The Lyapunov spectra of quantum thermalisation

A. Hallam (), J. G. Morley and A. G. Green
Additional contact information
A. Hallam: University College London
J. G. Morley: University College London
A. G. Green: University College London

Nature Communications, 2019, vol. 10, issue 1, 1-8

Abstract: Abstract Thermalisation in closed quantum systems occurs through a process of dephasing due to parts of the system outside of the window of observation, gradually revealing the underlying thermal nature of eigenstates. In contrast, closed classical systems thermalize due to dynamical chaos. We demonstrate a deep link between these processes. Projecting quantum dynamics onto variational states using the time-dependent variational principle, results in classical chaotic Hamiltonian dynamics. We study an infinite spin chain in two ways—using the matrix product state ansatz for the wavefunction and for the thermofield purification of the density matrix—and extract the full Lyapunov spectrum of the resulting dynamics. We show that the entanglement growth rate is related to the Kolmogorov–Sinai entropy of dynamics projected onto states with appropriate entanglement, extending previous results about initial entanglement growth to all times. The Lyapunov spectra for thermofield descriptions of thermalizing systems show a remarkable semi-circular distribution.

Date: 2019
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.nature.com/articles/s41467-019-10336-4 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:10:y:2019:i:1:d:10.1038_s41467-019-10336-4

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-019-10336-4

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().