2017
DOI: 10.1103/physrevlett.119.050601
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Slow Dynamics and Thermodynamics of Open Quantum Systems

Abstract: We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasi-static transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows to formally evaluate perturbations up to … Show more

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Cited by 172 publications
(180 citation statements)
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References 38 publications
(56 reference statements)
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“…CA c emerges in various specific models [27,53,57], and it has been derived by general arguments from linear irreversible thermodynamics [56], while the Schmiedl-…”
Section: This Is Corroborated By Various Results On Emp Bounds: the Cmentioning
confidence: 99%
See 1 more Smart Citation
“…CA c emerges in various specific models [27,53,57], and it has been derived by general arguments from linear irreversible thermodynamics [56], while the Schmiedl-…”
Section: This Is Corroborated By Various Results On Emp Bounds: the Cmentioning
confidence: 99%
“…Quantum thermodynamics [6][7][8] has emerged both as a field of fundamental interest, and as a potential candidate to improve the performance of thermal machines [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The optimal performance of these systems has been discussed within several frameworks and operational assumptions, ranging from low-dissipation and slow driving regimes [24][25][26][27][28], to shortcuts to adiabaticity approaches [29][30][31][32], to endoreversible engines [33,34]. Several techniques have been developed for the optimal control of two-level systems for achieving a variety of goals: from optimizing the speed [35][36][37], to generating efficient quantum gates [38,39], to controlling dissipation [40,41], and to optimizing thermodynamic performances [42][43][44][45][46][47].…”
Section: Introductionmentioning
confidence: 99%
“…To this end, there is a handful of microscopic models yielding reasonable expressions for σ. For relatively broad class of slowly driven systems (described by generalized Markovian master equation with a symmetric protocol for hot and cold isotherms), the dissipation ratio assumes the form σ = (T h /T c ) 1−ξ , where ξ stands for the exponent in the bath spectral density [33]. The limit σ → 0 thus corresponds to an infinitely super-Ohmic bath (ξ → ∞), while the opposite limit σ → ∞ is obtained for an infinitely sub-Ohmic bath (ξ → −∞).…”
Section: A Boundsmentioning
confidence: 99%
“…Therefore, they should be generally valid for slowly, but not quasi-statically, driven systems. Indeed, the decay of total dissipated heat with the inverse of duration was theoretically predicted for various quantum and classical setups [31][32][33][34] and observed in various experiments [35,36]. The second situation, where the assumption (1) and (2) holds for arbitrary cycle duration, are overdamped Brownian systems driven by special time-dependent protocols (usually minimizing dissipated energy during the isotherms [21,25,27,37,38]).…”
Section: Introductionmentioning
confidence: 99%
“…= mK s −1 , obtained maintaining the maximum real efficiency η real . Additional limitations to the maximum real efficiency attainable can come from the finite-time nature of the isothermal transformations, as shown in [36,37].The quantification of the performance of our UAEs can be done using well established techniques. The measurement of the level population of the K atom P n can be inferred by using Raman sideband spectroscopy [38], while the temperature of the Rb bath can be obtained with standard time-of-flight imaging.…”
Section: Resultsmentioning
confidence: 99%