Non-stationary quantum many-body dynamics
Berislav Buca
Non-stationary processes are special types of non-mixing dynamics characterised by long-time deterministic dynamics. They are ubiquitous in the real world around us - from biological to social phenomena. Likewise, on the quantum level, any successful long circuit depth calculation on a quantum computer is, by definition, non-stationary.
Therefore, understanding how non-stationarity emerges from the microscopic quantum laws is of fundamental scientific and technological importance. I will discuss simple algebraic conditions that prevent a quantum many-body system from ever reaching a stationary state, not even a non-equilibrium one. I give several physically relevant examples in both closed and open quantum many-body systems, including an XXZ spin chain in a strong tilt field, a spin-1/2 Creutz ladder with oscillating out-of-time-order correlators, a spin-dephased Fermi-Hubbard model, and a two-component BEC in a lossy optical cavity which was recently experimentally studied.
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