Reformulation of steady state nonequilibrium quantum statistical mechanics

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{${\mathit{e}}^{\mathrm{-}\mathrm{\beta }\left(\mathit{H}\mathrm{-}\mathit{Y}\right)}$A} /Tr{${\mathit{e}}^{\mathrm{-}\mathrm{\beta }\left(\mathit{H}\mathrm{-}\mathit{Y}\right)}$}, where H is the Hamiltonian, β 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.