Thermalization processes induced by quantum monitoring in multi-level systems release_stltlfxjh5hwlcxjblmpltbnt4

by Stefano Gherardini, Guido Giachetti, Stefano Ruffo, Andrea Trombettoni

Released as a article .

2020  

Abstract

We study the heat statistics of an 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 of measurements. In this context, conditions allowing for Infinite-Temperature Thermalization (ITT), induced by the 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 non-equilibrium evolution of the system and its initial state. Exceptions to ITT take place when the observable of the intermediate measurements is commuting (or quasi-commuting) with the Hamiltonian of the system, or when the time interval between measurements is smaller or comparable with the energy scale of the quantum system (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N →∞) - describing continuous systems with a discrete spectrum - are presented. By denoting with M the number of quantum measurements, we show that the order of the limits M →∞ and N →∞ matters: when N is fixed and M diverges, then there is ITT. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A non trivial result is obtained fixing M/N^2 where partial ITT occurs. Finally, an example of incomplete thermalization applicable to rotating two-dimensional gases is presented.
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Type  article
Stage   submitted
Date   2020-12-30
Version   v1
Language   en ?
arXiv  2012.15216v1
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