Kinetic Theory of Quantum Electrodynamic Plasma in a Strong Electromagnetic Field: I. The Covariant Formalism

We present a covariant approach to the kinetic theory of quantum electrodynamic plasma in a strong electromagnetic field. The method is based on the relativistic von Neumann equation for the nonequilibrium statistical operator defined on spacelike hyperplanes in Minkowski space. We use the canonical quantization of the system on hyperplanes and a covariant generalization of the Coulomb gauge. The condensate mode associated with the mean electromagnetic field is separated from the photon degrees of freedom by a time-dependent unitary transformation of the dynamic variables and the nonequilibrium statistical operator. This allows using expansions of correlation functions and of the statistical operator in powers of the fine structure constant even in the presence of a strong electromagnetic field. We present a general scheme for deriving kinetic equations in the hyperplane formalism.     

Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations

We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.     

Master equation of the reduced statistical operator of an atom in a plasma

We use the nonequilibrium Liouville equation to derive the master equation for the reduced statistical operator in a heat bath represented by a many-particle environment. Focusing on the case of a weak system-bath coupling, we consider the Born-Markov approximation of the master equation and compare the result to different approaches. The master equation is elaborated for the special case of an atom as a reduced system in a plasma background. We find that the dynamical structure factor determines the effect of the plasma on the reduced system. We consider the operator equation in the atomic eigenstate and in the phase-space representation, which yields two limiting cases: quantum mechanical behavior similar to the isolated atom for the lower strongly bound levels and a semiclassical one for highly excited Rydberg levels. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 31–62, January, 2008.     

Nonequilibrium statistical operator in the generalized molecular hydrodynamics of fluids

We discuss the important role of the Zubarev nonequilibrium statistical operator method in the generalized molecular hydrodynamics of fluids. Using this method allows developing a consistent approach of generalized collective excitations for simple, ion, polar, magnetic, and some other fluids. We construct a nonequilibrium statistical operator and derive the corresponding transport equations for a system that relaxes and passes into the state of molecular hydrodynamics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 91–101, January, 2008.     

Statistical hydrodynamics of magnetic fluids. I. the nonequilibrium statistical operator method

The Zubarev nonequilibrium statistical operator is used to describe the generalized hydrodynamic state of a magnetic fluid in an external magnetic field. The magnetic fluid is modeled with “liquid-state” and “magnetic” subsystems described using the classical and quantum statistics methods respectively. Equations of the generalized statistical hydrodynamics for a magnetic fluid in a nonhomogeneous external magnetic field with the Heisenberg spin interaction are derived for “liquid-state” and “magnetic” subsystems characterized by different nonequilibrium temperatures. These equations can be used to describe both the weakly and strongly nonequilibrium states. Some limiting cases are analyzed in which the variables of one of the subsystems can be formally neglected. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 115, No. 1, pp. 132–153, April, 1998.     

Memory Effects and Nonequilibrium Correlations in the Dynamics of Open Quantum Systems

We propose a systematic approach to the dynamics of open quantum systems in the framework of Zubarev’s nonequilibrium statistical operator method. The approach is based on the relation between ensemble means of the Hubbard operators and the matrix elements of the reduced statistical operator of an open quantum system. This key relation allows deriving master equations for open systems following a scheme conceptually identical to the scheme used to derive kinetic equations for distribution functions. The advantage of the proposed formalism is that some relevant dynamical correlations between an open system and its environment can be taken into account. To illustrate the method, we derive a non-Markovian master equation containing the contribution of nonequilibrium correlations associated with energy conservation.     

Nonequilibrium statistical thermodynamics of cascade processes in solids: the quasi temperature of cascade particles

Displacement cascades in solids are investigated in the framework of nonequilibrium statistical thermodynamics. The quasi temperature of a subsystem of cascade particles in metals and semiconductors is derived using the energy balance equation for a cascade process.     

Electrical Conductivity of Charged Particle Systems and Zubarev’s Nonequilibrium Statistical Operator Method

One of the fundamental problems in physics that are not yet rigorously solved is the statistical mechanics of nonequilibrium processes. An important contribution to describing irreversible behavior starting from reversible Hamiltonian dynamics was given by D. N. Zubarev, who invented the method of the nonequilibrium statistical operator. We discuss this approach, in particular, the extended von Neumann equation, and as an example consider the electrical conductivity of a system of charged particles. We consider the selection of the set of relevant observables. We show the relation between kinetic theory and linear response theory. Using thermodynamic Green’s functions, we present a systematic treatment of correlation functions, but the convergence needs investigation. We compare different expressions for the conductivity and list open questions.     

