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:
-
- Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
- Georgia Inst. of Technology, Atlanta, GA (United States). School of Physics
- Publication Date:
- Research Org.:
- Argonne National Laboratory (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. https://doi.org/10.1103/PhysRevLett.119.036801
Matveev, K. A., and Pustilnik, M. Thu .
"Viscous Dissipation in One-Dimensional Quantum Liquids". United States. https://doi.org/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 = {Thu Jul 20 00:00:00 EDT 2017},
month = {Thu Jul 20 00:00:00 EDT 2017}
}
Web of Science
Works referenced in this record:
Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states
journal, June 1990
- Wen, X. G.
- Physical Review B, Vol. 41, Issue 18
Observation of Shock Waves in a Strongly Interacting Fermi Gas
journal, April 2011
- Joseph, J. A.; Thomas, J. E.; Kulkarni, M.
- Physical Review Letters, Vol. 106, Issue 15
Equilibration in a chiral Luttinger liquid
journal, May 2015
- Protopopov, I. V.; Gutman, D. B.; Mirlin, A. D.
- Physical Review B, Vol. 91, Issue 19
Electron-electron-scattering-induced size effects in a two-dimensional wire
journal, February 1994
- Molenkamp, L. W.; de Jong, M. J. M.
- Physical Review B, Vol. 49, Issue 7
Electrical and Thermal Transport in Inhomogeneous Luttinger Liquids
journal, June 2015
- DeGottardi, Wade; Matveev, K. A.
- Physical Review Letters, Vol. 114, Issue 23
Many-body physics with ultracold gases
journal, July 2008
- Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
- Reviews of Modern Physics, Vol. 80, Issue 3
Hydrodynamic Effects in Solids at low Temperature
journal, February 1968
- Gurzhi, R. N.
- Soviet Physics Uspekhi, Vol. 11, Issue 2
Solitons in a one-dimensional Wigner crystal
journal, April 2015
- Pustilnik, M.; Matveev, K. A.
- Physical Review B, Vol. 91, Issue 16
Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids
journal, December 1981
- Haldane, F. D. M.
- Physical Review Letters, Vol. 47, Issue 25
Effective mass of elementary excitations in Galilean-invariant integrable models
journal, September 2016
- Matveev, K. A.; Pustilnik, M.
- Physical Review B, Vol. 94, Issue 11
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
Negative local resistance caused by viscous electron backflow in graphene
journal, February 2016
- Bandurin, D. A.; Torre, I.; Kumar, R. K.
- Science, Vol. 351, Issue 6277
Hydrodynamic Hamiltonian for a nonideal Bose gas
journal, May 1972
- Popov, V. N.
- Theoretical and Mathematical Physics, Vol. 11, Issue 2
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
Decay of Bogoliubov excitations in one-dimensional Bose gases
journal, July 2016
- Ristivojevic, Zoran; Matveev, K. A.
- Physical Review B, Vol. 94, Issue 2
Dynamical structure factor at small q for the XXZ spin-1/2 chain
journal, August 2007
- Pereira, R. G.; Sirker, J.; Caux, J-S
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 08
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
Dynamical Spin Structure Factor for the Anisotropic Spin- Heisenberg Chain
journal, June 2006
- Pereira, R. G.; Sirker, J.; Caux, J. -S.
- Physical Review Letters, Vol. 96, Issue 25
Condensed Matter Theory of Dipolar Quantum Gases
journal, April 2012
- Baranov, M. A.; Dalmonte, M.; Pupillo, G.
- Chemical Reviews, Vol. 112, Issue 9
Lifetime of excitations in a clean Luttinger liquid
journal, August 1998
- Samokhin, K. V.
- Journal of Physics: Condensed Matter, Vol. 10, Issue 31
Fate of classical solitons in one-dimensional quantum systems
journal, November 2015
- Pustilnik, M.; Matveev, K. A.
