Statistical mechanics of Floquet systems with regular and chaotic states

Abstract

We investigate the asymptotic state of time-periodic quantum systems with regular and chaotic Floquet states weakly coupled to a heat bath. The asymptotic occupation probabilities of these two types of states follow fundamentally different distributions. Among regular states the probability decreases from the state in the center of a regular island to the outermost state by orders of magnitude, while chaotic states have almost equal probabilities. We derive an analytical expression for the occupations of regular states of kicked systems, which depends on the winding numbers of the regular tori and the parameters temperature and driving frequency. For a constant winding number within a regular island it simplifies to Boltzmann-like weights $\exp(-\betaeff \Ereg_m)$, similar to time-independent systems. For this we introduce the regular energies $\Ereg_m$ of the quantizing tori and an effective winding-number-dependent temperature $1/\betaeff$, different from the actual bath temperature. Furthermore, the occupations of other typical Floquet states in a mixed phase space are studied, i.e. regular states on nonlinear resonances, beach states, and hierarchical states, giving rise to distinct features in the occupation distribution. Avoided crossings involving a regular state lead to drastic consequences for the entire set of occupations. We introduce a simplified rate model whose analytical solutions describe the occupations quite accurately.

18 pages, 11 figures

References in corpus (2)

• Regular-to-chaotic tunneling rates using a fictitious integrable system
• Switching mechanism in periodically driven quantum systems with dissipation

Cited by in corpus (25)

• Floquet States in Open Quantum Systems
• Unpaired Floquet Majorana fermions without magnetic fields
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Kilohertz-driven Bose-Einstein condensates in optical lattices
• Classification of Floquet Statistical Distribution for Time-Periodic Open Systems
• Floquet systems coupled to particle reservoirs
• Kinetics and thermodynamics of a driven open quantum system
• Autoparametric resonance extending the bit-flip time of a cat qubit up to 0.3 s
• High-frequency expansions for time-periodic Lindblad generators
• Cavity-based reservoir engineering for Floquet-engineered superconducting circuits
• Quantum diffusion and thermalization at resonant tunneling
• Keldysh approach to periodically driven systems with a fermionic bath: non-equilibrium steady state, proximity effect and dissipation
• Long time asymptotic state of periodically driven open quantum systems
• Structurally stable subharmonic regime of a driven quantum Josephson circuit
• Floquet-heating-induced Bose condensation in a scar-like mode of an open driven optical-lattice system
• Periodic thermodynamics of the parametrically driven harmonic oscillator
• Periodically-driven Kondo impurity in nonequilibrium steady states
• Non-equilibrium steady state of sparse systems
• Quantum Dissipation at Conical Intersections of Quasienergies
• The missing quantum number of the Floquet states
• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering
• Frozonium: Freezing Anharmonicity in Floquet Superconducting Circuits
• Environment-controlled Floquet-state paramagnetism
• The open driven two-level system at conical intersections of quasienergies
• Classical periodic trajectories and quantum scars in many-spin systems