Geometric phaselike effects in a quantum heat engine

Abstract

By periodically driving the temperature of reservoirs in a quantum heat engine, geometric or Pancharatnam-Berry phase-like (PBp) effects in the thermodynamics can be observed. The PBp can be identified from a generating function (GF) method within an adiabatic quantum Markovian master equation formalism. The GF is shown not to lead to a standard open quantum system's fluctuation theorem in presence of phase-different modulations with an inapplicability in the use of large deviation theory. Effect of quantum coherences in optimizing the flux is nullified due to PBp contributions. The linear coefficient, 1/2, which is universal in the expansion of the efficiency at maximum power in terms of Carnot efficiency no longer holds true in presence of PBp effects.

Nonequilibrium thermal transport and thermodynamic geometry in periodically driven systems

“…基于随机热力学的研究方法 [38] , Ren等 [15] 提出了量子分子结的声子热输运中, 驱动热库温度 等参数产生几何相热流的热泵. 随后, 几何相热流 也在包含经典布朗系统 [17] , 自旋-玻色系统 [18,39] , 量 子光力系统 [16] 等大量系统中得到了广泛研究. 特 别地, 在自旋-玻色系统中, 研究人员发展运用了极 化子变换的方法 [40] , 系统性探讨了系统-热库耦合 从弱到强的变化对于几何相热流的影响 [18,41] .…”

Nonequilibrium fluctuations of a driven quantum heat engine via machine learning

“…It has been shown by us previously that in the dQHE the affinity is given by [26] A = lnñ l tp 0 (1 + n c (t ))n h (t )dt n l tp 0 n c (t )(1 + n h (t ))dt ,…”

“…We consider a 4 level QHE coupled asymmetrically to two thermal baths and an unimodal cavity, Fig.(1). This model has been studied in several works [13,26,[42][43][44]. The model consists of two thermal baths at temperatures T h (t) and T c (t).…”

“…We will now proceed to quantify the PES between system and cavity. We employ an adiabatic Markovian quantum master equation approach combined with a standard generating function technique to evaluate the statistics such that |ρ(λ, t) =L(λ, t)|ρ(λ, t) , where λ is a field that counts the number of photon exchanged between system and cavity [26]. |ρ(λ, t) = {ρ 11 , ρ 22 , ρ aa , ρ bb , (ρ 12 )} is the reduced system density vector with ρ ii , i = 1, 2, a, b being system's many body states and (ρ 12 ) is the thermal induced coherences between states |1 and |2 .L(λ, t) is the adiabatic effective evolution Liouvillian superoperator within the Markov approximation.…”

“…Recently, we showed that in a 4 level driven quantum heat engine (dQHE) coupled to a unimodal cavity, there exists a competition between thermally induced quantum coherences and the geometric contributions such that the latter stops the former to optimize the flux into the cavity mode when the temperature of the two thermal reservoirs are periodically modulated in time in an adiabatic fashion [26]. In this work, we focus on the geometric contributions to the higher order nonequilibrium fluctuations (noise) with a view to further understand the role of the geometric effects on the statistics.…”