Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.12202/6448
Title: Timescales in the quench dynamics of many-body quantum systems: Participation ratio versus out-of-time ordered correlator.
Authors: Santos, Lea F.
Borgonovi, F.
Izrailev, F.M.
0000-0001-9400-2709
Keywords: Nonequilibrium statistical mechanics
Statistical Physics
Issue Date: 31-May-2019
Publisher: American Physical Society
Citation: Santos, Lea F., Fausto Borgonovi, Felix M Izrailev. (2019). Timescales in the quench dynamics of many-body quantum systems: Participation ratio versus out-of-time ordered correlator. Physical Review E 99(5): 052143
Series/Report no.: Physical Review E;99(5)
Abstract: We study quench dynamics in the many-body Hilbert space using two isolated systems with a finite number of interacting particles: a paradigmatic model of randomly interacting bosons and a dynamical (clean) model of interacting spins-1/2. For both systems in the region of strong quantum chaos, the number of components of the evolving wave function, defined through the number of principal components Npc (or participation ratio), was recently found to increase exponentially fast in time [Phys. Rev. E 99, 010101(R) (2019)]. Here, we ask whether the out-of-time ordered correlator (OTOC), which is nowadays widely used to quantify instability in quantum systems, can manifest analogous time dependence. We show that Npc can be formally expressed as the inverse of the sum of all OTOCs for projection operators. While none of the individual projection OTOCs show an exponential behavior, their sum decreases exponentially fast in time. The comparison between the behavior of the OTOC with that of the Npc helps us better understand wave packet dynamics in the many-body Hilbert space, in close connection with the problems of thermalization and information scrambling.
Description: Research article, peer-reviewed. Open Access.
URI: https://doi.org/10.1103/PhysRevE.99.052143
https://hdl.handle.net/20.500.12202/6448
ISSN: Print: 1539-3755 Electronic: 1550-2376
Appears in Collections:Stern College for Women -- Faculty Publications

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