Thermalization processes induced by quantum monitoring in multilevel systems

Year: 2021

Authors: Gherardini S.; Giachetti G.; Ruffo S.; Trombettoni A.

Autors Affiliation: 1) SISSA, via Bonomea 265, I-34136 Trieste, & INFN, Italy; Department of Physics and Astronomy & LENS, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy; CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy. 2) SISSA, via Bonomea 265, I-34136 Trieste, & INFN, Italy. 3) SISSA, via Bonomea 265, I-34136 Trieste, & INFN, Italy; Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy. 4) Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy; SISSA, via Bonomea 265, I-34136 Trieste, & INFN, Italy; CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy.

Abstract: We study the heat statistics of a multilevel N-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number M of measurements (M -> infinity). In this context, the conditions allowing for an infinite-temperature thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the nonequilibrium evolution of the system and its initial state. Exceptions to ITT, which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasicommuting) with the Hamiltonian of the quantum system or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N -> infinity), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits M -> infinity and N -> infinity matters: When N is fixed and M diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A nontrivial result is obtained fixing M/N-2 where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented.


Volume: 104 (3)      Pages from: 034114-1  to: 034114-14

More Information: The authors gratefully acknowledge N. Fabbri, S. Hernandez-Gomez, and F. Poggiali for useful discussions. This work was financially supported by the MISTI Global Seed Funds MIT-FVG Collaboration Grant “NV centers for the test of the Quantum Jarzynski Equality (NVQJE) ” and the MIUR-PRIN2017 project “Coarse-grained description for nonequilibrium systems and transport phenomena (CO-NEST) ” No. 201798CZL.
KeyWords: FLUCTUATION RELATIONS, Quantum monitoring, Thermalization
DOI: 10.1103/PhysRevE.104.034114