and magnetic circular dichroism spectra of [N(n-Bu)_4]"+[(MeCp)_3PrCl]"- dissolved in 2-MeTHF were measured at room and at low temperatures. On the basis of these spectra the crystal field splitting pattern could be derived. The parameters of an empirical Hamiltonian were fitted to the energies of 42 levels to give an r.m.s. deviation of 23 cm"-"1. From the crystal field parameters obtained the crystal field strength of the ligand collective was estimated. Compared with neutral Cp_3Pr circle B complexes the crystal field strength of the anionic [(MeCp)_3PrCl]"- moiety is unusually low. (orig.)

1998-07-24

Effective equations of motion for constrained quantum systems: A study of the Bianchi I loop quantum cosmology

The absorption spectra of an unoriented single crystal of the title compound (1) have been measured at room and at low temperatures. Assuming a similar sequence of crystal field (CF) levels as for the previously analyzed Nd[N(SiMe_3)_2]_3 (2) a truncated CF splitting pattern is derived from the spectra obtained. The parameters of an empirical Hamiltonian are fitted to the energies of 71 levels to give an r.m.s. deviation of 24.2 cm"-"1. The parameters obtained are compared with those of 2 and Nd[N(SiMe_3)_2]_3(CNC_6H_1_1)_2 (3). The observed trends of CF parameters are consistent with the results of simple model calculations in the framework of the angular overlap model. (orig.)

1998-07-24

Dynamical Quasi-Stationary States in a system with long-range forces

A new mathematical framework is formulated to derive the effective equations of motion for the constrained quantum system which possesses an internal clock. In the realm close to classical behavior, the quantum evolution is approximated by a finite system of coupled but ordinary differential equations adhered to the weakly imposed Hamiltonian constraint. For the simplified version of loop quantum cosmology in the Bianchi I model with a free massless scalar filed, the resulting effective equations of motion affirm the bouncing scenario predicted by the previous studies: The big bang singularity is resolved and replaced by the big bounces, which take place up to three times, once in each diagonal direction, whenever the directional density approaches the critical value in the regime of Planckian density. It is also revealed that back-reaction arises from the quantum corrections and modifies the precise value of the directional density at the bouncing epoch. ...

2008-01-01

Dielectronic recombination into excited levels of Ne-like titanium from F-like low-lying states

The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the critical point. In particular, when the particles are prepared in a ``water bag'' initial state, the relaxation to equilibrium is very slow. In the transient time the system lives in a dynamical quasi-stationary state and exhibits anomalous (enhanced) diffusion and L\\'evy walks. In this paper we study temperature and velocity distribution of the quasi-stationary state and we show that the lifetime of such a state increases with N. In particular when the $N\\to \\infty$ limit is taken before the $t \\to \\infty$ limit, the results obtained are different from the expected canonical predictions. This scenario seems to confirm a recent conjecture proposed by C.Tsallis.

2001-01-01

Crystal Field Studies on MgGa2O4:Ni2+

The energy levels, wavelengths, oscillator strengths, Auger rates and level-to-level dielectronic recombination rate coefficients describing dielectronic recombination into excited levels of Ne-like titanium from F-like low-lying states are calculated. Our calculations are based on Dr. R.D. Cowan's semi-relativistic mass-velocity and Darwin corrections are included in the Hamiltonian, and the distorted-wave model is used for the calculation of free electron wavefunctions. In order to set the recombination rate coefficients on a level by level basis, in a manner compatible with detailed level population kinetics modelling of highly-stripped ions in plasma, the dielectronic recombination rate coefficients as a function of free electron temperatures are given in an analytical form, which is not only very convenient in practice, but also hopefully accurate compared with the exactly calculated numerical results. (orig.).

1993-01-01

BPS Condensates, Matrix Models and Emergent String Theory

The energy levels scheme of octahedrally coordinated Ni2+ ion in single crystal, powder nano-single crystal, ceramics and glass-ceramics of MgGa2O4 host matrix, has been calculated in the exchange charge model of crystal field. The parameters of the crystal field acting on the Ni2+ ion are calculated from the crystal structure data, after optimization of the geometry of the system. The energy level schemes have been calculated by diagonalization of the crystal field Hamiltonian of this system. The obtained results were compared with experimental data; a good agreement were demonstrated, which confirm the validity of the model and used method.

2010-08-04

Algebraic structures and eigenstates for integrable collective field theories

A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS condensates" which, in certain limit, have a dual description as null geodesics on the $S^5$. In the gauge theory, the condensate is similar to a representative of the chiral ring and it is described by a background of commuting matrices. Excitations around these condensates correspond to excitations around this background and take the form of ``string bits" which are dual to the "giant magnons" of Hofman and Maldacena. In fact, the matrix model approach gives a {\\it quantum} description of these string configurations and explains why the infinite momentum limit suppresses the quantum effects. This method allows, not only to derive part of the classical sigma model Hamiltonian of the dual string (in the infinite momentum ...

