Starting from the usual formulation of nonequilibrium quantum statistical mechanics, the expectation value of an operator A in a steady state nonequilibrium quantum system is shown to have the form 〈A〉 =Tr{${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}(\mathit{H}\mathrm{\ensuremath{-}}\mathit{Y})}$A} /Tr{${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}(\mathit{H}\mathrm{\ensuremath{-}}\mathit{Y})}$}, where H is the Hamiltonian, \ensuremath{\beta} is the inverse of the temperature, and Y is an operator which depends on how the system is driven out of equilibrium. Because 〈A〉 is not expressed as a sum of correlation functions integrated over real time, one can now consider performing nonperturbative calculations in interacting nonequilibrium quantum problems.Starting from the usual formulation of nonequilibrium quantum statistical mechanics, the expectation value of an operator A in a steady state nonequilibrium quantum system is shown to have the form 〈A〉 =Tr{${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}(\mathit{H}\mathrm{\ensuremath{-}}\mathit{Y})}$A} /Tr{${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}(\mathit{H}\mathrm{\ensuremath{-}}\mathit{Y})}$}, where H is the Hamiltonian, \ensuremath{\beta} is the inverse of the temperature, and Y is an operator which depends on how the system is driven out of equilibrium. Because 〈A〉 is not expressed as a sum of correlation functions integrated over real time, one can now consider performing nonperturbative calculations in interacting nonequilibrium quantum problems.

Physical Review LettersApr 5, 1993139 citations

Models in nonequilibrium quantum statistical mechanics

Max Dresden, Frank D. Feiock

Journal of Statistical PhysicsJan 1, 197219 citations

A stochastic process in nonequilibrium quantum statistical mechanics

P. L. Torres

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoSep 1, 19772 citations

Transport in a Luttinger liquid in the presence of a time-dependent impurity

D. Schmeltzer

We show that the macroscopic current and charge can be formulated as a quantum-mechanical zero-mode problem. We find that the current is given by the velocity operator of a particle restricted to move around a circle. As an explicit example we investigated a Luttinger liquid of length L that is perturbed by a time-dependent impurity. Using the statistical mechanics of zero modes we computed the nonequilibrium current. In particular we show that in the low-temperature limit, ${L}_{T}/L>1,$ the zero-mode method introduced here becomes essential for computing the current.We show that the macroscopic current and charge can be formulated as a quantum-mechanical zero-mode problem. We find that the current is given by the velocity operator of a particle restricted to move around a circle. As an explicit example we investigated a Luttinger liquid of length L that is perturbed by a time-dependent impurity. Using the statistical mechanics of zero modes we computed the nonequilibrium current. In particular we show that in the low-temperature limit, ${L}_{T}/L>1,$ the zero-mode method introduced here becomes essential for computing the current.

arXiv:cond-mat/0010498Physical review. B, Condensed matterMar 13, 200117 citations

{L}_{T}/L>1,

the zero-mode method introduced here becomes essential for computing the current.