Floquet systems coupled to particle reservoirs

Abstract

Open quantum systems, when driven by a periodic field, can relax to effective statistical ensembles that resemble their equilibrium counterparts. We consider a class of problems in which a periodically- driven quantum system is allowed to exchange both energy and particles with a thermal reservoir. We demonstrate that, even for noninteracting systems, effective equilibration to the grand canonical ensemble requires both fine tuning the system-bath coupling and selecting a sufficiently simple driving protocol. We study a tractable subclass of these problems in which the long-time steady state of the system can be determined analytically, and demonstrate that the system effectively thermalizes with fine tuning, but does not thermalize for general values of the system-bath couplings. When the driven system does not thermalize, it supports a tunable persistent current in the steady state without external bias. We compute this current analytically for two examples of interest: 1) a driven double quantum dot, where the current is interpreted as a DC electrical current, and 2) driven Dirac fermions in graphene, where it is interpreted as a valley current.

15 pages, 6 figures; Revised version includes small changes. Note title change (in response to referees' comments)

References in corpus (15)

• Photovoltaic Hall effect in graphene
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Driven quantum transport on the nanoscale
• Equilibrium states of generic quantum systems subject to periodic driving
• Electron fractionalization in two-dimensional graphenelike structures
• Periodically driven ergodic and many-body localized quantum systems
• Dissipative Floquet Topological Systems
• Condition for emergence of the Floquet-Gibbs state in periodically driven open systems
• Materials design from non-equilibrium steady states: driven graphene as a tunable semiconductor with topological properties
• Stochastic thermodynamics of rapidly driven systems
• Statistical mechanics of Floquet systems with regular and chaotic states
• Charge transport through a molecule driven by a high-frequency field
• Classification of Floquet Statistical Distribution for Time-Periodic Open Systems
• Stroboscopic versus non-stroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian
• Photo-induced superconductivity in semiconductors

Cited by in corpus (8)

• Occupation of topological Floquet bands in open systems
• Floquet analysis of a quantum system with modulated periodic driving
• Floquet band structure of a semi-Dirac system
• Effects of interactions on periodically driven dynamically localized systems
• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• 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
• Periodically-driven Kondo impurity in nonequilibrium steady states