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Title: Quantum Hall effect in a one-dimensional dynamical system

Abstract

We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.

Authors:
; ;  [1];  [2]
  1. Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, NL-2300 RA Leiden (Netherlands)
  2. Institute of Theoretical Physics, University of Warsaw, Hoza 69, PL-00-681 Warsaw (Poland)
Publication Date:
OSTI Identifier:
21596870
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 84; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevB.84.115133; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HALL EFFECT; HAMILTONIANS; INTERFERENCE; LASER RADIATION; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; PHASE TRANSFORMATIONS; QUANTUM MECHANICS; REDUCTION; STARK EFFECT; TIME DEPENDENCE; TWO-DIMENSIONAL CALCULATIONS; CHEMICAL REACTIONS; ELECTROMAGNETIC RADIATION; MATHEMATICAL OPERATORS; MECHANICS; QUANTUM OPERATORS; RADIATIONS; VARIATIONS

Citation Formats

Dahlhaus, J. P., Edge, J. M., Beenakker, C. W. J., and Tworzydlo, J. Quantum Hall effect in a one-dimensional dynamical system. United States: N. p., 2011. Web. doi:10.1103/PHYSREVB.84.115133.
Dahlhaus, J. P., Edge, J. M., Beenakker, C. W. J., & Tworzydlo, J. Quantum Hall effect in a one-dimensional dynamical system. United States. doi:10.1103/PHYSREVB.84.115133.
Dahlhaus, J. P., Edge, J. M., Beenakker, C. W. J., and Tworzydlo, J. Thu . "Quantum Hall effect in a one-dimensional dynamical system". United States. doi:10.1103/PHYSREVB.84.115133.
@article{osti_21596870,
title = {Quantum Hall effect in a one-dimensional dynamical system},
author = {Dahlhaus, J. P. and Edge, J. M. and Beenakker, C. W. J. and Tworzydlo, J.},
abstractNote = {We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.},
doi = {10.1103/PHYSREVB.84.115133},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 11,
volume = 84,
place = {United States},
year = {2011},
month = {9}
}