2007-01-01

Renormalization-group theory of structural phase transitions in A-15 compounds

Conditions for the construction of polynomial eigen-operators for the Hamiltonian of collective string field theories are explored. Such eigen-operators arise for only one monomial potential v(x)=#mu#x"2 in the collective field theory. They form a w_#infinity#-algebra isomorphic to the algebra of vertex operators in 2d gravity. Polynomial potentials of orders only strictly larger or smaller than 2 have no non-zero-energy polynomial eigen-operators. This analysis leads us to consider a particular potential #nu#(x)=#mu#x"2+g/x"2. A Lie algebra of polynomial eigen-operators is then constructed for this potential. It is a symmetric 2-index Lie algebra, also represented as a subalgebra of U(sl(2)). (orig.).

1992-02-01

Science.gov (United States)

Hamiltonians of Landau-Ginzburg-Wilson type are constructed for order parameters which are bases for certain high-dimensional irreducible or physically irreducible representations in A-15 structure. These are all the representations with wave vectors ?, X, and R and encompass cases of dimension 1, 2, 3, 4, and 6. A renormalization-group analysis was performed on each new distinct Hamiltonian using the Wilson-Fisher "? expansion" method to order ?, in order to determine fixed points and stability, and critical exponents. For representations of R wave-vector symmetry, only the two-dimensional R(1) has a stable fixed point and may produce a second-order phase transition; for all other R wave vector representations, fluctuations prevent second-order transition. No X point representation gives a second-order transition. Representations at ? which are permitted to be second order by "Landau theory" remain so in this analysis. Generally, if the ...

1978-06-01

A systematic analysis of the spectra of trivalent actinide chlorides in D_3_h site symmetry

A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations

The optical spectra of actinide ions in the compound AnCl_3 and doped into single crystal LaCl_3 were interpreted in terms of transitions within 5f"N configurations. Energy-level calculations were carried out using an effective operator Hamiltonian, the parameters of which were determined by fitting experimental data. Atomic and crystal-field matrices were diagonalized simultaneously assuming an approximate D_3_h site symmetry. The spectroscopic data were taken from the literature but in most cases supplemented by unpublished measurements in absorption and in fluorescence. Spectroscopic data for each ion were analyzed independently, then the model parameters were intercompared and in many cases adjusted such that in the final fitting process the principal interactions showed uniform trends in parameter values with increasing atomic number. Consistent with analyses of the spectra of lanthanide ions in both LaCl_3 and LaF_3, abrupt changes in magnitude of certain ...

1986-08-01

Variational approach to nuclear matter

We present an efficient parallel algorithm and its implementation for computing the diagonal of $H^-1$ where $H$ is a 2D Kohn-Sham Hamiltonian discretized on a rectangular domain using a standard second order finite difference scheme. This type of calculation can be used to obtain an accurate approximation to the diagonal of a Fermi-Dirac function of $H$ through a recently developed pole-expansion technique \\cite{LinLuYingE2009}. The diagonal elements are needed in electronic structure calculations for quantum mechanical systems \\citeHohenbergKohn1964, KohnSham 1965,DreizlerGross1990. We show how elimination tree is used to organize the parallel computation and how synchronization overhead is reduced by passing data level by level along this tree using the technique of local buffers and relative indices. We analyze the performance of our implementation by examining its load balance and communication overhead. We show that our implementation exhibits an excellent ...

2009-09-25

The projector augmented wave method: A fast all-electron procedure for the ab-initio molecular dynamics

We calculated the energies of asymmetric nuclear matter at zero and finite temperatures with the cluster variational method. At zero temperature, the expectation value of the two-body Hamiltonian composed of the kinetic energies and the AV18 two-body forces is calculated with the Jastrow wave function in the two-body cluster approximation. The obtained two-body energy is in good agreement with the result with the Fermi Hypernetted Chain (FHNC) calculation by Akmal et al. The energy caused by the UIX three-body forces is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation point. Furthermore, the parameters included in the three-body energy are readjusted so that the Thomas-Fermi (TF) calculations with use of the obtained energy of nuclear matter reproduce the gross feature of the experimental data on atomic nuclei. The nuclear species in the neutron star crust obtained by the TF calculation are reasonable. The free ...

