Quantum Hall effect in a one-dimensional dynamical system
  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. 
J. P. Dahlhaus, J. M. Edge, J. Tworzydlo, and C. W. J. Beenakker
cond-mat.mes-hall cond-mat.quant-gas