aqora

Nonequilibrium Steady States and MacLennan-Zubarev Ensembles in a Quantum Junction System

Shuichi Tasaki, Junko Takahashi

Based on a recent progress in nonequilibrium statistical mechanics of infinitely extended quantum systems, a nonequlibrium steady state (NESS) is constructed for a single-level quantum dot interacting with two free reservoirs under less general but more practically useful conditions than the previous works. As an example, a model of an Ahoronov-Bohm ring with a quantum dot is studied in detail. Then, NESS is shown to be regarded as a MacLennan-Zubarev ensemble. A formal relation between response and correlation at NESS is derived as well.Based on a recent progress in nonequilibrium statistical mechanics of infinitely extended quantum systems, a nonequlibrium steady state (NESS) is constructed for a single-level quantum dot interacting with two free reservoirs under less general but more practically useful conditions than the previous works. As an example, a model of an Ahoronov-Bohm ring with a quantum dot is studied in detail. Then, NESS is shown to be regarded as a MacLennan-Zubarev ensemble. A formal relation between response and correlation at NESS is derived as well.

arXiv:cond-mat/0606259Progress of Theoretical Physics SupplementJan 1, 200618 citations

Statistical mechanics of quantum-classical systems. Nonequilibrium systems

V. I. Gerasimenko, D. Ya. Petrina

Theoretical and Mathematical PhysicsJan 1, 19808 citations

On the Nonequilibrium Statistical Operator Method

Roberto Luzzi, Aurea Rosas Vasconcellos

We describe the large applicability of the Nonequilibrium Statistical Operator Method (NSOM) for the study of dissipative dynamic systems far from equilibrium. It is shown that the NSOM can be encompassed by a unifying variational principle, which produces a large family of NSO that contains existing examples as particular cases. Further, we review the application of the NSOM for the construction of a nonlinear quantum theory of large scope, and for the generation of a response function theory, for far-from-equilibrium Hamiltonian systems. An accompanying non-equilibrium thermodynamic Green's function theory is briefly described. Also it is shown that the NSOM provides mechano-statistical foundations for phenomenological irreversible thermodynamics, and for the important question of stability of far-from-equilibrium steady states and the emergence of self-organized dissipative structures in condensed matter.We describe the large applicability of the Nonequilibrium Statistical Operator Method (NSOM) for the study of dissipative dynamic systems far from equilibrium. It is shown that the NSOM can be encompassed by a unifying variational principle, which produces a large family of NSO that contains existing examples as particular cases. Further, we review the application of the NSOM for the construction of a nonlinear quantum theory of large scope, and for the generation of a response function theory, for far-from-equilibrium Hamiltonian systems. An accompanying non-equilibrium thermodynamic Green's function theory is briefly described. Also it is shown that the NSOM provides mechano-statistical foundations for phenomenological irreversible thermodynamics, and for the important question of stability of far-from-equilibrium steady states and the emergence of self-organized dissipative structures in condensed matter.

Fortschritte der Physik/Progress of PhysicsJan 1, 1990107 citations

Equilibrium and Nonequilibrium Aspects of Phase Transitions in Quantum Physics

Ricardo Puebla

Springer thesesJan 1, 20184 citations

Equilibrium and Nonequilibrium Aspects of Phase Transitions in Quantum Physics Foreword

Martin Bodo Plenio

Jan 1, 20180 citations

Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator

H. Ness

In this paper, we formally demonstrate that the nonequilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev nonequilibrium ensemble. The correction term in this pseudoequilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact that both methods state that a nonequilibrium steady state can be mapped onto a pseudoequilibrium, permits us to develop nonequilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a nonequilibrium distribution function for the electron population in a scattering region in the context of quantum transport.In this paper, we formally demonstrate that the nonequilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev nonequilibrium ensemble. The correction term in this pseudoequilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact that both methods state that a nonequilibrium steady state can be mapped onto a pseudoequilibrium, permits us to develop nonequilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a nonequilibrium distribution function for the electron population in a scattering region in the context of quantum transport.

arXiv:1305.4479Physical Review EAug 13, 201319 citations

Nonequilibrium Steady States and MacLennan-Zubarev Ensembles in a Quantum Junction System(Physics of Non-Equilibrium Systems: Self-Organized Structures and Dynamics Far from Equilibrium)

Related papers

Nonequilibrium Steady States and MacLennan-Zubarev Ensembles in a Quantum Junction System(Physics of Non-Equilibrium Systems: Self-Organized Structures and Dynamics Far from Equilibrium)

Related papers