Zero-temperature limit of thermodynamic quantum master equations

Abstract

We investigate the zero-temperature limit of thermodynamic quantum master equations that govern the time evolution of density matrices for dissipative quantum systems. The quantum master equations for T = 0 and for T > 0 possess completely different structures: (i) the equation for T = 0 is linear in the deviation from the ground-state density matrix, whereas the equation for T > 0, in general, is seriously nonlinear, and (ii) the Gibbs state is obtained as the steady-state solution of the nonlinear equation for T > 0, whereas the ground state cannot be found from the equation for T = 0. Nevertheless, the equation for T = 0 can reproduce the behavior for T 0 remarkably well. We discuss some implications of that observation for dissipative quantum field theory.

Dissipation in spin chains using quantized nonequilibrium thermodynamics

“…We choose f α (u) = f α constant, thus fulfilling such condition. In [40] it was shown that for a single two-level system described by H free = ωσ z , the rate f (u) can be chosen as exp(2uω/k B T ) if Q = σ + . The same reasoning was later on extended to a multi-mode bosonic field with Q k = a k [46].…”

“…While the reversible part is associated to the standard commutator of the density matrix with the system's Hamiltonian, the irreversible part leads to a term that is nonlinear in the density matrix but guarantees thermodynamic consistency and correct steady-state properties. This master equation was successfully applied to traditional open system scenarios, such as spontaneous decay of a two-level atom and the Caldeira-Legget model where numerical solutions were found by using deterministic integration methods for nonlinear equations as well as adaptations of stochastic unraveling [36][37][38][39][40]. Here, for the first time, we apply this framework to the study of dissipation in a many-body system, that is, and open spin chain described by the XXZ model.…”