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: Department of Physics and Astronomy, University of Florence, via G. Sansone 1, Sesto Fiorentino, I-50019, Italy; CNR-INO, QSTAR, LENS, via N. Carrara 1, Sesto Fiorentino, I-50019, Italy; INFN, Sezione di Firenze, via G. Sansone 1, Sesto Fiorentino, I-50019, Italy; Department of Information Engineering, University of Florence, via S. Marta 3, Florence, I-50139, Italy; CNR-IOM DEMOCRITOS Simulation Center, via Bonomea 265, Trieste, I-34136, Italy; SISSA, via Bonomea 265, Trieste, I-34136, Italy; Istituto Dei Sistemi Complessi, CNR, via Madonna del Piano 10, Sesto Fiorentino, I-50019, Italy; Istituto Dei Sistemi Complessi, CNR, via Madonna del Piano 10, Sesto Fiorentino, I-50019, Italy; INFN, Sezione di Trieste, Trieste, I-34151, 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: 19
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