2007/03/19 by S. I. Denisov, S. Denisov, L. Morales-Molina +4 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Eigenvalues and eigenvectors #Floquet theory #Hamiltonian (control theory) #Homogeneous space #Mathematics #Nonlinear Dynamics and Pattern Formation #Phase space #Physics #Quantum #Quantum chaos #Quantum dynamics #Quantum mechanics #Ratchet #Spectroscopy and Quantum Chemical Studies #cond-mat.stat-mech #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreva.75.063424
published as Phys. Rev. A, 75 (2007) 063424 · 10 pages, 10 figures
arxiv created 2007/03/19 · openalex publication_date 2007/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the quantum version of a tilting and flashing Hamiltonian ratchet, consisting of a periodic potential and a time-periodic driving field. The system dynamics is governed by a Floquet evolution matrix bearing the symmetry of the corresponding Hamiltonian. The dc-current appears due to the desymmetrization of Floquet eigenstates, which become transporting when all the relevant symmetries are violated. Those eigenstates that mostly contribute to a directed transport reside in phase space regions corresponding to classical resonances. Quantum dynamics leads to the dependence of the average velocity on the initial phase of the ac-field. A resonant enhancement (or suppression) of the dc-current, due to avoided crossings between different Floquet states, takes place upon tuning some control parameters. Our studies are predominantly aimed at experimental realizations of ac-driven quantum ratchets with cold atoms.