- Physical Review B, Vol. 92, Issue 19
Coulomb Drag by Small Momentum Transfer between Quantum Wires
journal, September 2003
- Pustilnik, M.; Mishchenko, E. G.; Glazman, L. I.
- Physical Review Letters, Vol. 91, Issue 12
Dynamics of Dark Solitons in Elongated Bose-Einstein Condensates
journal, August 2002
- Muryshev, A.; Shlyapnikov, G. V.; Ertmer, W.
- Physical Review Letters, Vol. 89, Issue 11
Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
journal, October 2007
- Khodas, M.; Pustilnik, M.; Kamenev, A.
- Physical Review B, Vol. 76, Issue 15
Kinetics of Mobile Impurities and Correlation Functions in One-Dimensional Superfluids at Finite Temperature
journal, April 2014
- Arzamasovs, M.; Bovo, F.; Gangardt, D. M.
- Physical Review Letters, Vol. 112, Issue 17
Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons
journal, August 1998
- Olshanii, M.
- Physical Review Letters, Vol. 81, Issue 5
Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas
journal, May 2014
- Ristivojevic, Zoran; Matveev, K. A.
- Physical Review B, Vol. 89, Issue 18
Electron tunneling spectroscopy of a quantum antidot in the integer quantum Hall regime
journal, March 2008
- Goldman, V. J.; Liu, Jun; Zaslavsky, A.
- Physical Review B, Vol. 77, Issue 11
Interaction effects on thermal transport in quantum wires
journal, September 2011
- Levchenko, Alex; Micklitz, Tobias; Ristivojevic, Zoran
- Physical Review B, Vol. 84, Issue 11
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
The transport coefficients of a fermi liquid
journal, January 1970
- Sykes, J.; Brooker, G. A.
- Annals of Physics, Vol. 56, Issue 1
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum
journal, May 1963
- Lieb, Elliott H.
- Physical Review, Vol. 130, Issue 4
Single-particle states, Kohn anomaly, and pairing fluctuations in one dimension
journal, April 1974
- Luther, A.; Peschel, I.
- Physical Review B, Vol. 9, Issue 7
Negative Temperature Derivative of Resistivity in Thin Potassium Samples: The Gurzhi Effect?
journal, January 1984
- Yu, Z. -Z.; Haerle, M.; Zwart, J. W.
- Physical Review Letters, Vol. 52, Issue 5
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
book, June 2004
- Sutherland, Bill
The theory of a fermi liquid (the properties of liquid 3He at low temperatures)
journal, January 1959
- Abrikosov, A. A.; Khalatnikov, I. M.
- Reports on Progress in Physics, Vol. 22, Issue 1
Evidence for hydrodynamic electron flow in PdCoO2
journal, February 2016
- Moll, P. J. W.; Kushwaha, P.; Nandi, N.
- Science, Vol. 351, Issue 6277
Gapless boundary excitations in the quantum Hall states and in the chiral spin states
journal, May 1991
- Wen, X. G.
- Physical Review B, Vol. 43, Issue 13
Theory of the edge States in Fractional Quantum hall Effects
journal, May 1992
- Wen, Xiao-Gang
- International Journal of Modern Physics B, Vol. 06, Issue 10
Relaxation of weakly interacting electrons in one dimension
journal, April 2013
- Ristivojevic, Zoran; Matveev, K. A.
- Physical Review B, Vol. 87, Issue 16
Soliton operators for the quantized sine-Gordon equation
journal, May 1975
- Mandelstam, S.
- Physical Review D, Vol. 11, Issue 10
Hydrodynamic electron flow in high-mobility wires
journal, May 1995
- de Jong, M. J. M.; Molenkamp, L. W.
- Physical Review B, Vol. 51, Issue 19
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
Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
journal, February 2016
- Crossno, J.; Shi, J. K.; Wang, K.
- Science, Vol. 351, Issue 6277
Fermionic quasiparticle representation of Tomonaga-Luttinger Hamiltonian
journal, September 2005
- Rozhkov, A. V.
