Many-Particle Correlations and Boundary Conditions in the Quantum Kinetic Theory

Abstract

The problem of many-particle correlations in different approaches to the quantum kinetic theory is treated on the basis of Zubarev's method of the nonequilibrium statistical operator. It is shown that long-lived correlations can be incorporated through boundary conditions for reduced manyparticle density matrices and the nonequilibrium real-time Green functions. Within the method of Green functions the boundary conditions are conveniently formulated in terms of the "mixed" Green functions defined on a directed contour with the real-time evolution governed by the Hamiltonian of the system and the "imaginary-time" evolution governed by the entropy operator. The perturbation expansion of the mixed Green function is obtained in terms of the interaction part of the Hamiltonian and the correlation part of the entropy operator.

Zubarev's Method of a Nonequilibrium Statistical Operator and Some Challenges in the Theory of Irreversible Processes

“…This point is discussed in our paper [25]. Suffice it to note here that, in fact, these approaches complement each other and their combination appears to have a considerable promise.…”

“…Having constructed the relevant statistical operator with the kinetic and collective dynamical variables, one can use equation (2.1) to obtain the corresponding boundary conditions for the classical or quantum hierarchy. For a more detailed discussion of this point see our paper in this issue [25] and [2,4].…”

Current-Induced Forces for Nonadiabatic Molecular Dynamics

“…In the limit of extremely slow nuclear driving, the relevant distribution ρ̂ rel ( t ) becomes identical with the steady-state electron distribution ρ ss t for the nuclear frame Q ( t ) so that [ Ĥ e ( Q ( t ));ρ̂ rel ( t )] ≈ 0 and . Using eq in eq yields Substituting this result into eq leads to the Langevin equation in the form where are the effective (renormalized) nuclear force and the friction tensor, respectively.…”

“…In the limit of extremely slow nuclear driving, the relevant distribution ρr el (t) becomes identical with the steady-state electron distribution ρ ss t for the nuclear frame Q(t)41 …”

“…In the limit of extremely slow nuclear driving, when the relevant distribution becomes identical with steadystate electron distribution, ρrel (t ) ≈ ρt ss (ρ t ss is steadystate electronic distribution for nuclear frame Q(t )) [35], so that Ĥe Q(t ) ; ρrel (t ) ≈ 0 and ∂ t ρrel (t ) ≈ β ∂ β ρt ss Qβ (t ), using ( 18) in ( 12) yields the Langevin equation ( 16) in the form…”