2010-12-01

The mixmaster universe in Horava-Lifshitz gravity

In this thesis, a new ab-initio method for molecular dynamics within the framework of density functional theory was developed and implemented. It is strongly related to the projector-augmented-wave method (PAW) by P. Bloechl, but also includes elements of a pseudocharge method proposed by M. Weinert for the full-potential linearized augmented plane wave method (FLAPW). Like the FLAPW-method, the PAW-method is an all-electron method. In the later case, the hamiltonian takes quite a simple form similar to the one obtained when using normconserving Kleinman-Bylander-type pseudopotentials or ultrasoft Vanderbilt pseudopotentials. The PAW-method allows for an efficient calculation of systems containing virtually any element of the periodic table, including those which require high numerical effort when treated using normconserving pseudopotentials (e.g. 2p-elements like oxygen or 3d-transitional metals like copper). In addition, a higher accuracy compared to the ...

The mixmaster universe in Horava-Lifshitz gravity

We consider spatially homogeneous (but generally non-isotropic) cosmologies in the recently proposed Horava-Lifshitz gravity and compare them to those of general relativity using Hamiltonian methods. In all cases, the problem is described by an effective point particle moving in a potential well with exponentially steep walls. Focusing on the closed-space cosmological model (Bianchi type IX), the mixmaster dynamics is now completely dominated by the quadratic Cotton tensor potential term for a very small volume of the universe. Unlike general relativity, where the evolution toward the initial singularity always exhibits chaotic behavior with alternating Kasner epochs, the anisotropic universe in Horava-Lifshitz gravity (with parameter lambda > 1/3) is described by a particle moving in a frozen potential well with fixed (but arbitrary) energy E. Alternating Kasner epochs still provide a good description of the early universe for very large E, but the ...

2010-02-21

Study of the electron paramagnetic resonance spectra of Zn(antipyrine)_2(NO_3)_2:VO"2"+

We consider spatially homogeneous (but generally non-isotropic) cosmologies in the recently proposed Horava-Lifshitz gravity and compare them to those of general relativity using Hamiltonian methods. In all cases, the problem is described by an effective point particle moving in a potential well with exponentially steep walls. Focusing on the closed-space cosmological model (Bianchi type IX), the mixmaster dynamics is now completely dominated by the quadratic Cotton tensor potential term for a very small volume of the universe. Unlike general relativity, where the evolution toward the initial singularity always exhibits chaotic behavior with alternating Kasner epochs, the anisotropic universe in Horava-Lifshitz gravity (with parameter #lambda# > 1/3) is described by a particle moving in a frozen potential well with fixed (but arbitrary) energy E. Alternating Kasner epochs still provide a good description of the early universe for very large E, but the evolution ...

2010-02-21

Spectroscopic properties of Er"3"+ ions in cadmium and alkali cadmium borosulphate glasses

In this work, a full ligand-field energy matrix (10x10) diagonalization treatment for 3d"1 ions in tetragonal symmetry is developed on the basis of the two-s.o.-coupling-parameter model. Spin Hamiltonian parameters (g factors g_|_|, g_p_e_r_p_e_n_d_i_c_u_l_a_r and hyperfine structure constants A_|_|, A_p_e_r_p_e_n_d_i_c_u_l_a_r) of the tetragonal V"4"+ center in Zn(antipyrine)_2(NO_3)_2 are calculated from the complete energy matrix diagonalization method and the perturbation theory method. The calculated results from both methods are not only close to each other but also in good agreement with the experimental values. Furthermore, the compressed defect structure of V"4"+ center is discussed.

2010-08-01

Some remarks on the coherent-state variational approach to nonlinear boson models

Spectroscopic properties of Er"3"+ : CBS (CdSO_4 + B_2O_3 and R_2SO_4 + CdSO_4 + B_2O_3, R_2SO_4 = Li_2SO_4.H_2O, Na_2SO_4, K_2SO_4 and Gd_2(SO_4)_3.8H_2O) glasses are reported. The assigned energy level data of Er"3"+(4f"1"1) in these glasses are analysed in terms of a parametrized model Hamiltonian. The standard deviations of the data fits are between 39 and 47 cm"-"1 so that the energy level schemes of the Er"3"+(4f"1"1) ions in borosulphate (CBS) glasses are reasonably well reproduced. Radiative properties for the fluorescent levels of Er"3"+ : CBS glasses are determined by using the Judd-Ofelt theory. The potential laser transitions are identified with the help of predicted radiative properties which are compared and discussed with similar results. (author).

1997-01-01

100

Sequence of Potentials Lying Between the U(5) and X(5) Symmetries

The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial states $|F>$, number-preserving states $|\\xi >$ and Glauber-like trial states $|Z>$ are compared to evidence the specific properties of such schemes. After deriving the Hamiltonian picture relevant to $|Z>$ from that based on $|F>$, the latter is shown to exhibit a Poisson algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the $|Z>$-based picture. Then states $|Z>$ are shown to be a superposition of $\\cal N$-boson states $|\\xi>$ and the similarities/differences of the $|Z>$-based and $|\\xi>$-based pictures are discussed. Finally, after proving that the simple, symmetric state $|\\xi>$ indeed corresponds to a SU(M) coherent state, a dual version of states $|Z>$ and ...

