Quantum Brownian motion in a quasiperiodic potential

We study the behavior of a quantum particle in one dimension subject to Ohmic dissipation, moving in a bichromatic quasiperiodic potential. The bath is described by the Caldeira-Leggett model; absent the potentials, the particle-bath system resolves the Langevin equation in the classical limit. In a single-period potential, the particle undergoes a zero-temperature localization-delocalization transition as dissipation strength is decreased. We show that the delocalized phase is absent in the quasiperiodic case, even when the deviation from periodicity is infinitesimal. Using the renormalization group, we determine how the crossover time to the localized phase depends on the dissipation strength and incommensurability of the two frequencies, and from this, extract a localization length. Finally, we show that a similar problem can be realized as the strong-coupling limit of a mobile impurity moving in a periodic optical lattice and immersed in a one-dimensional Fermi or Bose gas.