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 $T\ensuremath{\gtrsim}0$ remarkably well. We discuss some implications of that observation for dissipative quantum field theory.
Highlights
Understanding and controlling quantum dissipation is a key problem in developing a variety of modern quantum technologies
To present a density matrix ρt for the two-level system, we show either ρt11 or ρt00 because these diagonal density-matrix elements are related by ρt00 + ρt11 = 1
A proper zero-temperature quantum master equation is obtained by first linearizing a thermodynamic quantum master equation and passing to the limit of vanishing temperature
Summary
Understanding and controlling quantum dissipation is a key problem in developing a variety of modern quantum technologies. The final step of the development of thermodynamic quantum master equations has been made in [5], where the setting has been generalized so that the linear Davies Lindblad master equations [13] are contained as a special class of thermodynamic master equations. It has been shown in [14] that the nonlinear quantum master equations proposed in [5] have the potential to explain ultralong coherence of a qubit.
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