2015/08/19 by Maximilian Genske, Achim Rosch · 2 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Floquet theory #Hamiltonian (control theory) #Mathematics #Physics #Quantum #Quantum electrodynamics #Quantum many-body systems #Quantum mechanics #Quasiparticle #Scattering #Semiclassical physics #Topological Materials and Phenomena #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.92.062108
published as Phys. Rev. A 92, 062108 (2015) · 12 pages + 3 pages of appendix, 13 figures
arxiv created 2015/08/19 · openalex publication_date 2015/12/07 · arxiv updated 2015/12/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 T0=2\ensuremathπ/\mathrm\ensuremathΩ are treated using the Floquet formalism and quasiparticles are defined as eigenstates of a noninteracting Floquet Hamiltonian. The dynamics on much longer time scales, however, is modeled by a Boltzmann equation which describes the semiclassical dynamics of the Floquet quasiparticles and their scattering processes. As the energy is conserved only modulo \ensuremathℏ\mathrm\ensuremathΩ, 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 [G. Jotzu et al., Nature (London) 515, 237 (2014)].