Fluctuations of work in nearly adiabatically driven open quantum systems

Suomela, Samu; Salmilehto, Juha; Savenko, I. G.; Ala-Nissilä, Tapio; Möttönen, Mikko

doi:10.1103/physreve.91.022126

Cited by 24 publications

(35 citation statements)

References 73 publications

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“…The approximate approaches provide these features qualitatively; however, quantitatively they differ quite substantially from the exact results. We note that an extended scheme for time-dependent driving with the LME [25][26][27][28] and slow driving with the QJ [33] have been developed recently, which account for the influence of the driving onto the dissipator in a more elaborate way, e.g., using the Floquet formalism. Instead, the SLN applies to arbitrary pulse forms and driving strengths, particularly to those obtained from optimal control schemes [22].…”

Section: Numerical Resultsmentioning

confidence: 99%

Work and heat for two-level systems in dissipative environments: Strong driving and non-Markovian dynamics

et al. 2015

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Work, moments of work and heat flux are studied for the generic case of a strongly driven twolevel system immersed in a bosonic heat bath in domains of parameter space where perturbative treatments fail. This includes particularly the interplay between non-Markovian dynamics and moderate to strong external driving. Exact data are compared with predictions from weak coupling approaches. Further, the role of system-bath correlations in the initial thermal state and their impact on the heat flux are addressed. The relevance of these results for current experimental activities on solid state devices is discussed.

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Section: Numerical Resultsmentioning

confidence: 99%

Work and heat for two-level systems in dissipative environments: Strong driving and non-Markovian dynamics

et al. 2015

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“…Furthermore, the impact of decoherence in the form of pure dephasing can be straightforwardly added as a new set of quantum jumps operators [53]. In the future, our approach may also be refined by taking into account the effects of the boson-boson interactions and the drive in the quantum-jump operators [54,55]. In this Appendix, we express the coupling Hamiltonian between the polaritons and the phonon bath in a convenient form which we later employ in Appendix C to derive the master equation of the polariton system.…”

Section: Discussionmentioning

confidence: 99%

Quantum treatment of the Bose-Einstein condensation in nonequilibrium systems

et al. 2015

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We develop a fully quantum-mechanical approach, based on stochastic trajectories, for an incoherently pumped system of interacting bosons in contact with a thermal reservoir. It enables a complete characterization of coherence in such a multimode system. We apply our model to microcavity exciton polaritons interacting with acoustic phonons and observe the formation of a macroscopic occupation in the lowest-energy mode accompanied by the simultaneous establishment of temporal and spatial coherence. We describe the transition from thermal to coherent statistics together with the expected emergence of an off-diagonal long-range order.

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“…First, Eqs. (27) and (28) are in fact valid for any initial density matrix that is diagonalized in terms of the energy basis [12,24], e.g.,…”

Section: Appendix I: An Explanation Of Eq (19)mentioning

confidence: 99%

Calculating work in weakly driven quantum master equations: Backward and forward equations

Liu

2016

Phys. Rev. E

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I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014)], while the other is based on two energy measurements on the combined system and reservoir [Silaev, et al., Phys. Rev. E 90, 022103 (2014)]. These represent backward and forward methods, respectively, which adopt a very similar approach to that of the Kolmogorov backward and forward equations used in classical stochastic theory. The microscopic basis for the former method is also clarified. In addition, a previously unnoticed equality related to the heat is also revealed. Introduction. Recently, there has been growing interest in the heat and work of nonequilibrium quantum processes . Studies focusing on this issue have mainly been motivated by an interest in extending the important classical fluctuation relations into the quantum regime, e.g., the celebrated Bochkov-Kuzovlev equality [1] and the Jarzynski equality (JE) [31].Compared with their classical counterparts [32], which are physically intuitive, the definitions of fluctuating heat and work become very delicate in the quantum case. In order to formulate a quantum JE, in a closed quantum system, a two-energy measurements (TEM) scheme was proposed by Kurchan [2] to define the work. Although this definition still faces criticisms related to the fact that the scheme may destroy the initial quantum-coherent superposition of the system [33], it has been widely accepted in the field [12,13,34]. Because closed quantum systems are not common in reality, there have also been many attempts to generalize this definition to include open quantum systems [35]. These efforts can be roughly divided into two types of method. The first type [11,12,25] involves the combination of the system and its surrounding heat reservoir as a composite system. The TEM scheme is then conducted on the system and reservoir. As the interaction between these is weak, the energy eigenvalue change obtained using the TEM for the system is referred to as the internal energy change, while the energy eigenvalue change obtained by the TEM for the reservoir is referred to as the heat released from the system, Q T EM . Therefore, the work done on the open system, W T EM , is the sum of the internal energy change and the heat. The second type of method is based on the quantum jump trajectory (QJT) that is unraveled from the Lindblad quantum master equations [6,9,17,18,[21][22][23][24]36]. Under this notion, the energy change of the heat reservoir is continuously measured. This is interpreted as the released heat along a trajectory, Q QJT . If one preserves the internal energy change of the system mentioned above, an alternative work, W QJT , is then the sum of the heat and internal energy change along the same trajectory. Figure (1) schematically illustrates the difference between these two types of work in a two-level qu...

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Fluctuations of work in nearly adiabatically driven open quantum systems

Cited by 24 publications

References 73 publications

Work and heat for two-level systems in dissipative environments: Strong driving and non-Markovian dynamics

Work and heat for two-level systems in dissipative environments: Strong driving and non-Markovian dynamics

Quantum treatment of the Bose-Einstein condensation in nonequilibrium systems

Calculating work in weakly driven quantum master equations: Backward and forward equations

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