2008-01-01

1 2 3 4 5 6 7

101

Semirelativistic technique for k#centre dot#p calculations: Optical properties of Pd and Pt

Starting from the original collective Hamiltonian of Bohr and separating the beta and gamma variables as in the X(5) model of Iachello, an exactly soluble model corresponding to a harmonic oscillator potential in the beta-variable (to be called X(5)-$\\beta^2$) is constructed. Furthermore, it is proved that the potentials of the form $\\beta^{2n}$ (with n being integer) provide a ``bridge'' between this new X(5)-$\\beta^2$ model (occuring for n=1) and the X(5) model (corresponding to an infinite well potential in the beta-variable, materialized for n going to infinity. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $\\beta^2$, $\\beta^4$, $\\beta^6$, $\\beta^8$, corresponding to E(4)/E(2) ratios of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2) ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this behaviour, as well as about potentials ...

2004-01-01

102

Quarkonia and QGP studies

A semirelativistic two-component extended linear augmented plane-wave k#centre dot#p method is described. In order to ensure a high accuracy of the k#centre dot#p method, it is necessary to include into the radial-basis set, which is used for the augmentation of the plane waves, functions that are neither solutions of the Schrodinger equation nor their energy derivatives. The usual scalar relativistic procedure, which is nonlinear in energy, is not applicable to such basis sets. As an alternative, we suggest an approximation to the Foldy-Wouthuysen Hamiltonian that produces an explicitly Hermitean matrix in the augmented plane wave representation. The technique is applied to the calculation of the full dielectric matrix and optical properties of palladium and platinum metals over the photon energy region up to 100 eV. Special attention is paid to the far ultraviolet absorption by the excitations of semicore Pd 4p and Pt 5p and 4f states. A strong effect of local ...

2001-06-15

103

Particle Swarm Optimization: An efficient method for tracing periodic orbits in 3D galactic potentials

We summarize results of recent studies of heavy quarkonia correlators and spectral functions at finite temperatures from lattice QCD and systematic T-matrix studies using QCD motivated finite-temperature potentials. We argue that heavy quarkonia dissociation shall occur in the temperature range $1.2 \\le T_d/T_c \\le 1.5$ by the interplay of both screening and absorption in the strongly correlated plasma medium. We discuss these effects on the quantum mechanical evolution of quarkonia states within a time-dependent harmonic oscillator model with complex oscillator strength and compare the results with data for $R_{\\rm AA}/R_{\\rm AA}^{\\rm CNM}$ from RHIC and SPS experiments. We speculate whether the suppression pattern of the rather precise NA60 data from In-In collisions may be related to the recently discovered X(3872) state. Theoretical support for this hypothesis comes from the cluster expansion of the plasma Hamiltonian for heavy quarkonia in a strongly ...

2011-01-01

104

On the origin of the unconventional two-hole bound state in the t-J model

We propose the Particle Swarm Optimization (PSO) as an alternative method for locating periodic orbits in a three--dimensional (3D) model of barred galaxies. We develop an appropriate scheme that transforms the problem of finding periodic orbits into the problem of detecting global minimizers of a function, which is defined on the Poincar\\'{e} Surface of Section (PSS) of the Hamiltonian system. By combining the PSO method with deflection techniques, we succeeded in tracing systematically several periodic orbits of the system. The method succeeded in tracing the initial conditions of periodic orbits in cases where Newton iterative techniques had difficulties. In particular, we found families of 2D and 3D periodic orbits associated with the inner 8:1 to 12:1 resonances, between the radial 4:1 and corotation resonances of our 3D Ferrers bar model. The main advantages of the proposed algorithm is its simplicity, its ability to work using function values solely, as ...

2005-01-01

105

On the origin of the unconventional two-hole bound state in the t-J model

We present a description of the ground state and low-lying excited states of two holes in the 4x4 cluster t-J model in terms of a simple model for the motion of a single bipolaron. The existence of short-range antiferromagnetic correlations has been assumed. According to the suggested scenario, the formation of the bipolaron is mediated by the reduction of the magnetic energy in the case of two holes occupying nearest neighbor sites. The relevant part of the Hilbert space consists of wave functions corresponding to holes oscillating around pairs of nearest neighbor sites and trapped in a potential well due to strings of spin defects. Virtual processes which connect these states involve both the kinetic term and the transverse part of the Heisenberg Hamiltonian. Many properties of energy level schemes obtained by numerical diagonalizations such as the sequence of the lowest states for each irreducible representation of the k vector point groups can be reproduced ...

