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Zhur. Eksptl'. i Teoret. Fiz.

IMPULSE EXCITATION OF A SYSTEM OF WEAKLY INTERACTING PARTICLES

U. Kh. Kopvillem

Published May 1, 1962• 0 citations
OpenAlex

Abstract

The equations of motion of macroscopic quantities characterizing the nonequilibrium state of a many-particle system with a discrete energy spectrnm and subjected to the strong action of a pulsed generator are deduced by applying the Schroedinger equation for the system. Simple algorithms for the operator transformations related to impluse excitation are derived. The general properties of pulsed generators and of physical systems leading to the appearance of oscillating and stationary response signals of the excited particle system are established. As an illustration of application of the general relations, the nonequilibrium states of electron and nuclear spin systems produced by cross magneto-acoustic excitation are investigated. The prospects of developing pulse techniques for investigating electric and orbital magnetic moment systems are discussed. (auth)

Related papers

Inductions and Echoes in Systems with Unequidistant Spectrum

V. R. Nagibarov, N. K. Solovarov

Abstract A general method is developed of calculation of response signals of N‐particle systems with an unequidistant spectrum to pulse action of coherent physical fields resonant for any transition of the system. The case of a particle system where each particle has three energy levels E1 < E2 < E3 is analysed. It is shown that if such a system is subjected to pulse action of two generators exciting transitions E1 ⟷ E2 and E2 ⟷ E3 at initial time and at time τ to pulse action of a generator with frequency ω31 = h−1 (E3 — E1), the system generates induction and echo signals with power proportional to N2 at all possible transitions. Echo signals arise at times (1 + ϵ) τ, 2 τ, and (1 + 1/ϵ) τ after the first pulse, where ϵ = E2 — E1/E3 — E2. The observed responses may have a physical nature which is both identical with the excitation and different from it. Supplements are given by which the responses of particle systems may be calculated to a series of pulses different from those considered here. When ϵ →1 the results transform to the case of equidistant spectrum.

physica status solidi (b)•Jan 1, 1970•9 citations

GENERALIZED KINETIC AND EVOLUTION EQUATIONS IN THE APPROACH OF THE NONEQUILIBRIUM STATISTICAL OPERATOR

A. L. KUZEMSKY

The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyze and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrödinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analyzed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.

arXiv:cond-mat/0502194•International Journal of Modern Physics B•Mar 10, 2005•39 citations

GENERALIZED KINETIC AND EVOLUTION EQUATIONS IN THE APPROACH OF THE NONEQUILIBRIUM STATISTICAL OPERATOR

A. L. Kuzemsky

The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyze and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrödinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analyzed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.

•Jan 1, 2005•32 citations

Theory of Many-Particle Systems. I

Paul C. Martin, Julian Schwinger

This is the first of a series of papers dealing with many-particle systems from a unified, nonperturbative point of view. It contains derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers. In a short introduction the general method of approach is summarized, and its relationship to other field-theoretic problems indicated. In the second section the macroscopic properties of the spectra of many-particle systems are described. Asymptotic evaluations are performed which characterize these macroscopic features in terms of intensive parameters, and the relationship of these parameters to thermodynamics is discussed. The special characteristics of the ground state are shown to follow as a limiting case of the asymptotic evaluations. The third section is devoted to the time-dependent field correlation functions, or Green's functions, which describe the microscopic behavior of a multiparticle system. These functions are defined, and related to intensive macroscopic variables when the energy and number of particles are large. Spectral representations and other properties of various one-particle Green's functions are derived. In the fourth section the treatment of non-equilibrium processes is considered. As a particular example, the electromagnetic properties of a system are expressed in terms of the special two-particle Green's function which describes current correlation. The discussion yields specifically a fluctuation-dissipation theorem, a sum rule for conductivity, and certain dispersion relations. The fifth section deals with the differential equations which determine the Green's functions. The boundary conditions that characterize the Green's function equations are exhibited without reference to adiabatic decoupling. A method for solving the equations approximately, by treating the correlations among successively larger numbers of particles, is considered. The first approximation in this sequence is shown to yield a generalized Hartree-like equation. A related, but rigorous, identity for the single-particle Green's function is then derived. A second approximation, which takes certain two-particle correlations into account, is shown to produce various additional effects: The interaction between particles is altered in a manner characterized by the intensive macroscopic parameters, and the modification and spread of the energy-momentum relation come into play. In the final section compact formal expressions for the Green's functions and other physical quantities are derived. Alternative equations and systematic approximations for the Green's functions are obtained.

