title: Quantum systems equilibrate rapidly for most observables.
abstract: Considering any Hamiltonian, any initial state, and measurements with a small number of possible outcomes compared to the dimension, we show that most measurements are already equilibrated. To investigate nontrivial equilibration, we therefore consider a restricted set of measurements. When the initial state is spread over many energy levels, and we consider the set of observables for which this state is an eigenstate, most observables are initially out of equilibrium yet equilibrate rapidly. Moreover, all two-outcome measurements, where one of the projectors is of low rank, equilibrate rapidly.
authors.affiliation: H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom.
authors.forename: Artur S L
authors.initials: AS
authors.lastname: Malabarba
authors.affiliation: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
authors.forename: Luis Pedro
authors.initials: LP
authors.lastname: García-Pintos
authors.affiliation: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
authors.forename: Noah
authors.initials: N
authors.lastname: Linden
authors.affiliation: DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom.
authors.forename: Terence C
authors.initials: TC
authors.lastname: Farrelly
authors.affiliation: H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom.
authors.forename: Anthony J
authors.initials: AJ
authors.lastname: Short
mesh_terms: D011789:Quantum Theory; D013696:Temperature