Viscous Dissipation in One-Dimensional Quantum Liquids

Matveev, K. A.; Pustilnik, M.

doi:10.1103/PhysRevLett.119.036801

Viscous Dissipation in One-Dimensional Quantum Liquids

Journal Article · Thu Jul 20 00:00:00 EDT 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.119.036801· OSTI ID:1393190

Matveev, K. A. ^[1]; Pustilnik, M. ^[2]

Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
Georgia Inst. of Technology, Atlanta, GA (United States). School of Physics

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.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Materials Sciences and Engineering Division

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1393190

Alternate ID(s):: OSTI ID: 1372133

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 3 Vol. 119; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (64)

On the theory of the superfluidity of two- and one-dimensional bose systems Popov, V. N. Theoretical and Mathematical Physics, Vol. 11, Issue 3 https://doi.org/10.1007/BF01028373	journal	June 1972
Hydrodynamic Hamiltonian for a nonideal Bose gas Popov, V. N. Theoretical and Mathematical Physics, Vol. 11, Issue 2 https://doi.org/10.1007/BF01028563	journal	May 1972
Quantization of the (sin?)2 interaction in terms of fermion variables Pogrebkov, A. K.; Sushko, V. N. Theoretical and Mathematical Physics, Vol. 24, Issue 3 https://doi.org/10.1007/BF01029883	journal	September 1975
The transport coefficients of a fermi liquid Sykes, J.; Brooker, G. A. Annals of Physics, Vol. 56, Issue 1 https://doi.org/10.1016/0003-4916(70)90002-3	journal	January 1970
Condensed Matter Theory of Dipolar Quantum Gases Baranov, M. A.; Dalmonte, M.; Pupillo, G. Chemical Reviews, Vol. 112, Issue 9 https://doi.org/10.1021/cr2003568	journal	April 2012
Interacting electrons in one dimension beyond the Luttinger-liquid limit Barak, Gilad; Steinberg, Hadar; Pfeiffer, Loren N. Nature Physics, Vol. 6, Issue 7 https://doi.org/10.1038/nphys1678	journal	May 2010
New wave‐operator identity applied to the study of persistent currents in 1D Mattis, Daniel C. Journal of Mathematical Physics, Vol. 15, Issue 5 https://doi.org/10.1063/1.1666693	journal	May 1974
Hydrodynamic Effects in Solids at low Temperature Gurzhi, R. N. Soviet Physics Uspekhi, Vol. 11, Issue 2 https://doi.org/10.1070/PU1968v011n02ABEH003815	journal	February 1968
'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 Haldane, F. D. M. Journal of Physics C: Solid State Physics, Vol. 14, Issue 19 https://doi.org/10.1088/0022-3719/14/19/010	journal	July 1981
The theory of a fermi liquid (the properties of liquid 3He at low temperatures) Abrikosov, A. A.; Khalatnikov, I. M. Reports on Progress in Physics, Vol. 22, Issue 1 https://doi.org/10.1088/0034-4885/22/1/310	journal	January 1959
Lifetime of excitations in a clean Luttinger liquid Samokhin, K. V. Journal of Physics: Condensed Matter, Vol. 10, Issue 31 https://doi.org/10.1088/0953-8984/10/31/002	journal	August 1998
Functional theories of thermoelectric phenomena Eich, F. G.; Di Ventra, M.; Vignale, G. Journal of Physics: Condensed Matter, Vol. 29, Issue 6 https://doi.org/10.1088/1361-648X/29/6/063001	journal	December 2016
Searching for perfect fluids: quantum viscosity in a universal Fermi gas Cao, C.; Elliott, E.; Wu, H. New Journal of Physics, Vol. 13, Issue 7 https://doi.org/10.1088/1367-2630/13/7/075007	journal	July 2011
Dynamical structure factor at small q for the XXZ spin-1/2 chain Pereira, R. G.; Sirker, J.; Caux, J-S Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 08 https://doi.org/10.1088/1742-5468/2007/08/P08022	journal	August 2007