1994-04-01

106

Lattice calculation of nonleptonic charm decays

1993-08-01

107

Holomorphic wave function of the Universe

The decays of charmed mesons into two body nonleptonic final states are investigated. Weak interaction amplitudes of interest in these decays are extracted from lattice four-point correlation functions using a effective weak Hamiltonian including effects to order G{sub f} in the weak interactions yet containing effects to all orders in the strong interactions. The lattice calculation allows a quantitative examination of non-spectator processes in charm decays helping to elucidate the role of effects such as color coherence, final state interactions and the importance of the so called weak annihilation process. For D {yields} K{pi}, we find that the non-spectator weak annihilation diagram is not small, and we interpret this as evidence for large final state interactions. Moreover, there is indications of a resonance in the isospin {1/2} channel to which the weak annihilation process contributes exclusively. Findings from the lattice calculation are compared to ...

1991-11-01

108

Holomorphic wave function of the Universe

The quantum behavior of the vacuum Bianchi type-IX universe with the cosmological constant is investigated in terms of the Ashtekar variables. An exact solution to the quantum Hamiltonian constraint in the holomorphic representation is given. This solution reduces to the Hartle-Hawking wave function in the spatially isotropic sector and extends in the triad representation to the classically forbidden region where the determinant of the spatial metric becomes negative. The analysis of the quantum Robertson-Walker universe indicates that if the superspace is extended to such a classically forbidden region, the holomorphic representation picks up some restricted class of solutions in general. This observation leads to a new ansatz on the boundary condition of the Universe. In particular, the behavior of the Lorentzian and Euclidean WKB orbits corresponding to the solution suggests a new picture on the semiclassical behavior of the quantum Universe: that the Universe ...

1990-10-15

109

High resolution Fourier transform spectroscopy and crystal-field analysis in Tm,Ho:BaY{sub 2}F{sub 8}

110

High resolution Fourier transform spectroscopy and crystal-field analysis in Tm,Ho:BaY_2F_8

A Tm{sup 3+}- Ho{sup 3+} -codoped single crystal of monoclinic BaY{sub 2}F{sub 8} has been characterized by means of high resolution FTIR spectroscopy in the wave number range 2000-24000 cm{sup -1} and in the temperature range 9-300 K. The energy level schemes of the two lanthanide ions as determined by the optical absorption spectra is presented, analyzed, and fitted within a single ion Hamiltonian model. The very small energy separation (about 0.6-1.6 cm{sup -1}) measured between the first and second sublevels of the ground state manifolds for both the ions is in line with the theoretical predictions. The impurity-phonon coupling is put into evidence by the thermally induced line shift and broadening, and by the detection of vibronic replicas of a few lines. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

2005-01-01

111

Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O_2 molecule

A Tm"3"+- Ho"3"+ -codoped single crystal of monoclinic BaY_2F_8 has been characterized by means of high resolution FTIR spectroscopy in the wave number range 2000-24000 cm"-"1 and in the temperature range 9-300 K. The energy level schemes of the two lanthanide ions as determined by the optical absorption spectra is presented, analyzed, and fitted within a single ion Hamiltonian model. The very small energy separation (about 0.6-1.6 cm"-"1) measured between the first and second sublevels of the ground state manifolds for both the ions is in line with the theoretical predictions. The impurity-phonon coupling is put into evidence by the thermally induced line shift and broadening, and by the detection of vibronic replicas of a few lines. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

2005-01-01

112

Full Spin and Spatial Symmetry Adapted Technique for Correlated Electronic Hamiltonians: Application to an Icosahedral Cluster

The linearized-augmented-plane-wave (LAPW) method for thin films is generalized by removing the remaining shape approximation to the potential inside the atomic spheres. A new technique for solving Poisson's equation for a general charge density and potential is described and implemented in the film LAPW method. In the resulting full-potential LAPW method (FLAPW), all contributions to the potential are completely taken into account in the Hamiltonian matrix elements. The accuracy of the method: already well known for clean metal surfaces: is demonstrated for the case of a nearly free (noninteracting) O_2 molecule which is a severe test case of the method because of its large anisotropic charge distribution. Detailed comparisons show that the accuracy of the FLAPW results for O_2 exceeds that of existing state-of-the-art local-density linear-combination-of-atomic-orbitals (LCAO)-type calculations, and that taking the full potential LAPW results as a reference, the ...

113

Entropy, confinement, and chiral symmetry breaking

While dealing with molecular systems, it is highly advantageous to work with a basis set which has definite total spin and also belongs to a definite irreducible representation of its symmetry (point) group. But unfortunately, there hadn't been any general simple technique to deal with the problem, especially when molecule possesses non-Abelian point group symmetry. In a previous paper \\cite{sahoo}, we presented a general technique which is a hybrid method based on Valence Bond basis and the basis of z-component of the total spin. The technique is applicable to all types of point groups and is easy to implement on computer. We illustrated the power of the method by applying it to a molecular magnetic system. Here we extend the method to electronic systems and demonstrate this extended technique by applying it to a model icosahedral half-filled electronic system (12 sites). Reasons we took this model are, its a system with huge Hilbert space (dimension 1,778,966; and we were able to ...