Dissipation,topography, and statistical theories for large-scale coherent structure

Various facets of the equilibrium statistical theories for large-scale coherent structures for two-dimensional flows with and without topography are studied here. The classical few-constraint statistical theories involving energy-enstrophy principles or point vortices are shown to be statistically sharp in the more recent statistical theories with an infinite number of constraints; in other words, at the macrostates of the few-constraint theories, the many-constraint theory provides no additional statistical information. These results are established through a general link between these statistical theories, generalized “selective decay” principles, and statistical sharpness. Through an asymptotic procedure, the many-constraint statistical theories for flows with topography and small-potential vorticity are shown to yield the simpler energy-enstrophy macroscopic states at leading order with systematic higher-order corrections involving a renormalized topography that includes higher moments of the microscopic potential vorticity distribution. For nonequilibrium flows with and without topography, the utility of crude approximate dynamics based on “adiabatic approximation” through the macrostates of few-constraint statistical theory is developed here. It is established that for nonequilibrium decaying flows with viscous dissipation, the crude dynamics based on macrostates involving statistical point vortices yields an excellent approximation; the role of “selective decay” principles is also clarified and compared quantitatively in this context through both mathematical theory and numerical experiments. Surprisingly, these approximate dynamics yield a much poorer approximation with moderate Ekman drag as the dissipative mechanism, and a simple analytical explanation is provided here. Finally, all of these issues are pursued more briefly for damped and driven flows with topography. © 1997 John Wiley & Sons, Inc.     

Statistical mechanics of relaxation processes in alternating fields

Using the nonequilibrium statistical operator method and the projection technique, we derive the system of exact relaxation equations for a quantum system interacting with an alternating external field. These equations hold in the case where some of the basic dynamical variables describing a nonequilibrium state depend explicitly on time. We obtain the exact expression for the entropy production in an alternating external field. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 102–112, January, 2008.     

Statistical Irreversible Thermodynamics in the Framework of Zubarev’s Nonequilibrium Statistical Operator Method

We describe the formalism of statistical irreversible thermodynamics constructed based on Zubarev’s nonequilibrium statistical operator (NSO) method, which is a powerful and universal tool for investigating the most varied physical phenomena. We present brief overviews of the statistical ensemble formalism and statistical irreversible thermodynamics. The first can be constructed either based on a heuristic approach or in the framework of information theory in the Jeffreys-Jaynes scheme of scientific inference; Zubarev and his school used both approaches in formulating the NSO method. We describe the main characteristics of statistical irreversible thermodynamics and discuss some particular considerations of several authors. We briefly describe how Rosenfeld, Bohr, and Prigogine proposed to derive a thermodynamic uncertainty principle.     

Balance equation and the quasitemperature of channeled particles in equilibrium

Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem “heating”), the dissipative process (“cooling”), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.     

Longitudinal electric current generated by a transverse electromagnetic field in a collisional plasma

We consider a collisional plasma with an arbitrary degree of degeneration of the electron gas. The plasma is located in an external electromagnetic field. We calculate the electric current generated in the plasma by the electromagnetic field. We show that the electric current has two nonzero components. One component is a transverse current, obtained by a linear analysis. The second component is a longitudinal current directed along the wave vector and orthogonal to the transverse current. We consider the case of small wave numbers. As the collision rate tends to zero, all the derived formulas pass into formulas for a collisionless plasma. We perform a graphical investigation of the dimensionless current density depending on the wave number, the oscillation frequency of the electromagnetic field, and the rate of electron collisions with plasma particles.     

Calculation of correlation functions in totally asymmetric exactly solvable models on a ring

We consider exactly solvable totally asymmetric models of low-dimensional nonequilibrium statistical physics on a periodic chain, namely, the totally asymmetric simple exclusion process and the totally asymmetric simple zero-range process. We describe the method for calculating correlation functions for the models on a periodic lattice and represent scalar products of state vectors of the model as determinants.     

Broken translation invariance in quasifree fermionic correlations out of equilibrium

Using the C^? algebraic scattering approach to study quasifree fermionic systems out of equilibrium in quantum statistical mechanics, we construct the nonequilibrium steady state in the isotropic XY chain whose translation invariance has been broken by a local magnetization and analyze the asymptotic behavior of the expectation value for a class of spatial correlation observables in this state. The effect of the breaking of translation invariance is twofold. Mathematically, the finite rank perturbation not only regularizes the scalar symbol of the invertible Toeplitz operator generating the leading order exponential decay but also gives rise to an additional trace class Hankel operator in the correlation determinant. Physically, in its decay rate, the nonequilibrium steady state exhibits a left mover-right mover structure affected by the scattering at the impurity.     

Extension of a simplified Baldwin–Lomax model to nonequilibrium turbulence: Model,analysis and algorithms

Complex turbulence not at statistical equilibrium is impossible to simulate using eddy viscosity models due to a backscatter. This research presents the way to correct the Baldwin–Lomax model for nonequilibrium effects and gives an analysis of the energy evolution in the corrected model. Furthermore, a finite element approximation of the corrected eddy model with first‐order and second‐order time discretization is also presented. A numerical test is given to support the theory.