Physical Review•Sep 15, 1959•1,813 citations

SINGLE PARTICLE EXCITATIONS AND SUPER-FLUIDITY IN SYSTEMS CONSISTING OF FERMI PARTICLES WITH AN ARBITRARY INTERACTION APPLICATION TO THE NUCLEUS

A.B. Migdal

An equation set describtng single particle excitations for excitation energies which are small compared with the chemical potential of the system can be obtained by investigating the analytical properties of the Green's functions and taking into account pair correlation. The equations are valid for an arbitrary interaction law. Equations are derived which describe the excited states of a system with a finite number of particles with an accuracy to terms of the order of N/sup -//sup 1//sup ///sup 3/ It is indicated how the results can be applied to real nuclei. (auth)

Zhur. Eksptl'. i Teoret. Fiz.•Feb 1, 1961•0 citations

Excitation Operators and Intrinsic Hamiltonians

ROBERT K. NESBET

An operator A† that satisfies [H, A†] = h/ωA† converts a stationary-state eigenfunction of the Hamiltonian H into another eigenfunction with energy eigenvalue increased by h/ω. Such operators describe collective excitations of many-particle systems, and their properties can be used to construct an intrinsic Hamiltonian that is dynamically independent of the collective degrees of freedom, without introducing subsidiary conditions. The procedure developed by Lipkin, valid when h/ω is real and positive, is extended to make possible the construction of an intrinsic Hamiltonian when h/ω vanishes and A† is Hermitian, and also when h/ω is complex. The nuclear cranking model is shown to be a special case of the proposed general method for vanishing h/ω in which effective moments of inertia occur as eigenvalues of linear equations. Several examples are worked out in detail, all dealing with an interacting phonon-electron system in the random-phase approximation. Results derived are the explicit screened Coulomb interaction resulting from electronic plasma excitations, a verification of the renormalized phonon frequency spectrum and phonon-electron interaction derived in the adiabatic approximation, and the resulting screened Coulomb and phonon-induced electronic interactions obtained when plasma and phonon excitations are treated simultaneously.

