From integrability to chaos in quantum Liouvillians

Rubio-García, Alvaro; Molina, Rafael; Dukelsky, Jorge

doi:10.21468/SciPostPhysCore.5.2.026

SciPost Physics Core

From integrability to chaos in quantum Liouvillians

Álvaro Rubio-García, Rafael A. Molina, Jorge Dukelsky

SciPost Phys. Core 5, 026 (2022) · published 2 May 2022

doi: 10.21468/SciPostPhysCore.5.2.026
pdf
Submissions/Reports

Abstract

The dynamics of open quantum systems can be described by a Liouvillian, which in the Markovian approximation fulfills the Lindblad master equation. We present a family of integrable many-body Liouvillians based on Richardson-Gaudin models with a complex structure of the jump operators. Making use of this new region of integrability, we study the transition to chaos in terms of a two-parameter Liouvillian. The transition is characterized by the spectral statistics of the complex eigenvalues of the Liouvillian operators using the nearest neighbor spacing distribution and by the ratios between eigenvalue distances.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.5.2.026
TI  - From integrability to chaos in quantum Liouvillians
PY  - 2022/05/02
UR  - https://www.scipost.org/SciPostPhysCore.5.2.026
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 5
IS  - 2
SP  - 026
A1  - Rubio-García, Alvaro
AU  - Molina, Rafael
AU  - Dukelsky, Jorge
AB  - The dynamics of open quantum systems can be described by a Liouvillian, which in the Markovian approximation fulfills the Lindblad master equation. We present a family of integrable many-body Liouvillians based on Richardson-Gaudin models with a complex structure of the jump operators. Making use of this new region of integrability, we study the transition to chaos in terms of a two-parameter Liouvillian. The transition is characterized by the spectral statistics of the complex eigenvalues of the Liouvillian operators using the nearest neighbor spacing distribution and by the ratios between eigenvalue distances.
ER  -

@Article{10.21468/SciPostPhysCore.5.2.026,
	title={{From integrability to chaos in quantum Liouvillians}},
	author={Álvaro Rubio-García and Rafael A. Molina and Jorge Dukelsky},
	journal={SciPost Phys. Core},
	volume={5},
	pages={026},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.5.2.026},
	url={https://scipost.org/10.21468/SciPostPhysCore.5.2.026},
}

Cited by 9

Authors / Affiliation: mappings to Contributors and Organizations

See all Organizations.

¹ Alvaro Rubio-García,
¹ Rafael Molina,
¹ Jorge Dukelsky

¹ Instituto de Estructura de la Materia / Institute for the Structure of Matter [IEM]

Funders for the research work leading to this publication

Consejo Superior de Investigaciones Científicas / Spanish National Research Council [CSIC]
Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])
Ministerio de Educación y Cultura - Spain (MEC) (through Organization: Ministerio de Educación y Cultura - España / Ministry of Education and Culture - Spain [MEC Spain])