Relaxation of Multitime Statistics in Quantum Systems

Neil Dowling; Pedro Figueroa-Romero; Felix A. Pollock; Philipp Strasberg; Kavan Modi

doi:10.22331/q-2023-06-01-1027

Relaxation of Multitime Statistics in Quantum Systems

Neil Dowling¹, Pedro Figueroa-Romero², Felix A. Pollock¹, Philipp Strasberg³, and Kavan Modi¹

¹School of Physics & Astronomy, Monash University, Victoria 3800, Australia
²Hon Hai Quantum Computing Research Center, Taipei, Taiwan
³Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain

Published:	2023-06-01, volume 7, page 1027
Eprint:	arXiv:2108.07420v4
Doi:	https://doi.org/10.22331/q-2023-06-01-1027
Citation:	Quantum 7, 1027 (2023).

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Abstract

Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one, unless the system is probed for an extremely large number of times or the observable is particularly fine-grained. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate.

Featured image: An arbitrary, time-dependent multitime expectation value $\langle \textbf{A}_\textbf{k} \rangle_{\Upsilon} (\Delta t_1, \dots,\Delta t_k ) $ is shown (top), which can be computed from a quantum process tensor $\Upsilon$, composed of unitary evolution superoperators $\mathcal{U}_i$ and some initial state $\rho$. For a system with where the initial state overlaps significantly with many energy eigenstates, if the system is not probed too many times $k$, we show that on average this multitime correlation function is indistinguishable from a time-independent equilibrium quantity (bottom), $\langle \textbf{A}_\textbf{k} \rangle_{\Omega}$.

Popular summary

Why are macroscopic properties of a many-body system usually approximately stationary despite the exact miscrostate constantly evolving? It is a widely held belief that quantum mechanics alone should be enough to derive statistical mechanics, without any additional assumptions. A key piece of this puzzle is determining how one can observe stationary quantities in an isolated quantum system. In this work we show that multitime expectation values look stationary on average in large systems, when the initial state is not highly fine tuned and when the observable is coarse in both space and time. This means that relevant multitime features, such as the amount of memory in the quantum system, are generically independent of the exact times probed.

► BibTeX data

@article{Dowling2023relaxationof,
  doi = {10.22331/q-2023-06-01-1027},
  url = {https://doi.org/10.22331/q-2023-06-01-1027},
  title = {Relaxation of {M}ultitime {S}tatistics in {Q}uantum {S}ystems},
  author = {Dowling, Neil and Figueroa-Romero, Pedro and Pollock, Felix A. and Strasberg, Philipp and Modi, Kavan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1027},
  month = jun,
  year = {2023}
}

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