Equilibration of multitime quantum processes in finite time intervals

Abstract

A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic processes, we prove that under loose assumptions, quantum processes equilibrate within finite time intervals. Sufficient conditions for this to occur are that multitime observables are coarse grained in both space and time, and that the initial state overlaps with many different energy eigenstates. These results help bridge the gap between (unitary) quantum and (non-unitary) statistical physics, i.e., when all multitime properties and correlations are well approximated by stationary quantities, which includes non-Markovianity and temporal entanglement. We discuss implications of this result for the emergence of classical stochastic processes from multitime measurements of an underlying genuinely quantum system.

Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach

“…For instance, classicality could here be only established for "mini-histories" with two measurement results and extending the derivation to longer histories, as done in a different context in Refs. [100][101][102][103], is highly desirable. Indeed, recent numerical results for up to five-time histories have confirmed that the emergence of classicality is a robust phenomenon [107].…”

“…However, abstracting from Refs. [100][101][102][103], where theorems about n-time correlations functions for large n were proven under different circumstances, it appears likely that approximate consistency continues to hold also for n > 2.…”