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Title: Viscous Dissipation in One-Dimensional Quantum Liquids

Abstract

We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zerotemperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. In conclusion, our consideration is applicable to all single-component Galilean- invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.

Authors:
 [1];  [2]
  1. Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
  2. Georgia Inst. of Technology, Atlanta, GA (United States). School of Physics
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Materials Sciences and Engineering Division; USDOE
OSTI Identifier:
1393190
Alternate Identifier(s):
OSTI ID: 1372133
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 119; Journal Issue: 3; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE

Citation Formats

Matveev, K. A., and Pustilnik, M. Viscous Dissipation in One-Dimensional Quantum Liquids. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.119.036801.
Matveev, K. A., & Pustilnik, M. Viscous Dissipation in One-Dimensional Quantum Liquids. United States. doi:10.1103/PhysRevLett.119.036801.
Matveev, K. A., and Pustilnik, M. Thu . "Viscous Dissipation in One-Dimensional Quantum Liquids". United States. doi:10.1103/PhysRevLett.119.036801. https://www.osti.gov/servlets/purl/1393190.
@article{osti_1393190,
title = {Viscous Dissipation in One-Dimensional Quantum Liquids},
author = {Matveev, K. A. and Pustilnik, M.},
abstractNote = {We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zerotemperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. In conclusion, our consideration is applicable to all single-component Galilean- invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.},
doi = {10.1103/PhysRevLett.119.036801},
journal = {Physical Review Letters},
number = 3,
volume = 119,
place = {United States},
year = {2017},
month = {7}
}

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Cited by: 4 works
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Works referenced in this record:

Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states
journal, June 1990


Observation of Shock Waves in a Strongly Interacting Fermi Gas
journal, April 2011


Equilibration in a chiral Luttinger liquid
journal, May 2015


Electron-electron-scattering-induced size effects in a two-dimensional wire
journal, February 1994


Electrical and Thermal Transport in Inhomogeneous Luttinger Liquids
journal, June 2015


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

Hydrodynamic Effects in Solids at low Temperature
journal, February 1968


Solitons in a one-dimensional Wigner crystal
journal, April 2015


Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids
journal, December 1981


Effective mass of elementary excitations in Galilean-invariant integrable models
journal, September 2016


New wave‐operator identity applied to the study of persistent currents in 1D
journal, May 1974

  • Mattis, Daniel C.
  • Journal of Mathematical Physics, Vol. 15, Issue 5
  • DOI: 10.1063/1.1666693

Negative local resistance caused by viscous electron backflow in graphene
journal, February 2016


Functional theories of thermoelectric phenomena
journal, December 2016


Hydrodynamic Hamiltonian for a nonideal Bose gas
journal, May 1972

  • Popov, V. N.
  • Theoretical and Mathematical Physics, Vol. 11, Issue 2
  • DOI: 10.1007/BF01028563

Three-particle collisions in quantum wires: Corrections to thermopower and conductance
journal, June 2007

  • Lunde, Anders Mathias; Flensberg, Karsten; Glazman, Leonid I.
  • Physical Review B, Vol. 75, Issue 24
  • DOI: 10.1103/PhysRevB.75.245418

Decay of Bogoliubov excitations in one-dimensional Bose gases
journal, July 2016


Dynamical structure factor at small q for the XXZ spin-1/2 chain
journal, August 2007


One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm
journal, September 2012

  • Imambekov, Adilet; Schmidt, Thomas L.; Glazman, Leonid I.
  • Reviews of Modern Physics, Vol. 84, Issue 3
  • DOI: 10.1103/RevModPhys.84.1253

Dynamical Spin Structure Factor for the Anisotropic Spin- 1 / 2 Heisenberg Chain
journal, June 2006


Condensed Matter Theory of Dipolar Quantum Gases
journal, April 2012

  • Baranov, M. A.; Dalmonte, M.; Pupillo, G.
  • Chemical Reviews, Vol. 112, Issue 9
  • DOI: 10.1021/cr2003568