2010-01-01

114

Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology

This paper studies the way in which confinement leads to chiral symmetry breaking (CSB) through a gap equation. We argue that entropic effects cut off infrared singularities in the standard confining effective propagator $1/p^4$, which should be replaced by $1/(p^2+m^2)^2$ for a finite mass $m\\sim K_F/M(0)$ [$M(0)$ is the zero-momentum value of the running quark mass]. Extension of an old calculation of the author yields a specific estimate for $m$. This cutoff propagator shows semi-quantitatively two critical properties of confinement: 1) a negative contribution to the confining potential coming from entropic forces; 2) an infrared cutoff required by gauge invariance and CSB itself. Entropic effects lead to a proliferation of pion branches and a $\\bar{q}q$ condensate, and contribute a negative term $\\sim -K_F/M(0)$ to the effective pion Hamiltonian allowing for a massless pion in the presence of positive kinetic energy and string energy. The resulting gap ...

2010-01-01

115

B-spline methods for radial Dirac equations

The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to three times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest ...

2007-01-01

116

Atomistic computer simulations of FePt nanoparticles. Thermodynamic and kinetic properties

Although B-spline techniques have been used to solve two-point boundary value problems with Dirac Hamiltonians for more than 20 years, the treatment of boundary conditions is still a matter of controversy. Spurious, non-physical, solutions are endemic when boundary conditions are not handled correctly. These pathological problems are absent when traditional finite difference methods are used as in computer packages such as GRASP. Accurate approximation using both finite differences and B-splines depends on controlling local approximation errors, and this common property suggests no a priori reason to suppose that B-spline algorithms should be more prone to generate spurious solutions. The relativistic Bloch operators of [24], when added to the Dirac differential operator, permit the construction of a self-adjoint differential operator for the two-point boundary value problem on a finite interval. Approximate solution of this problem exploiting the properties of ...

2009-03-14

117

Applications of Magnetic PsiDO Techniques to Space-adiabatic Perturbation Theory

In the present dissertation, a hierarchical multiscale approach for modeling FePt nanoparticles by atomistic computer simulations is developed. By describing the interatomic interactions on different levels of sophistication, various time and length scales can be accessed. Methods range from static quantum-mechanic total-energy calculations of small periodic systems to simulations of whole particles over an extended time by using simple lattice Hamiltonians. By employing these methods, the energetic and thermodynamic stability of non-crystalline multiply twinned FePt nanoparticles is investigated. Subsequently, the thermodynamics of the order-disorder transition in FePt nanoparticles is analyzed, including the influence of particle size, composition and modified surface energies by different chemical surroundings. In order to identify processes that reduce or enhance the rate of transformation from the disordered to the ordered state, the kinetics of the ordering ...

2007-12-20

118

Anisotropy in Magnetic Properties and Electronic Structure of Single Crystal LiFePO4

In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic $\\Psi$DO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular example, we extend results of [PST03] to a more general class of magnetic fields: we consider a single particle moving in a periodic potential which is subjectd to a weak and slowly-varying electromagnetic field. In addition to the semiclassical parameter $\\eps \\ll 1$ which quantifies the separation of spatial scales, we explore the influence of additional parameters that allow us to selectively switch off the magnetic field. We find that even in the case of magnetic fields with components in $C_b^{\\infty}(\\R^d)$, e. g. for constant magnetic fields, the results of Panati, Spohn and Teufel hold, i.e. to each isolated family of Bloch bands, there exists an associated almost invariant subspace of $L^2(\\R^d)$ and an effective hamiltonian which generates the dynamics ...

2010-01-01

119

Anisotropic magnetism in hybridizing uranium systems

We report the experimental and theoretical results on the anisotropies in the magnetic properties and x-ray absorption spectra of single-crystal LiFePO4. A mean-field theory is developed to explain the observed strong anisotropies in Lande g-factor, paramagnetic Curie temperature, and effective moment for LiFePO4 single crystals. The values of the in-plane nearest- and next-nearest-neighbor spin exchange (J1 and J2), interplane spin exchange (J{perpendicular}), and single-ion anisotropy (D), obtained recently from neutron scattering measurements, are used for calculating the Curie temperatures with the formulas derived from the mean-field Hamiltonian. It is found that the calculated Curie temperatures match well with that obtained by fitting the magnetic susceptibility curves to the modified Curie-Weiss law. For the polarized Fe K-edge x-ray absorption spectra of single-crystal LiFePO4, a different feature assignment for the 1s4p transition features is proposed and ...