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State Lieb, Elliott H.; Liniger, Werner Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1605	journal	May 1963
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum Lieb, Elliott H. Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1616	journal	May 1963
Chiral Luttinger liquid and the edge excitations in the fractional quantum Hall states Wen, X. G. Physical Review B, Vol. 41, Issue 18 https://doi.org/10.1103/PhysRevB.41.12838	journal	June 1990
Gapless boundary excitations in the quantum Hall states and in the chiral spin states Wen, X. G. Physical Review B, Vol. 43, Issue 13 https://doi.org/10.1103/PhysRevB.43.11025	journal	May 1991
Electron-electron-scattering-induced size effects in a two-dimensional wire Molenkamp, L. W.; de Jong, M. J. M. Physical Review B, Vol. 49, Issue 7 https://doi.org/10.1103/PhysRevB.49.5038	journal	February 1994
Hydrodynamic electron flow in high-mobility wires de Jong, M. J. M.; Molenkamp, L. W. Physical Review B, Vol. 51, Issue 19 https://doi.org/10.1103/PhysRevB.51.13389	journal	May 1995
Three-particle collisions in quantum wires: Corrections to thermopower and conductance Lunde, Anders Mathias; Flensberg, Karsten; Glazman, Leonid I. Physical Review B, Vol. 75, Issue 24 https://doi.org/10.1103/PhysRevB.75.245418	journal	June 2007
Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions Khodas, M.; Pustilnik, M.; Kamenev, A. Physical Review B, Vol. 76, Issue 15 https://doi.org/10.1103/PhysRevB.76.155402	journal	October 2007
Electron tunneling spectroscopy of a quantum antidot in the integer quantum Hall regime Goldman, V. J.; Liu, Jun; Zaslavsky, A. Physical Review B, Vol. 77, Issue 11 https://doi.org/10.1103/PhysRevB.77.115328	journal	March 2008
Incompleteness of the Landauer formula for electronic transport Vignale, Giovanni; Di Ventra, Massimiliano Physical Review B, Vol. 79, Issue 1 https://doi.org/10.1103/PhysRevB.79.014201	journal	January 2009
Spectral function of spinless fermions on a one-dimensional lattice Pereira, Rodrigo G.; White, Steven R.; Affleck, Ian Physical Review B, Vol. 79, Issue 16 https://doi.org/10.1103/PhysRevB.79.165113	journal	April 2009
Transport properties of partially equilibrated quantum wires Micklitz, Tobias; Rech, Jérôme; Matveev, K. A. Physical Review B, Vol. 81, Issue 11 https://doi.org/10.1103/PhysRevB.81.115313	journal	March 2010
Interaction effects on thermal transport in quantum wires Levchenko, Alex; Micklitz, Tobias; Ristivojevic, Zoran Physical Review B, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevB.84.115447	journal	September 2011
Relaxation of weakly interacting electrons in one dimension Ristivojevic, Zoran; Matveev, K. A. Physical Review B, Vol. 87, Issue 16 https://doi.org/10.1103/PhysRevB.87.165108	journal	April 2013
Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas Ristivojevic, Zoran; Matveev, K. A. Physical Review B, Vol. 89, Issue 18 https://doi.org/10.1103/PhysRevB.89.180507	journal	May 2014
Single-particle states, Kohn anomaly, and pairing fluctuations in one dimension Luther, A.; Peschel, I. Physical Review B, Vol. 9, Issue 7 https://doi.org/10.1103/PhysRevB.9.2911	journal	April 1974
Relaxation in Luttinger liquids: Bose-Fermi duality Protopopov, I. V.; Gutman, D. B.; Mirlin, A. D. Physical Review B, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevB.90.125113	journal	September 2014
Solitons in a one-dimensional Wigner crystal Pustilnik, M.; Matveev, K. A. Physical Review B, Vol. 91, Issue 16 https://doi.org/10.1103/PhysRevB.91.165416	journal	April 2015
