Hilbert-space localization in closed quantum systems

Doron Cohen, Vyacheslav I. Yukalov, Klaus Ziegler

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Quantum localization within an energy shell of a closed quantum system stands in contrast to the ergodic assumption of Boltzmann, and to the corresponding eigenstate thermalization hypothesis. The familiar case is the real-space Anderson localization and its many-body Fock-space version. We use the term Hilbert-space localization in order to emphasize the more general phase-space context. Specifically, we introduce a unifying picture that extends the semiclassical perspective of Heller, which relates the localization measure to the probability of return. We illustrate our approach by considering several systems of experimental interest, referring in particular to the bosonic Josephson tunneling junction. We explore the dependence of the localization measure on the initial state and on the strength of the many-body interactions using a recursive projection method.

Original languageEnglish
Article number042101
JournalPhysical Review A
Issue number4
StatePublished - 1 Apr 2016

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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