Quantum-Classical Correspondence Principle for Work Distributions

Jarzynski, Christopher; Quan, H. T.; Rahav, Saar

doi:10.1103/physrevx.5.031038

Cited by 112 publications

(173 citation statements)

References 81 publications

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“…(39), I may then prove Eq. (30). However, it is also easy to arrive at this equality if one applies the forward equation (9).…”

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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“…(39), I may then prove Eq. (30). However, it is also easy to arrive at this equality if one applies the forward equation (9).…”

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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“…During the process, an amount W of work is done on the system. The microscopic work performed on the system in each run is defined as [5][6][7] …”

Section: Introductionmentioning

confidence: 99%

Work distribution in a photonic system

et al. 2016

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We present a proposal of a set-up to measure the work distribution of a process acting on a quantum system emulated by the transverse degrees of freedom of classical light. Hermite-Gaussian optical modes are used to represent the energy eigenstates of a quantum harmonic oscillator prepared in a thermal state. The Fourier transform of the work distribution, or the characteristic function, can be obtained by measuring the light intensity at the output of a properly designed interferometer. The usefulness of the approach is illustrated by calculating the work distribution for a unitary operation that displaces the linear momentum of the oscillator. Other types of processes and quantum systems can be implemented with the same scheme. We also show that the set-up can be used to investigate the energy distribution for open dynamics described by completely positive maps. We discuss the feasibility of the experiment, which can be realized with simple linear optical components.

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“…Using proper definitions this result can be extended to the quantum case and to open systems [314,315].…”

Section: Quantum Thermodynamicsmentioning

confidence: 99%

Quantum systems under frequency modulation

et al. 2017

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Abstract. We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has been of constant interest both experimentally and theoretically since, with the simple two-state model providing an inexhaustible source of novel concepts. When the transition frequency of a quantum system is modulated, several phenomena can be observed, such as Landau-Zener-Stückelberg-Majorana interference, motional averaging and narrowing, and the formation of dressed states with the presence of sidebands in the spectrum. Adiabatic changes result in the accumulation of geometric phases, which can be used to create topological states. In recent years, an exquisite experimental control in the time domain was gained through the parameters entering the Hamiltonian, and high-fidelity readout schemes allowed the state of the system to be monitored non-destructively. These developments were made in the field of quantum devices, especially in superconducting qubits, as a well as in atomic physics, in particular in ultracold gases. As a result of these advances, it became possible to demonstrate many of the fundamental effects that arise in a quantum system when its transition frequencies are modulated. The purpose of this review is to present some of these developments, from two-state atoms and harmonic oscillators to multilevel and many-particle systems.

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Quantum-Classical Correspondence Principle for Work Distributions

Cited by 112 publications

References 81 publications

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

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

Work distribution in a photonic system

Quantum systems under frequency modulation

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