No Thermalization without Correlations

Abstract

The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well approximate thermal states. A quantum optical scheme for the laboratory assessment of the developed procedure is outlined.

Friction as a consistent quantum-mechanical concept

“…A simple computation shows that these solutions reduce to f k (p 1 )∝ep 1 κ k m 1 ω 1 obtained in Ref. [14]. The latter solution (and, more generally, the last term in Eq.…”

“…Later, free quantum Brownian motion was identified by Vacchini [20] to be such a special case. We have proven that no other exceptions exist among quantum systems with N ext translation degrees of freedom [14].…”

“…They generally should be treated as a phenomenological quantities and can be deduced from empirical fits to time evolution of higher-order averages, e.g., x 2 , p 2 . In the cases when the dissipative term L rel describes random collisions with light environmental particles, the values of κ k and f k (p) can be associated with the characteristic momentum exchange in a collision event and the scattering amplitude in the momentum space [14]. It is worth to show why the dissipative dynamics satisfying criteria i -iii deserves the name quantum friction.…”

“…The remaining possibility to obey condition (16) by setting α k =0 and κ k =0 in Eqs. (14) leads to exactly thermalizable dissipator L rel satisfying Eq. (7).…”

“…However, this model fails to account for proximity effects responsible for spatial and/or temporal system-bath correlations. These correlations turned out to be crucial for quantum thermalization [14]: Without them, microscopic perpetual motion would be possible. Internal degrees of freedom enable quantum friction by serving as an ancilla subsystem to phenomenologically mimic proximity effects on translation degrees of freedom.…”