Nonequilibrium quantum-heat statistics under stochastic projective measurements

Year: 2018

Authors: Gherardini S., Buffoni L., Muller MM., Caruso F., Campisi M., Trombettoni A., Ruffo S.

Autors Affiliation: Univ Florence, Dept Phys & Astron, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy; CNR, INO, QSTAR, Via N Carrara 1, I-50019 Sesto Fiorentino, Italy; LENS, Via N Carrara 1, I-50019 Sesto Fiorentino, Italy; INFN, Sez Firenze, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy; Univ Florence, Dept Informat Engn, Via S Marta 3, I-50139 Florence, Italy; CNR, IOM DEMOCRITOS, Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy; SISSA, Via Bonomea 265, I-34136 Trieste, Italy; INFN, Sez Trieste, I-34151 Trieste, Italy; CNR, Ist Sistemi Complessi, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy.

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.

Journal/Review: PHYSICAL REVIEW E

Volume: 98 (3)      Pages from: 032108-1  to: 032108-11

More Information: The authors gratefully acknowledge Giacomo Gori for fruitful discussions. S.G., M.M., and F.C. were financially supported from the Fondazione CR Firenze through the project Q-BIOSCAN. S.G. and L.B. also acknowledge the Scuola Internazionale Superiore di Studi Avanzati (SISSA) in Trieste for hospitality during the completion of this work.
KeyWords: Hamiltonians, Heat transfer, Probability density function, Quantum optics
DOI: 10.1103/PhysRevE.98.032108

Citations: 18
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