Equilibration Time Scales of Physically Relevant Observables

Luis Pedro Garcia Pintos, Noah Linden, Artur Malabarba, Tony Short, Andreas J Winter

Research output: Contribution to journalArticle (Academic Journal)peer-review

35 Citations (Scopus)
271 Downloads (Pure)


We address the problem of understanding from first principles the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand previously known general upper bounds on the time scales of equilibration were unrealistically long, with times scaling linearly with the dimension of the Hilbert space. These bounds proved to be tight, since
particular constructions of observables scaling in this way were found. On the other hand, the computed equilibration time scales for certain classes of typical measurements, or under the evolution of typical Hamiltonians, turn out to be unrealistically short. However neither classes of results cover physically relevant situations, which up to now had only been tractable in specific models. In this
paper we provide a new upper bound on the equilibration time scales which, under some physically reasonable conditions, give much more realistic results than previously known. In particular, we apply this result to the paradigmatic case of a system interacting with a thermal bath, where we obtain an upper bound for the equilibration time scale independent of the size of the bath. In this
way, we find general conditions that single out observables with realistic equilibration times within a physically relevant setup.
Original languageEnglish
Article number031027
Number of pages19
JournalPhysical Review X
Issue number3
Early online date10 Aug 2017
Publication statusPublished - Sep 2017

Structured keywords

  • QITG
  • Bristol Quantum Information Institute


  • Quantum Physics
  • Quantum Information
  • Statistical Physics

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