2008-01-01

120

Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation

The isostructural uranium monopnictides and monochalcogenides have become prototype systems in actinide research with respect to their unusual magnetic properties. We have investigated the origins in the electronic structure of the variation in magnetic behavior as the degree of 5f-electron localization changes from localized to itinerant on going up the pnictogen or chalcogen column, thus decreasing the U-U separation. We have applied a synthesis of: (1) A phenomenological theory of orbitally driven magnetic ordering which includes both the hybridization-induced and the RKKY exchange interactions on an equal footing, and (2) Ab initio electronic structure calculations, based on the linear-muffin-tin-orbital method, allowing a first-principles evaluation of the parameters entering the model Hamiltonian. We have investigated systematically characteristic trends and changes of the 5f-state resonance width, the hybridization potential, and the hybridization-induced ...

1 2 3 4 5 6 7

121

Tight-binding Hamiltonians for high-temperature superconductors and applications to coherent-potential-approximation calculations of the electronic properties of La/sub 2-//sub x/Ba/sub x/CuO/sub 4-//sub y/

Kohn-Sham density functional theory is one of the most widely used electronic structure theories. Uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number of basis functions per atom in order to resolve the rapid oscillations of the Kohn-Sham orbitals around the nuclei. Previous attempts to reduce the number of basis functions per atom include the usage of atomic orbitals and similar objects, but the atomic orbitals generally require fine tuning in order to reach the chemical accuracy. We present a novel discretization scheme that adaptively and systematically builds the rapid oscillations of the Kohn-Sham orbitals around the nuclei as well as environmental effects into the basis functions. The resulting basis functions are localized in the real space, and are discontinuous in the global domain. The continuous Kohn-Sham orbitals and the electron density are evaluated from the discontinuous basis functions using the discontinuous ...

2011-01-01

122

Simulation of the experimental crystal field splitting pattern of a mono tetrahydrofuran adduct derived from tris(bis(trimethylsilyl)amido)neodymium(III)

We present accurate tight-binding parametrizations of the first-principles augmented-plane-wave or linear-augmented-plane-wave band structures of LaCuO_3, La_2CuO_4, Ba_2CuO_4, and the high-temperature superconductor YBa_2Cu_3O_7. We discuss the methodology and efficient application of these fits, including as an example our tight-binding coherent-potential-approximation (CPA) calculations of the effects of disorder on the electronic structure of La/sub 2-//sub x/Ba/sub x/CuO/sub 4-//sub y/. Our CPA calculations support the hypothesis of a rigid-band lowering of the Fermi level for La/sub 2-//sub x/Ba/sub x/CuO_4, enhancing the density of states there. However, for La_2BaCuO/sub 4-//sub y/ they yield the interesting result that oxygen vacancies also lower E/sub F/ and raise N(E/sub F/). This is a significant result for the theory of superconductivity in these materials. In addition to CPA calculations, our parametrizations of the band structures should prove to be a useful tool for ...

123

Shell-model calculations for the energy levels of the N=50 isotones with A=80--87

Full text: In case of lanthanide (Ln) compounds the bis(trimethylsilyl)amido (btmsa) ligand is considered as a steric and electronic equivalent of the bis(trimethylsilyl)methanido (btmsm) group . Because of their extreme air and moisture sensitivity the chemistry of Ln(btmsm)_3 is very poor, whereas that of comparatively stable Ln(btmsa)_3 is much more developed. As we wish to extend the chemistry of Ln(btmsm)_3 and plan to derive and to parameterize the crystal field (CF) splitting patterns of the target molecules, it is recommended to study in advance the electronic structures of the corresponding compounds derived from Ln(btmsa)_3 . Beside (btmsa)_3 Nd(m-Cl)Li(THF)_3 a number of mono base adducts [(btmsa)_3 Ln.B] with sterically less demanding bases such as OPPh_3 , NCtBu or CNtBu have been described and were partly structurally characterized. Considering only the immediately coordinating atoms, the effective CF is of C_3_v symmetry. According to recent spectroscopic investigations, ...

1998-10-25

124

Shell-model calculations for the energy levels of the /ital N/=50 isotones with /ital A/=80--87

The detailed features of the calculated energy-level schemes and of the single-particle, orbit-occupancy properties of the low-lying levels of the N=50 isotones "8"0Zn, "8"1Ga, "8"2Ge, "8"3As, "8"4Se, "8"5Br, "8"6Kr, and "8"7Rb are presented and discussed. These results are obtained with a new effective Hamiltonian operator obtained empirically from an iterative fit to experimental energies taken from all experimentally studied (A=82--96) N=50 nuclei. The model space for the calculations consists of active 0f/sub 5/2/, 1p/sub 3/2/, 1p/sub 1/2/, and 0g/sub 9/2/ proton orbits relative to a nominal "7"8Ni core. This space is truncated internally by restricting the number of particles excited from the negative-parity orbits into the g/sub 9/2/ orbit to be no greater than four. The typical structures predicted for these lighter N=50 isotones are found to be dominated by well-mixed combinations of fp-orbit configurations, with the g/sub 9/2/ orbit playing a minor role in ...

