Non-Markovian Quantum Kinetics and Conservation Laws

A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle distribution function and the mean interaction energy are treated as independent nonequilibrium state parameters. The density operator method is used to derive a kinetic equation in second-order non-Markovian Born approximation and an evolution equation for the nonequilibrium quasi-temperature which is thermodynamically conjugated to the mean interaction energy. The kinetic equation contains a correlation contribution which exactly cancels the collision term in thermal equilibrium and ensures the energy conservation in nonequilibrium states. Explicit expressions for the entropy production in the non-Markovian regime and the time-dependent correlation energy are obtained.     

Nonlocal corrections to the Boltzmann equation for dense Fermi systems

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second-order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e. an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.     

Quantum kinetic equation for nonequilibrium dense systems

Using the density matrix method in the form developed by Zubarev, equations of motion for nonequilibrium quantum systems with continuous short range interactions are derived which describe kinetic and hydrodynamic processes in a consistent way. The T-matrix as well as the two-particle density matrix determining the nonequilibrium collision integral are obtained in the ladder approximation including the Hartree-Fock corrections and the Pauli blocking for intermediate states. It is shown that in this approximation the total energy is conserved. The developed approach to the kinetic theory of dense quantum systems is able to reproduce the virial corrections consistent with the generalized Beth-Uhlenbeck approximation in equilibrium. The contribution of many-particle correlations to the drift term in the quantum kinetic equation for dense systems is discussed.     

The density of energy flow of quasiparticles with arbitrary energy–momentum relation

In this paper, we consider the energy conservation law in a continuous medium with arbitrary energy–momentum relation. We use a new theoretical approach in which both the long wavelength and short wavelength thermal excitations are described in a unified way. The theory is based on the fact that in a quantum fluid, the thermal de Broglie wavelengths of the atoms overlap each other. In this case, the atoms are delocalized in space and we can treat a quantum fluid as a continuous medium without any restriction on length scale. So, in quantum liquids, we can determine the probabilistic values of the parameters of the continuous medium in every mathematical point of space. From the Hamiltonian of this system, we derive a system of linear equations for the general case of an ideal liquid, which has a nonlocal relationship between pressure and density. In the frame of this model from the energy conservation law, a general expression for the energy density flow is obtained. It is shown that for the wave packet, it is not affected by the freedom in its definition. A clear relation for the energy density flow of a wave packet is derived that generalizes the ordinary form of it to the case of arbitrary dispersion.     

Birkhoffian Symplectic Scheme for a Quantum System

In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.     

On the quantum kinetic equation for molecular gases: II. Noncentral interaction

A rigorous derivation of a quantum kinetic equation for dilute homogeneous diatomic gases with noncentral interactions is presented. This equation generalizes the Waldmann-Snyder equation, describing the relaxation of both diagonal and nondiagonal terms of the quantum distribution function $\text{f}{}_{\mathrm{\delta \delta \prime }}\text{(t,}\text{P}\text{)}$. The collision integral contains a term which describes the long-lived collisions and collisions with a large exchange of internal energy. The macroscopic conservation laws for mass density, total momentum density, total angular momentum density and energy density are derived. In the limit of monoatomic gases all known results are obtained.     

Vortex stretching as a mechanism for quantum kinetic energy decay

A pair of perturbed antiparallel quantum vortices, simulated using the three-dimensional Gross-Pitaevskii equations, is shown to be unstable to vortex stretching. This results in kinetic energy K(?ψ) being converted into interaction energy E(I) and eventually local kinetic energy depletion that is similar to energy decay in a classical fluid, even though the governing equations are Hamiltonian and energy conserving. The intermediate stages include the generation of vortex waves, their deepening, multiple reconnections, the emission of vortex rings and phonons, and the creation of an approximately -5/3 kinetic energy spectrum at high wave numbers. All of the wave generation and reconnection steps follow from interactions between the two original vortices. A four vortex example is given to demonstrate that some of these steps might be general.     

