# Quantum Brownian motion in a quasiperiodic potential

## TL;DR

This paper investigates how quantum particles in a quasiperiodic potential behave under dissipation, revealing the absence of a delocalized phase present in periodic systems and analyzing localization length dependence.

## Contribution

It demonstrates that the delocalized phase does not occur in quasiperiodic potentials, unlike in periodic ones, and connects this to the strong-coupling limit of a mobile impurity in a quantum gas.

## Key findings

- No delocalized phase in quasiperiodic potential with dissipation.
- Localization length depends on dissipation strength.
- Connection to impurity dynamics in quantum gases.

## Abstract

We consider a quantum particle subject to Ohmic dissipation, moving in a bichromatic quasiperiodic potential. In a periodic 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 effective localization length depends on the dissipation. We show that {a similar problem can emerge in} the strong-coupling limit of a mobile impurity moving in a periodic lattice and immersed in a one-dimensional quantum gas.