The Floquet-Boltzmann equation

Abstract

Periodically driven quantum systems can be used to realize quantum pumps, ratchets, artificial gauge fields and novel topological states of matter. Starting from the Keldysh approach, we develop a formalism, the Floquet-Boltzmann equation, to describe the dynamics and the scattering of quasiparticles in such systems. The theory builds on a separation of time-scales. Rapid, periodic oscillations occurring on a time scale $T_0=2\pi /\Omega$, are treated using the Floquet formalism and quasiparticles are defined as eigenstates of a non-interacting Floquet Hamiltonian. The dynamics on much longer time scales, however, is modelled by a Boltzmann equation which describes the semiclassical dynamics of the Floquet-quasiparticles and their scattering processes. As the energy is conserved only modulo $\hslash \Omega$, the interacting system heats up in the long-time limit. As a first application of this approach, we compute the heating rate for a cold-atom system, where a periodical shaking of the lattice was used to realize the Haldane model.

arXiv comment12 pages + 3 pages of appendix, 13 figures

References in corpus (39)

• Photonic Floquet Topological Insulators
• Experimental realisation of the topological Haldane model
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Photovoltaic Hall effect in graphene
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Topological characterization of periodically-driven quantum systems
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Dynamical control of matter-wave tunneling in periodic potentials
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Observation of topologically protected bound states in a one dimensional photonic system
• Many-body localization in periodically driven systems
• Floquet-Bloch theory and topology in periodically driven lattices
• Fate of many-body localization under periodic driving
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Floquet Fractional Chern Insulator in Doped Graphene
• Multiterminal Conductance of a Floquet Topological Insulator
• Periodic thermodynamics of isolated systems
• Directed Transport of Atoms in a Hamiltonian Quantum Ratchet
• Topological charge pumping in a one-dimensional optical lattice
• Dissipative Floquet Topological Systems
• Magnetically generated spin-orbit coupling for ultracold atoms
• Floquet topological transitions in a driven one-dimensional topological insulator
• Artificial graphene with tunable interactions
• Electric quantum walks with individual atoms
• Scattering Theory for Floquet-Bloch States
• Occupation of topological Floquet bands in open systems
• Phase-Space Berry Phases in Chiral Magnets: Dzyaloshinskii-Moriya Interaction and the Charge of Skyrmions
• Damping of Bloch oscillations in the Hubbard model
• Transport properties of a two-dimensional electron gas dressed by light
• Stability of a Floquet Bose-Einstein condensate in a one-dimensional optical lattice
• Fractional quantization of the topological charge pumping in a one-dimensional superlattice
• Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
• Directed motion of doublons and holes in periodically driven Mott insulators

Cited by in corpus (68)

• Atomic quantum gases in periodically driven optical lattices
• Keldysh Field Theory for Driven Open Quantum Systems
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• Direct observation of chiral currents and magnetic reflection in atomic flux lattices
• The theory of parametrically amplified electron-phonon superconductivity
• Heating and many-body resonances in a periodically driven two-band system
• Interaction dependent heating and atom loss in a periodically driven optical lattice
• Floquet dynamics in driven Fermi-Hubbard systems
• Time-dependent generalized Gibbs ensembles in open quantum systems
• Steady states and edge state transport in topological Floquet-Bloch systems
• Pumping approximately integrable systems
• Floquet band structure of a semi-Dirac system
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Effects of interactions on periodically driven dynamically localized systems
• Resonant thermalization of periodically driven strongly correlated electrons
• From localization to anomalous diffusion in the dynamics of coupled kicked rotors
• Periodically Driven Sachdev-Ye-Kitaev Models
• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• Universal chiral quasi-steady states in periodically driven many-body systems
• Time-induced second-order topological superconductors
• Steady state of interacting Floquet insulators
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• How periodic driving heats a disordered quantum spin chain
• Spin and topological order in a periodically driven spin chain
• Fermi's golden rule for heating in strongly driven Floquet systems
• An Autonomous Stabilizer for Incompressible Photon Fluids and Solids
• Pulsating flow and boundary layers in viscous electronic hydrodynamics
• A magnetic resonance in high-frequency viscosity of two-dimensional electrons
• Probing Topological signatures in an optically driven $\alpha$-$T_3$ Lattice
• Interband heating processes in a periodically driven optical lattice
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• The Floquet Engineer's Handbook
• Entanglement entropy in a periodically driven Ising chain
• Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal
• Quantum-optical magnets with competing short- and long-range interactions: Rydberg-dressed spin lattice in an optical cavity
• The optimal frequency window for Floquet engineering in optical lattices
• Effects of local periodic driving on transport and generation of bound states
• Floquet bound states around defects and adatoms in graphene
• Entanglement entropy in a periodically driven quantum Ising chain
• Floquet-Drude conductivity
• Floquet topological systems in the vicinity of band crossings: Reservoir induced coherence and steady-state entropy production
• Many-body dynamics and gap opening in interacting periodically driven systems
• Absence of Criticality in the Phase Transitions of Open Floquet Systems
• Stability of a Bose-Einstein condensate in a driven optical lattice: Crossover between weak and tight transverse confinement
• Stability of Floquet Majorana box qubits
• The Floquet Fermi Liquid
• Functional renormalization group in Floquet space
• Time Crystals in the Driven Transverse Field Ising Model under Quasiperiodic Modulation
• Floquet Heating in Interacting Atomic Gases with an Oscillating Force
• Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates
• Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
• Transport signatures in topological systems coupled to AC fields
• Inducing exceptional points, enhancing plasmon quality and creating correlated plasmon states with modulated Floquet parametric driving
• Semiclassical dynamics of electrons in space-time crystal: Magnetization, polarization, and current response
• Electronic Floquet Liquid Crystals
• Dynamic renormalization group theory for open Floquet systems
• Light controlled THz plasmonic time varying media: momentum gaps, entangled plasmon pairs, and pulse induced time reversal
• Optical Control of Slow Topological Electrons in Moiré Systems
• Floquet Graphene Antidot Lattices
• Prethermalization and wave condensation in a nonlinear disordered Floquet system
• Dynamics of photo-induced ferromagnetism in oxides with orbital degeneracy
• Floquet Renormalization Group Approach to the Periodically Driven Kondo Model
• Ultra-critical Floquet Non-Fermi Liquid
• Extended nonergodic regime and spin subdiffusion in disordered SU(2)-symmetric Floquet systems
• Superfluidity vs prethermalisation in a nonlinear Floquet system
• Controlling magnetic correlations in a driven Hubbard system far from half-filling
• Multiple particle-hole pair creation in the Fermi-Hubbard model by a pump laser
• Quantized Acoustoelectric Floquet Effect in Quantum Nanowires