Transport theory for quantum crystals

A correlation function approach is developed to treat non-equilibrium phenomena of quantum crystals at low frequency and long wavelength within the renormalized harmonic approximation (RHA). The derivation of the transport equations is carried out by studying the hierarchy of equations of motion for the retarded Green's functions of a pure, nonprimitive, nonionic, anharmonic lattice. Using a factorization technique to take into account the most important terms due to the particle fluctuations and the leading contributions to the hydrodynamic singularities of the phonon self-energy, we find a differential equation for the displacement field and a generalized transport equation for the phonon gas. The microscopic RHA expressions for the local temperature, the local heat density and the energy current are derived; the quasiparticle parameters (elastic constants, generalized Grüneisen parameters, quasiparticle interaction) entering the equations of motion are shown to be consistent with the RHA. In the hydrodynamic regime the general equations are reduced to two coupled differential equations for the lattice deformations and for the local temperature. Then only the displacement-displacement, the displacement-energy density and the energy density-energy density correlation functions show macroscopic fluctuations; for these functions thermodynamical sum-rules are derived.     

Optical pumping in a L-system by parametric luminescence light

We examine the optical pumping effect in an ensemble of three-level atoms with a Λ configuration of the energy sublevels excited by parametric luminescence light in the squeezed state. We derive quantum kinetic equations that describe the evolution of the density matrix of atoms irradiated by low-intensity squeezed light with a finite-width spectrum. In particular, we show that because of the quantum statistical properties of the squeezed light there can be a redistribution of atoms among the lower energy sublevels, despite the equality of the intensities of the spectral components of the light that resonantly excites optical transitions in the Λ-system. The relation of the optical pumping effect to the correlation and spatial-temporal spectral properties of squeezed light is discussed in detail. Finally, we show that the effects are closely linked to the finiteness of the width of the squeezed-light spectrum. Zh. éksp. Teor. Fiz. 112, 137–162 (July 1997)     

光线量子理论研究薄膜介质光场能量分布

因为光线量子力学方程的光线哈密顿算符不表示能量,而是具有可变折射率的物理意义,因此应用光线量子论讨论波导中光场能量分布是一个有待研究的问题.本文借鉴量子力学几率密度和几率密度矢量概念推导出光场能量分布的普遍性公式,并证明流线结构的光场中守恒定律的成立.     

Nonlocal conserved quantities,balance laws,and equations of motion

A formalism is developed whereby balance laws are directly obtained from nonlocal (integrodifferential) linear second-order equations of motion for systems described by several dependent variables. These laws augment the equations of motion as further useful information about the physical system and, under certain conditions, are shown to reduce to conservation laws. The formalism can be applied to physical systems whose equations of motion may be relativistic and either classical or quantum. It is shown to facilitate obtaining global conservation laws for quantities which include energy and momentum. Applications of the formalism are given for a nonlocal Schrödinger equation and for a system of local relativistic equations of motion describing particles of arbitrary integral spin.     

Spontaneous emission of the non-Wiener type

The spontaneous emission of a quantum particle and superradiation of an ensemble of identical quantum particles in a vacuum electromagnetic field with zero photon density are examined under the conditions of significant Stark particle and field interaction. New fundamental effects are established: suppression of spontaneous emission by the Stark interaction, an additional “decay” shift in energy of the decaying level as a consequence of Stark interaction unrelated to the Lamb and Stark level shifts, excitation conservation phenomena in a sufficiently dense ensemble of identical particles and suppression of superradiaton in the decay of an ensemble of excited quantum particles of a certain density. The main equations describing the emission processes under conditions of significant Stark interaction are obtained in the effective Hamiltonian representation of quantum stochastic differential equations. It is proved that the Stark interaction between a single quantum particle and a broadband electromagnetic field is represented as a quantum Poisson process and the stochastic differential equations are of the non-Wiener (generalized Langevin) type. From the examined case of spontaneous emission of a quantum particle, the main rules are formulated for studying open systems in the effective Hamiltonian representation.     

Quantum macroscopic equations from Bohm potential and propagation of waves

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation. In the present work, moments of this kinetic equation are taken, thus deriving conservation equations. These macroscopic equations are then applied to study the propagation of longitudinal density perturbations in neutral gases and plasmas, of either fermions or bosons. The dispersion relation is derived and the effect of the Bohm potential shown; the speed of propagation calculated and the difference between fermions and bosons investigated. Pseudosonic waves in quantum plasmas are obtained including the effect of the Bohm potential.     

Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.     

