Non-additive dissipation in open quantum networks out of equilibrium

Abstract

We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.

Boosting the performance of small autonomous refrigerators via common environmental effects

“…These assumptions imply that the three environments are not correlated to each other and lead to a Born-Markov master equation where the dissipative part is the sum of three separate contributions, each of them due to one of the three reservoirs. Furthermore, in the limit of g small with respect to the natural energies, a local approach to the master equation can be adopted, which allows one to compute the Lindbladian using local operators [65][66][67][68][69].…”

Reconciliation of quantum local master equations with thermodynamics

“…The origin of these effects, as shown in [75], lies in the fact that the heat fluxes become of the same order of magnitude as the neglected nonlocal terms They thus suggest to use the GME to fix such thermodynamic anomalies. These findings generated a considerable stream of investigations on the comparison between global and LMEs [49,52,53,61,[76][77][78][79][80][81][82] as well as clever possible alternatives [83,84].Recent results indicate, however, that it is possible to construct a consistent thermodynamic framework for LMEs, resolving these seeming contradictions. First and foremost, it is important to mention that, unlike Redfield equations, LMEs are in Lindblad form and therefore generate completely positive trace preserving (CPTP) maps.…”

Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation

“…In this particular case, the global master equation with partial secular approximation, even if accurate, would be unnecessarily more complicate than the local one. For instance, this is the case when addressing a Markovian scenario with very high temperature in which the autocorrelation functions of the bath decay faster than the system itself [29].…”

“…In particular, spontaneous synchronization of the spinning frequencies of two uncoupled qubits in a common bath has been predicted using a Bloch-Redfield master equation without any further secular approximation [17]. Using the master equation (29) in partial secular approximation we have observed quantum synchronization starting from a time t≈6000, while the same master equation in full secular approximation never displays synchronization of the qubit frequencies, and it is therefore not suitable to analyze such a phenomenon.…”

“…in presence of interactions between its subsystems (here the two qubits), while the local one follows from the approximation which neglects these interactions. Recently, the problem of characterizing the range of applicability of the local rather than global master equation has received much interest [25][26][27][28][29], mostly related to the consistency of this decription in quantum thermodynamics. It is our aim to show here that an accurate application of the secular approximation in the global approach always leads to a correct Markovian master equation, independently of the value of the coupling constant between the subsystems.…”