From integrability to chaos in quantum Liouvillians
Álvaro Rubio-García, Rafael A. Molina, J. Dukelsky
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.
Topics & Concepts
Eigenvalues and eigenvectorsIntegrable systemMaster equationQuantum chaosQuantumMathematicsStatistical physicsJumpDistribution (mathematics)Mathematical physicsCHAOS (operating system)Pure mathematicsPhysicsQuantum mechanicsMathematical analysisQuantum dynamicsComputer scienceComputer securityQuantum many-body systemsQuantum chaos and dynamical systemsSpectroscopy and Quantum Chemical Studies