解流体力学方程组的一种隐式完全守恒差分格式

对Lagrange非守恒流体力学方程组给出了一种隐式完全守恒差分格式,既保证了质量、动量和总能量守恒的差分近似,又能满足内能与动能的平衡特性,提高了数值解的精度。并用该格式对两个可压缩理想流体模型进行了数值计算,并与其它差分格式作了比较。     

Quantum theory of pure liquid metals as two-component systems

With the ultimate aims of clarifying the interpretation and the utility of effective ion-ion interactions in liquid metals, and of understanding the unusual isotopic mass dependence of the shear viscosity of liquid metal Li, a fully quantum statistical mechanical theory is developed from the many-body Hamiltonian of the conduction electron-positive ion assembly.We have set up quantum equations of motion which are analogs of classical continuity and conservation equations by expanding the equation for the Wigner distribution function about its diagonal. The most important of these equations for our present purposes relates the time derivative of the current density j(r, t) to the flux of current and to density-density correlation functions for electrons, electron-ions, and ions.This theory is then applied to neutron scattering by liquid metals. While the theory is sufficiently general in principle to treat electron-ion interaction of arbitrary strength, it is shown that when the interacion is weak, the usual results are recovered, along with the effective ion-ion interaction. In this latter connection, it is also demonstrated how the effective Ornstein-Zernike function C(q) in a liquid metal is related to bare ion and bare electron direct correlation functions and to the bare electron partial structure factor. Combining C(q) with one of the classical equations of liquid structure such as Born-Green or Percus-Yevick then relates the effective ion-ion interaction to the partial correlation functions of the bare ions and electrons.It is further shown how gradient expansions of the correlation functions lead to equations of motion for the density, current, and energy density which are simply the hydrodynamic equations of the present quantum theory of two-component systems. It is pointed out that the analog of the Navier-Stokes equation for the two-component system may be used to identify the quantity $\text{4}\text{3}\text{η + ζ}$ for the liquid metal, η and ζ being respectively the shear and bulk viscosities. Finally, it is demonstrated that $\text{4}\text{3}\text{η + ζ}$ depends explicitly on functional derivatives of the nonequilibrium pair distribution functions of ion-ion, electron-ion, and electron-electron correlations.     

量子非欧姆阻尼环境中的重核熔合概率及热核裂变速率

考虑处于量子非欧姆阻尼环境下的重核熔合及热核裂变系统的动力学,给出了数值模拟相应c数量子广义朗之万方程的方法。其中提出的产生任意关联量子色噪声的数值方法,适用于任意非马尔科夫过程噪声的产生。利用此方法计算了重核熔合概率,结果表明量子涨落对重核熔合具有“低抬高压”的效应:当粒子的初始动能小于（大于）临界初始动能时,量子涨落会增大（减小）粒子鞍点通过概率。非欧姆阻尼环境中粒子稳定通过概率随δ值的变化是非单调的,且当粒子初始动能小于（大于）临界初始动能,量子涨落会使稳定通过概率随δ值变化曲线的极大值位置向右（向左）漂移。此外,在热核裂变系统中,超欧姆阻尼环境会增大裂变速率,而量子涨落不仅显著增大裂变速率,还使裂变速率随δ值变化曲线的极大值位置发生漂移。Dynamics of heavy-ion fusion and nuclear fission system in a quantum non-Ohmic environment have been considered and a numerical simulation method to solve the corresponding c-number quantum generalized Langevin equation is proposed. The method of generating quantum colored noise with arbitrary correlation can be applied to generate noise of arbitrary non-Markov process. Calculating fusion probability of heavy nuclei with this method, the result has shown that the passing probability is enlarged (decreased) by the quantum fluctuation when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Steady passing probability of particle in non-Ohmic environment versus is nonmonotonic. Quantum fluctuation makes the maximum position of the curve drift towards right (left), when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Furthermore, nuclear fission rate is larger in super-Ohmic environment. Quantum fluctuation enlarges nuclear fission rate and makes the the maximum position of nuclear fission rate versus δ drift.     

General Navier–Stokes-like momentum and mass-energy equations

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.     

On the balance laws of extended thermodynamics (ET) for non-ideal gases

The conservation laws of mass and momentum and the equations of balance of momentum flux and energy flux as well as the higher order balance laws are derived by means of the modified Klimontovich kinetic equation for non-ideal gases. The effect of the body forces and inertial forces during the persistence of a collision is taken into account in order to have the balance laws valid for general frames of reference. The sequence of macroscopic quantities appearing in the balance equations is decomposed into convective and non-convective parts and this decomposition is explained on the basis of statistical mechanics. A problem of symmetry or non-symmetry of tensors associated with the presence of interactions between microscopic particles is discussed from a molecular point of view. Explicit expressions for the energy density, the pressure, the pressure tensor, the heat flux and the other expressions characteristic for ET are given in terms of microscopic variables.