9110-01-01

125

Luminescence and laser transition studies of Dy3+:K-Mg-Al fluorophosphate glasses

The detailed features of the calculated energy-level schemes and of thesingle-particle, orbit-occupancy properties of the low-lying levels of the/ital N/=50 isotones /sup 80/Zn, /sup 81/Ga,/sup 82/Ge, /sup 83/As, /sup 84/Se,/sup 85/Br, /sup 86/Kr, and /sup 87/Rb arepresented and discussed. These results are obtained with a new effectiveHamiltonian operator obtained empirically from an iterative fit to experimentalenergies taken from all experimentally studied (/ital A/=82--96)/ital N/=50 nuclei. The model space for the calculations consists ofactive 0/ital f//sub 5/2/, 1/ital p//sub 3/2/,1/ital p//sub 1/2/, and 0/ital g//sub 9/2/ proton orbits relativeto a nominal /sup 78/Ni core. This space is truncated internally byrestricting the number of particles excited from the negative-parity orbitsinto the /ital g//sub 9/2/ orbit to be no greater than four. The typicalstructures predicted for these lighter /ital N/=50 isotones are found tobe dominated by well-mixed ...

1989-07-01

126

Crystal field analysis of the energy level structure of Cs{sub 2}NaAlF{sub 6}:Cr{sup 3+}

Dysprosium ion doped fluorophosphate glasses with compositions of PKMAFDy: (56-x/2) P2O5+17K2O+8Al2O3+(15-x/2)MgO+4AlF3+xDy2O3 (x=0.01, 0.05, 0.1, 1.0 and 2.0 mol%) have been prepared by melt quenching technique and are characterized by optical absorption, emission spectra and fluorescence lifetime measurements. The observed bands in the absorption spectrum are analysed by using free-ion Hamiltonian (HFI) model. The Judd-Ofelt (JO) analysis has been performed and the intensity parameters (??, ?=2, 4, 6) have been evaluated that are used to predict radiative properties. From emission spectra, the effective bandwidth (??eff) and the stimulated emission cross-section (?(?p)) were evaluated. The fluorescence decay from the 4F9/2 level of Dy3+ ions have been measured by monitoring the intense 4F9/2#->#6H13/2 transition (573 nm). The lifetimes (?) are found to decrease with increasing concentration due to concentration quenching. The decay curves are single ...

2009-02-28

127

Crystal field analysis of the energy level structure of Cs2NaAlF6:Cr3+

An analysis of the energy level structure of Cr{sup 3+} ions in Cs{sub 2}NaAlF{sub 6} crystal is performed using the exchange charge model (ECM) together with the crystal field analysis/microscopic spin Hamiltonian (CFA/MSH) computer package. Utilizing the crystal structure data, our approach enables modelling of the crystal field parameters (CFPs) and thus the energy level structure for Cr{sup 3+} ions at the two crystallographically inequivalent sites in Cs{sub 2}NaAlF{sub 6}. Using the ECM initial adjustment procedure, the CFPs are calculated in the crystallographic axis system centred at the Cr{sup 3+} ion at each site. Additionally the CFPs are also calculated using the superposition model (SPM). The ECM and SPM predicted CFP values match very well. Consideration of the symmetry aspects for the so-obtained CFP datasets reveals that the latter axis system matches the symmetry-adapted axis system related directly to the six Cr-F bonds well. Using the ECM ...

2006-06-07

128

Analysis of the optical spectra and paramagnetic susceptibility of DyOF

An analysis of the energy level structure of Cr3+ ions in Cs2NaAlF6 crystal is performed using the exchange charge model (ECM) together with the crystal field analysis/microscopic spin Hamiltonian (CFA/MSH) computer package. Utilizing the crystal structure data, our approach enables modelling of the crystal field parameters (CFPs) and thus the energy level structure for Cr3+ ions at the two crystallographically inequivalent sites in Cs2NaAlF6. Using the ECM initial adjustment procedure, the CFPs are calculated in the crystallographic axis system centred at the Cr3+ ion at each site. Additionally the CFPs are also calculated using the superposition model (SPM). The ECM and SPM predicted CFP values match very well. Consideration of the symmetry aspects for the so-obtained CFP datasets reveals that the latter axis system matches the symmetry-adapted axis system related directly to the six Cr-F bonds well. Using the ECM predicted CFPs as an input for the CFA/MSH ...

2006-06-07

129