Nonequilibrium Density Operator Research Articles

Reworking Zubarev’s Approach to Nonequilibrium Quantum Statistical Mechanics

In this work, the nonequilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at a local thermodynamic equilibrium is revisited. This method, which was used to obtain the first “Kubo” formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of Quark–Gluon Plasma in relativistic nuclear collisions.

Transport Coefficients of the Second Order Hydrodynamics and the Applicability of Hydrodynamic Model

Based on the Nakajima-Zubarev type nonequilibrium density operator, we derive microscopic formulae of the transport coefficients in the second order hydrodynamics.

Nonequilibrium density operator approach to domain wall resistivity

We derive the static resistivity due to the Bloch domain wall using the nonequilibrium density operator technique by Zubarev in the ballistic limit of electronic transport.

Nonlinear quantum evolution equations to model irreversible adiabatic relaxation with maximal entropy production and other nonunitary processes

We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum theory of irreversibility and thermodynamics for a single isolated or adiabatic particle, qubit, or qudit, and recently rediscovered by other authors. The nonlinear equation generates a dynamical group, not just a semigroup, providing a deterministic description of irreversible conservative relaxation towards equilibrium from any non-equilibrium density operator. It satisfies a very restrictive stability requirement equivalent to the Hatsopoulos-Keenan statement of the second law of thermodynamics. We then examine the form of the evolution equation we proposed to describe multipartite isolated or adiabatic systems. This hinges on novel nonlinear projections defining local operators that we interpret as ``local perceptions'' of the overall system's energy and entropy. Each component particle contributes an independent local tendency along the direction of steepest increase of the locally perceived entropy at constant locally perceived energy. It conserves both the locally-perceived energies and the overall energy, and meets strong separability and non-signaling conditions, even though the local evolutions are not independent of existing correlations. We finally show how the geometrical construction can readily lead to other thermodynamically relevant models, such as of the nonunitary isoentropic evolution needed for full extraction of a system's adiabatic availability.

Current-constraining variational approaches to quantum transport

Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the non-equilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.

Baryo-exodus in the standard model

The electroweak theory includes anomalous baryon and lepton number ( B+ L) violations which can cause any B+ L, generated at temperatures above the weak scale, to relax to its equilibrium value of zero. This will happen if the relaxation rate R for this process is greater than the expansion rate. We use an analytic expression for R to derive an explicit relation between the relaxation rate at high temperatures and the cross sections for baryon violating processes due to electroweak interactions at high energies. The analytic expression for R was obtained (Khlebnikov and Shaposhnikov, and Raby, Starkman and Mottola) by using an explicit form for the nonequilibrium density operator to describe the out of equilibrium baryon density. We then use some recent estimates of the high energy baryon number violating amplitudes to obtain a lower bound on R.

Statistical foundation of nonequilibrium contact quantities bridging phenomenological and statistical nonequilibrium-thermodynamics

Intensive variables of discrete nonequilibrium systems are defined by inequalities which are derivable quantumstatistically for contacts between discrete equilibrium and nonequilibrium systems. These contacts are described by a generalized grand-canonical nonequilibrium density operator of maximal entropy by which heat-, mass-, and power-exchange through the contact can be evaluated. A straightforward calculation yields inequalities whose interpretation enables definitions of intensive nonequilibrium quantities for discrete systems.

Nonequilibrium transport of an electron-phonon-hole system in a semiconductor quantum well.

The recently developed transport theory of two-dimensional carriers has been applied to an electron-lattice-hole system with an applied electric field in GaAs-Ga/sub 1-//sub x/Al/sub x/As heterojunction. The renormalized carrier-carrier coupled potentials and the renormalized carrier-phonon coupled potentials (including hole-lattice deformation potential) are derived in the ring diagram approximation. Force and energy balance equations of electrons and holes are obtained by a nonequilibrium density operator technique. These four balance equations are solved numerically in the steady state. The result shows that the electrons are heated in the applied electric field much more than the holes and the electron-hole interaction enhances the energy and momentum loss rate of electrons. These results are in agreement with recently experimental data.

Non-equilibrium thermodynamics of cross-relaxation

Cross-relaxation of two nuclear-spin subsystems is discussed in terms of classical in terms of classical and quantum-statistical non-equilibrium thermodynamics, using Morï's assumption of local equilibrium and Zubarev's non-equilibrium density operator.