- The European Physical Journal B, Vol. 47, Issue 2
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
journal, May 1963
- Lieb, Elliott H.; Liniger, Werner
- Physical Review, Vol. 130, Issue 4
Transport properties of partially equilibrated quantum wires
journal, March 2010
- Micklitz, Tobias; Rech, Jérôme; Matveev, K. A.
- Physical Review B, Vol. 81, Issue 11
Spectral function of spinless fermions on a one-dimensional lattice
journal, April 2009
- Pereira, Rodrigo G.; White, Steven R.; Affleck, Ian
- Physical Review B, Vol. 79, Issue 16
Searching for perfect fluids: quantum viscosity in a universal Fermi gas
journal, July 2011
- Cao, C.; Elliott, E.; Wu, H.
- New Journal of Physics, Vol. 13, Issue 7
'Luttinger liquid theory' of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas
journal, July 1981
- Haldane, F. D. M.
- Journal of Physics C: Solid State Physics, Vol. 14, Issue 19
Coulomb Oscillations in Antidots in the Integer and Fractional Quantum Hall Regimes
journal, June 2012
- Kou, A.; Marcus, C. M.; Pfeiffer, L. N.
- Physical Review Letters, Vol. 108, Issue 25
Relaxation of a High-Energy Quasiparticle in a One-Dimensional Bose Gas
journal, August 2010
- Tan, Shina; Pustilnik, Michael; Glazman, Leonid I.
- Physical Review Letters, Vol. 105, Issue 9
Quantum Dipolar Gases in Boson or Fermion Flavor
journal, May 2012
- Laburthe-Tolra, Bruno
- Physics, Vol. 5
Relaxation in Luttinger liquids: Bose-Fermi duality
journal, September 2014
- Protopopov, I. V.; Gutman, D. B.; Mirlin, A. D.
- Physical Review B, Vol. 90, Issue 12
Dynamic Response of One-Dimensional Interacting Fermions
journal, May 2006
- Pustilnik, M.; Khodas, M.; Kamenev, A.
- Physical Review Letters, Vol. 96, Issue 19
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
Dynamics of Excitations in a One-Dimensional Bose Liquid
journal, September 2007
- Khodas, M.; Pustilnik, M.; Kamenev, A.
- Physical Review Letters, Vol. 99, Issue 11
Universal Quantum Viscosity in a Unitary Fermi Gas
journal, December 2010
- Cao, C.; Elliott, E.; Joseph, J.
- Science, Vol. 331, Issue 6013
Hydrodynamic Description of Transport in Strongly Correlated Electron Systems
journal, June 2011
- Andreev, A. V.; Kivelson, Steven A.; Spivak, B.
- Physical Review Letters, Vol. 106, Issue 25
Breakdown of Integrability in a Quasi-1D Ultracold Bosonic Gas
journal, May 2008
- Mazets, I. E.; Schumm, T.; Schmiedmayer, J.
- Physical Review Letters, Vol. 100, Issue 21
Dynamical Corrections to the DFT-LDA Electron Conductance in Nanoscale Systems
journal, May 2005
- Sai, Na; Zwolak, Michael; Vignale, Giovanni
- Physical Review Letters, Vol. 94, Issue 18
Incompleteness of the Landauer formula for electronic transport
journal, January 2009
- Vignale, Giovanni; Di Ventra, Massimiliano
- Physical Review B, Vol. 79, Issue 1
Decay of Fermionic Quasiparticles in One-Dimensional Quantum Liquids
journal, December 2013
- Matveev, K. A.; Furusaki, A.
- Physical Review Letters, Vol. 111, Issue 25
Works referencing / citing this record:
Entropy production in one-dimensional quantum fluids
journal, October 2019
- Idrisov, Edvin G.; Schmidt, Thomas L.
- Physical Review B, Vol. 100, Issue 16