Journal of Mathematical Physics•Apr 1, 1965•15 citations
The equations of motion of macroscopic quantities characterizing the nonequilibrium state of a many-particle system with a discrete energy spectrnm and subjected to the strong action of a pulsed generator are deduced by applying the Schroedinger equation for the system. Simple algorithms for the operator transformations related to impluse excitation are derived. The general properties of pulsed generators and of physical systems leading to the appearance of oscillating and stationary response signals of the excited particle system are established. As an illustration of application of the general relations, the nonequilibrium states of electron and nuclear spin systems produced by cross magneto-acoustic excitation are investigated. The prospects of developing pulse techniques for investigating electric and orbital magnetic moment systems are discussed. (auth)
Abstract A general method is developed of calculation of response signals of N‐particle systems with an unequidistant spectrum to pulse action of coherent physical fields resonant for any transition of the system. The case of a particle system where each particle has three energy levels E1 < E2 < E3 is analysed. It is shown that if such a system is subjected to pulse action of two generators exciting transitions E1 ⟷ E2 and E2 ⟷ E3 at initial time and at time τ to pulse action of a generator with frequency ω31 = h−1 (E3 — E1), the system generates induction and echo signals with power proportional to N2 at all possible transitions. Echo signals arise at times (1 + ϵ) τ, 2 τ, and (1 + 1/ϵ) τ after the first pulse, where ϵ = E2 — E1/E3 — E2. The observed responses may have a physical nature which is both identical with the excitation and different from it. Supplements are given by which the responses of particle systems may be calculated to a series of pulses different from those considered here. When ϵ →1 the results transform to the case of equidistant spectrum.
The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyze and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrödinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analyzed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.
The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyze and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrödinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analyzed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.
This is the first of a series of papers dealing with many-particle systems from a unified, nonperturbative point of view. It contains derivations and discussions of various field-theoretical techniques which will be applied in subsequent papers. In a short introduction the general method of approach is summarized, and its relationship to other field-theoretic problems indicated. In the second section the macroscopic properties of the spectra of many-particle systems are described. Asymptotic evaluations are performed which characterize these macroscopic features in terms of intensive parameters, and the relationship of these parameters to thermodynamics is discussed. The special characteristics of the ground state are shown to follow as a limiting case of the asymptotic evaluations. The third section is devoted to the time-dependent field correlation functions, or Green's functions, which describe the microscopic behavior of a multiparticle system. These functions are defined, and related to intensive macroscopic variables when the energy and number of particles are large. Spectral representations and other properties of various one-particle Green's functions are derived. In the fourth section the treatment of non-equilibrium processes is considered. As a particular example, the electromagnetic properties of a system are expressed in terms of the special two-particle Green's function which describes current correlation. The discussion yields specifically a fluctuation-dissipation theorem, a sum rule for conductivity, and certain dispersion relations. The fifth section deals with the differential equations which determine the Green's functions. The boundary conditions that characterize the Green's function equations are exhibited without reference to adiabatic decoupling. A method for solving the equations approximately, by treating the correlations among successively larger numbers of particles, is considered. The first approximation in this sequence is shown to yield a generalized Hartree-like equation. A related, but rigorous, identity for the single-particle Green's function is then derived. A second approximation, which takes certain two-particle correlations into account, is shown to produce various additional effects: The interaction between particles is altered in a manner characterized by the intensive macroscopic parameters, and the modification and spread of the energy-momentum relation come into play. In the final section compact formal expressions for the Green's functions and other physical quantities are derived. Alternative equations and systematic approximations for the Green's functions are obtained.
An equation set describtng single particle excitations for excitation energies which are small compared with the chemical potential of the system can be obtained by investigating the analytical properties of the Green's functions and taking into account pair correlation. The equations are valid for an arbitrary interaction law. Equations are derived which describe the excited states of a system with a finite number of particles with an accuracy to terms of the order of N/sup -//sup 1//sup ///sup 3/ It is indicated how the results can be applied to real nuclei. (auth)
An operator A† that satisfies [H, A†] = h/ωA† converts a stationary-state eigenfunction of the Hamiltonian H into another eigenfunction with energy eigenvalue increased by h/ω. Such operators describe collective excitations of many-particle systems, and their properties can be used to construct an intrinsic Hamiltonian that is dynamically independent of the collective degrees of freedom, without introducing subsidiary conditions. The procedure developed by Lipkin, valid when h/ω is real and positive, is extended to make possible the construction of an intrinsic Hamiltonian when h/ω vanishes and A† is Hermitian, and also when h/ω is complex. The nuclear cranking model is shown to be a special case of the proposed general method for vanishing h/ω in which effective moments of inertia occur as eigenvalues of linear equations. Several examples are worked out in detail, all dealing with an interacting phonon-electron system in the random-phase approximation. Results derived are the explicit screened Coulomb interaction resulting from electronic plasma excitations, a verification of the renormalized phonon frequency spectrum and phonon-electron interaction derived in the adiabatic approximation, and the resulting screened Coulomb and phonon-induced electronic interactions obtained when plasma and phonon excitations are treated simultaneously.