Zero-temperature limit of thermodynamic quantum master equations
Hans Christian Öttinger · Physical Review A · 2018
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 $T\ensuremath{\gtrsim}0$ remarkably well. We discuss some implications of that observation for dissipative quantum field theory.