Equilibration in a chiral Luttinger liquid Protopopov, I. V.; Gutman, D. B.; Mirlin, A. D. Physical Review B, Vol. 91, Issue 19 https://doi.org/10.1103/PhysRevB.91.195110	journal	May 2015
Fate of classical solitons in one-dimensional quantum systems Pustilnik, M.; Matveev, K. A. Physical Review B, Vol. 92, Issue 19 https://doi.org/10.1103/PhysRevB.92.195146	journal	November 2015
Decay of Bogoliubov excitations in one-dimensional Bose gases Ristivojevic, Zoran; Matveev, K. A. Physical Review B, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevB.94.024506	journal	July 2016
Effective mass of elementary excitations in Galilean-invariant integrable models Matveev, K. A.; Pustilnik, M. Physical Review B, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevB.94.115436	journal	September 2016
Soliton operators for the quantized sine-Gordon equation Mandelstam, S. Physical Review D, Vol. 11, Issue 10 https://doi.org/10.1103/PhysRevD.11.3026	journal	May 1975
Breakdown of Integrability in a Quasi-1D Ultracold Bosonic Gas Mazets, I. E.; Schumm, T.; Schmiedmayer, J. Physical Review Letters, Vol. 100, Issue 21 https://doi.org/10.1103/PhysRevLett.100.210403	journal	May 2008
Relaxation of a High-Energy Quasiparticle in a One-Dimensional Bose Gas Tan, Shina; Pustilnik, Michael; Glazman, Leonid I. Physical Review Letters, Vol. 105, Issue 9 https://doi.org/10.1103/PhysRevLett.105.090404	journal	August 2010
Observation of Shock Waves in a Strongly Interacting Fermi Gas Joseph, J. A.; Thomas, J. E.; Kulkarni, M. Physical Review Letters, Vol. 106, Issue 15 https://doi.org/10.1103/PhysRevLett.106.150401	journal	April 2011
Hydrodynamic Description of Transport in Strongly Correlated Electron Systems Andreev, A. V.; Kivelson, Steven A.; Spivak, B. Physical Review Letters, Vol. 106, Issue 25 https://doi.org/10.1103/PhysRevLett.106.256804	journal	June 2011
Coulomb Oscillations in Antidots in the Integer and Fractional Quantum Hall Regimes Kou, A.; Marcus, C. M.; Pfeiffer, L. N. Physical Review Letters, Vol. 108, Issue 25 https://doi.org/10.1103/PhysRevLett.108.256803	journal	June 2012
Decay of Fermionic Quasiparticles in One-Dimensional Quantum Liquids Matveev, K. A.; Furusaki, A. Physical Review Letters, Vol. 111, Issue 25 https://doi.org/10.1103/PhysRevLett.111.256401	journal	December 2013
Kinetics of Mobile Impurities and Correlation Functions in One-Dimensional Superfluids at Finite Temperature Arzamasovs, M.; Bovo, F.; Gangardt, D. M. Physical Review Letters, Vol. 112, Issue 17 https://doi.org/10.1103/PhysRevLett.112.170602	journal	April 2014
Electrical and Thermal Transport in Inhomogeneous Luttinger Liquids DeGottardi, Wade; Matveev, K. A. Physical Review Letters, Vol. 114, Issue 23 https://doi.org/10.1103/PhysRevLett.114.236405	journal	June 2015
Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids Haldane, F. D. M. Physical Review Letters, Vol. 47, Issue 25 https://doi.org/10.1103/PhysRevLett.47.1840	journal	December 1981
Negative Temperature Derivative of Resistivity in Thin Potassium Samples: The Gurzhi Effect? Yu, Z. -Z.; Haerle, M.; Zwart, J. W. Physical Review Letters, Vol. 52, Issue 5 https://doi.org/10.1103/PhysRevLett.52.368	journal	January 1984
Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons Olshanii, M. Physical Review Letters, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevLett.81.938	journal	August 1998
Dynamics of Dark Solitons in Elongated Bose-Einstein Condensates Muryshev, A.; Shlyapnikov, G. V.; Ertmer, W. Physical Review Letters, Vol. 89, Issue 11 https://doi.org/10.1103/PhysRevLett.89.110401	journal	August 2002
Coulomb Drag by Small Momentum Transfer between Quantum Wires Pustilnik, M.; Mishchenko, E. G.; Glazman, L. I. Physical Review Letters, Vol. 91, Issue 12 https://doi.org/10.1103/PhysRevLett.91.126805	journal	September 2003
