Equilibrium states of generic quantum systems subject to periodic driving

Achilleas Lazarides; Arnab Das; Roderich Moessner

doi:10.1103/PhysRevE.90.012110

paper

Equilibrium states of generic quantum systems subject to periodic driving

arXiv:1403.2946 · doi:10.1103/PhysRevE.90.012110

Abstract

When a closed quantum system is driven periodically with period $T$ , it approaches a periodic state synchronized with the drive in which any local observable measured stroboscopically approaches a steady value. For integrable systems, the resulting behaviour is captured by a periodic version of a generalized Gibbs ensemble. By contrast, here we show that for generic non-integrable interacting systems, local observables become independent of the initial state entirely. Essentially, this happens because Floquet eigenstates of the driven system at quasienergy $ω_{α}$ consist of a mixture of the exponentially many eigenstates of the undriven Hamiltonian which are thus drawn from the entire extensive undriven spectrum. This is a form of equilibration which depends only on the Hilbert space of the undriven system and not on any details of its Hamiltonian.

Equilibrium states of generic quantum systems subject to periodic driving

Abstract

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