In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with the external environment under sequences of quantum measurements performed at random times. Both quenched and annealed averages are considered. The information about fluctuations is encoded in the quantum-heat probability density function, or equivalently in its characteristic function, whose general expression for a quantum system with arbitrary Hamiltonian is derived. We prove that, when a stochastic protocol of measurements is applied, the quantum Jarzynski equality is obeyed. Therefore, the fluctuation relation is robust against the presence of randomness in the times intervals between measurements. Then, for the paradigmatic case of a two-level system, we analytically characterize the quantum-heat transfer. Particular attention is devoted to the limit of large number of measurements and to the effects caused by the stochastic fluctuations. The relation with the stochastic Zeno regime is also discussed.

Nonequilibrium quantum-heat statistics under stochastic projective measurements / Gherardini, Stefano; Buffoni, Lorenzo; Müller, Matthias M.; Caruso, Filippo; Campisi, Michele; Trombettoni, Andrea; Ruffo, Stefano. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 98:3(2018), pp. 1-11. [10.1103/PhysRevE.98.032108]

Nonequilibrium quantum-heat statistics under stochastic projective measurements

Gherardini, Stefano;Buffoni, Lorenzo;Campisi, Michele;Trombettoni, Andrea;Ruffo, Stefano
2018

Abstract

In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with the external environment under sequences of quantum measurements performed at random times. Both quenched and annealed averages are considered. The information about fluctuations is encoded in the quantum-heat probability density function, or equivalently in its characteristic function, whose general expression for a quantum system with arbitrary Hamiltonian is derived. We prove that, when a stochastic protocol of measurements is applied, the quantum Jarzynski equality is obeyed. Therefore, the fluctuation relation is robust against the presence of randomness in the times intervals between measurements. Then, for the paradigmatic case of a two-level system, we analytically characterize the quantum-heat transfer. Particular attention is devoted to the limit of large number of measurements and to the effects caused by the stochastic fluctuations. The relation with the stochastic Zeno regime is also discussed.
98
3
1
11
032108
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.032108
https://arxiv.org/abs/1805.00773
Gherardini, Stefano; Buffoni, Lorenzo; Müller, Matthias M.; Caruso, Filippo; Campisi, Michele; Trombettoni, Andrea; Ruffo, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/88162
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