skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on August 7, 2020

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. doi: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. doi:10.1103/PhysRevB.100.060301.
@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 = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on August 7, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Exploring complex phenomena using ultracold atoms in bichromatic lattices
journal, July 2010


Quantum diffusion of a particle in a periodic potential with ohmic dissipation
journal, March 1985


Many-body localization phase transition
journal, November 2010


Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
journal, April 2018


Many-body physics with ultracold gases
journal, July 2008

  • Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
  • Reviews of Modern Physics, Vol. 80, Issue 3
  • DOI: 10.1103/RevModPhys.80.885

On Many-Body Localization for Quantum Spin Chains
journal, April 2016


Quantum Brownian motion in a periodic potential and the multichannel Kondo problem
journal, March 1998


Transport in a one-channel Luttinger liquid
journal, February 1992


Observation of many-body localization of interacting fermions in a quasirandom optical lattice
journal, July 2015


Noise correlation scalings: Revisiting the quantum phase transition in incommensurate lattices with hard-core bosons
journal, January 2012


Quantum ohmic dissipation: Particle on a one-dimensional periodic lattice
journal, September 1985


Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
journal, December 2017


Absence of Diffusion in Certain Random Lattices
journal, March 1958


Spectral features of a many-body-localized system weakly coupled to a bath
journal, August 2014


Fibonacci optical lattices for tunable quantum quasicrystals
journal, December 2015


Quantum Brownian motion in a periodic potential
journal, November 1985


Phase diagram of the dissipative Hofstadter model
journal, May 1992


Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states
journal, May 2006


Noise correlations of fermions and hard core bosons in a quasi-periodic potential
journal, February 2007


Many-body localization in the presence of a small bath
journal, January 2017


Dynamics of a heavy particle in a Luttinger liquid
journal, April 1996


Diffusion and Localization of a Particle in a Periodic Potential Coupled to a Dissipative Environment
journal, January 1985


Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas
journal, December 1992


Quantum tunnelling in a dissipative system
journal, September 1983


Many-Body Localization and Thermalization in Quantum Statistical Mechanics
journal, March 2015


Signatures of Many-Body Localization in a Controlled Open Quantum System
journal, March 2017


Many-body localization in a quasiperiodic system
journal, April 2013


Localization and Symmetry Breaking in the Quantum Quasiperiodic Ising Glass
journal, September 2017


Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid
journal, June 2009


The theory of a general quantum system interacting with a linear dissipative system
journal, October 1963


Many body localized systems weakly coupled to baths: Many body localized systems weakly coupled to baths
journal, November 2016

  • Nandkishore, Rahul; Gopalakrishnan, Sarang
  • Annalen der Physik, Vol. 529, Issue 7
  • DOI: 10.1002/andp.201600181

Griffiths effects and slow dynamics in nearly many-body localized systems
journal, April 2016

  • Gopalakrishnan, Sarang; Agarwal, Kartiek; Demler, Eugene A.
  • Physical Review B, Vol. 93, Issue 13
  • DOI: 10.1103/PhysRevB.93.134206

Stability and instability towards delocalization in many-body localization systems
journal, April 2017


Influence of Dissipation on Quantum Tunneling in Macroscopic Systems
journal, January 1981


Phenomenology of fully many-body-localized systems
journal, November 2014


Many-body localization: stability and instability
journal, October 2017

  • De Roeck, Wojciech; Imbrie, John Z.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 375, Issue 2108
  • DOI: 10.1098/rsta.2016.0422

Critical theories of the dissipative Hofstadter model
journal, March 1993