Dynamical Corrections to the DFT-LDA Electron Conductance in Nanoscale Systems Sai, Na; Zwolak, Michael; Vignale, Giovanni Physical Review Letters, Vol. 94, Issue 18 https://doi.org/10.1103/PhysRevLett.94.186810	journal	May 2005
Dynamic Response of One-Dimensional Interacting Fermions Pustilnik, M.; Khodas, M.; Kamenev, A. Physical Review Letters, Vol. 96, Issue 19 https://doi.org/10.1103/PhysRevLett.96.196405	journal	May 2006
Dynamical Spin Structure Factor for the Anisotropic Spin- 1 / 2 Heisenberg Chain Pereira, R. G.; Sirker, J.; Caux, J. -S. Physical Review Letters, Vol. 96, Issue 25 https://doi.org/10.1103/PhysRevLett.96.257202	journal	June 2006
Dynamics of Excitations in a One-Dimensional Bose Liquid Khodas, M.; Pustilnik, M.; Kamenev, A. Physical Review Letters, Vol. 99, Issue 11 https://doi.org/10.1103/PhysRevLett.99.110405	journal	September 2007
Quantum Dipolar Gases in Boson or Fermion Flavor Laburthe-Tolra, Bruno Physics, Vol. 5 https://doi.org/10.1103/Physics.5.58	journal	May 2012
Many-body physics with ultracold gases Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.885	journal	July 2008
One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm Imambekov, Adilet; Schmidt, Thomas L.; Glazman, Leonid I. Reviews of Modern Physics, Vol. 84, Issue 3 https://doi.org/10.1103/RevModPhys.84.1253	journal	September 2012
Universal Quantum Viscosity in a Unitary Fermi Gas Cao, C.; Elliott, E.; Joseph, J. Science, Vol. 331, Issue 6013 https://doi.org/10.1126/science.1195219	journal	December 2010
Evidence for hydrodynamic electron flow in PdCoO2 Moll, P. J. W.; Kushwaha, P.; Nandi, N. Science, Vol. 351, Issue 6277 https://doi.org/10.1126/science.aac8385	journal	February 2016
Negative local resistance caused by viscous electron backflow in graphene Bandurin, D. A.; Torre, I.; Kumar, R. K. Science, Vol. 351, Issue 6277 https://doi.org/10.1126/science.aad0201	journal	February 2016
Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene Crossno, J.; Shi, J. K.; Wang, K. Science, Vol. 351, Issue 6277 https://doi.org/10.1126/science.aad0343	journal	February 2016
Fermionic quasiparticle representation of Tomonaga-Luttinger Hamiltonian Rozhkov, A. V. The European Physical Journal B, Vol. 47, Issue 2 https://doi.org/10.1140/epjb/e2005-00312-3	journal	September 2005
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems Sutherland, Bill https://doi.org/10.1142/5552	book	June 2004
Theory of the edge States in Fractional Quantum hall Effects Wen, Xiao-Gang International Journal of Modern Physics B, Vol. 06, Issue 10 https://doi.org/10.1142/S0217979292000840	journal	May 1992

Cited By (1)

Entropy production in one-dimensional quantum fluids Idrisov, Edvin G.; Schmidt, Thomas L. Physical Review B, Vol. 100, Issue 16 https://doi.org/10.1103/physrevb.100.165404	journal	October 2019

Similar Records

Viscous dissipation in a gas of one-dimensional fermions with generic dispersion

Journal Article · Mon Feb 27 19:00:00 EST 2023 · Physical Review. B · OSTI ID:1991610

Two-fluid dynamics of one-dimensional quantum liquids in the absence of Galilean invariance

Journal Article · Sun Jul 14 20:00:00 EDT 2019 · Physical Review B · OSTI ID:1546066

Viscous Properties of a Degenerate One-Dimensional Fermi Gas

Journal Article · Mon Aug 10 20:00:00 EDT 2020 · Physical Review Letters · OSTI ID:1656853

Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS

Viscous Dissipation in One-Dimensional Quantum Liquids

Citation Formats

References (64)

Cited By (1)

Similar Records

Related Subjects