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Solvable model of deep thermalization with distinct design times

Matteo IppolitiWen Wei Ho
Aug 2022
摘要
We study the emergence over time of a universal, uniform distribution ofquantum states on a finite subsystem, induced by projectively measuring therest of the system. Dubbed deep thermalization, this phenomenon represents aform of equilibration in quantum many-body systems stronger than regularthermalization, which only constrains the ensemble-averaged values ofobservables. While there exist quantum circuit models of dynamics in onedimension where this phenomenon can be shown to arise exactly, these arespecial in that deep thermalization occurs at precisely the same time asregular thermalization. Here, we present an exactly-solvable model of chaoticdynamics where the two processes can be shown to occur over different timescales. The model is composed of a finite subsystem coupled to an infiniterandom-matrix bath through a small constriction, and highlights the role oflocality and imperfect thermalization in constraining the formation of suchuniversal wavefunction distributions. We test our analytical predictionsagainst exact numerical simulations, finding excellent agreement.
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