Lifetime of excitations in a clean Luttinger liquid
journal, August 1998


Fate of classical solitons in one-dimensional quantum systems
journal, November 2015


Coulomb Drag by Small Momentum Transfer between Quantum Wires
journal, September 2003


Dynamics of Dark Solitons in Elongated Bose-Einstein Condensates
journal, August 2002


Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
journal, October 2007


Kinetics of Mobile Impurities and Correlation Functions in One-Dimensional Superfluids at Finite Temperature
journal, April 2014


Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
journal, August 1998


Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas
journal, May 2014


Electron tunneling spectroscopy of a quantum antidot in the integer quantum Hall regime
journal, March 2008


Interaction effects on thermal transport in quantum wires
journal, September 2011


On the theory of the superfluidity of two- and one-dimensional bose systems
journal, June 1972

  • Popov, V. N.
  • Theoretical and Mathematical Physics, Vol. 11, Issue 3
  • DOI: 10.1007/BF01028373

The transport coefficients of a fermi liquid
journal, January 1970


Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
journal, May 1963


Single-particle states, Kohn anomaly, and pairing fluctuations in one dimension
journal, April 1974


Negative Temperature Derivative of Resistivity in Thin Potassium Samples: The Gurzhi Effect?
journal, January 1984


The theory of a fermi liquid (the properties of liquid 3He at low temperatures)
journal, January 1959


Evidence for hydrodynamic electron flow in PdCoO2
journal, February 2016


Gapless boundary excitations in the quantum Hall states and in the chiral spin states
journal, May 1991


Theory of the edge States in Fractional Quantum hall Effects
journal, May 1992


Relaxation of weakly interacting electrons in one dimension
journal, April 2013


Soliton operators for the quantized sine-Gordon equation
journal, May 1975


Hydrodynamic electron flow in high-mobility wires
journal, May 1995


Interacting electrons in one dimension beyond the Luttinger-liquid limit
journal, May 2010

  • Barak, Gilad; Steinberg, Hadar; Pfeiffer, Loren N.
  • Nature Physics, Vol. 6, Issue 7
  • DOI: 10.1038/nphys1678

Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
journal, February 2016


Fermionic quasiparticle representation of Tomonaga-Luttinger Hamiltonian
journal, September 2005


Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
journal, May 1963


Transport properties of partially equilibrated quantum wires
journal, March 2010


Spectral function of spinless fermions on a one-dimensional lattice
journal, April 2009


Searching for perfect fluids: quantum viscosity in a universal Fermi gas
journal, July 2011


Coulomb Oscillations in Antidots in the Integer and Fractional Quantum Hall Regimes
journal, June 2012


Relaxation of a High-Energy Quasiparticle in a One-Dimensional Bose Gas
journal, August 2010


Quantum Dipolar Gases in Boson or Fermion Flavor
journal, May 2012


Relaxation in Luttinger liquids: Bose-Fermi duality
journal, September 2014


Dynamic Response of One-Dimensional Interacting Fermions
journal, May 2006


Quantization of the (sin?)2 interaction in terms of fermion variables
journal, September 1975

  • Pogrebkov, A. K.; Sushko, V. N.
  • Theoretical and Mathematical Physics, Vol. 24, Issue 3
  • DOI: 10.1007/BF01029883

Dynamics of Excitations in a One-Dimensional Bose Liquid
journal, September 2007


Universal Quantum Viscosity in a Unitary Fermi Gas
journal, December 2010


Hydrodynamic Description of Transport in Strongly Correlated Electron Systems
journal, June 2011


Breakdown of Integrability in a Quasi-1D Ultracold Bosonic Gas
journal, May 2008


Dynamical Corrections to the DFT-LDA Electron Conductance in Nanoscale Systems
journal, May 2005


Incompleteness of the Landauer formula for electronic transport
journal, January 2009


Decay of Fermionic Quasiparticles in One-Dimensional Quantum Liquids
journal, December 2013