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Title: Quantum Brownian motion in a quasiperiodic potential

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. Finally, 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.

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics, Clarendon Lab.; Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy
  2. Univ. of Massachusetts, Amherst, MA (United States)
  3. Univ. of Cambridge (United Kingdom). Cavendish Lab.
  4. Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics, Clarendon Lab.
Publication Date:
Research Org.:
Univ. of Massachusetts, Amherst, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Engineering and Physical Sciences Research Council (EPSRC)
OSTI Identifier:
1593356
Alternate Identifier(s):
OSTI ID: 1547990
Grant/Contract Number:  
SC0019168; DGE-1321846; DMR-1455366; EP/P034616/1
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 100; Journal Issue: 6; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Friedman, Aaron J., Vasseur, Romain, Lamacraft, Austen, and Parameswaran, S. A. Quantum Brownian motion in a quasiperiodic potential. United States: N. p., 2019. Web. doi:10.1103/PhysRevB.100.060301.
Friedman, Aaron J., Vasseur, Romain, Lamacraft, Austen, & Parameswaran, S. A. Quantum Brownian motion in a quasiperiodic potential. United States. https://doi.org/10.1103/PhysRevB.100.060301
Friedman, Aaron J., Vasseur, Romain, Lamacraft, Austen, and Parameswaran, S. A. Wed . "Quantum Brownian motion in a quasiperiodic potential". United States. https://doi.org/10.1103/PhysRevB.100.060301. https://www.osti.gov/servlets/purl/1593356.
@article{osti_1593356,
title = {Quantum Brownian motion in a quasiperiodic potential},
author = {Friedman, Aaron J. and Vasseur, Romain and Lamacraft, Austen and Parameswaran, S. A.},
abstractNote = {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. Finally, 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.},
doi = {10.1103/PhysRevB.100.060301},
journal = {Physical Review B},
number = 6,
volume = 100,
place = {United States},
year = {Wed Aug 07 00:00:00 EDT 2019},
month = {Wed Aug 07 00:00:00 EDT 2019}
}

Journal Article:

Citation Metrics:
Cited by: 2 works
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Figures / Tables:

FIG. 1 FIG. 1: Localization length ξ as a function of dissipation α for quasiperiodic potential with γ = ϕ (solid green). Inset: same plot on log-log scale. As α is decreased, ξ is a piecewise function that changes non-analytically for ααn = ϕ−2n between successive ξn = $\frac{q0}{2π}\sqrt\frac{2ℓ_n}{α}$ (seemore » Eq. 9).« less

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