# 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 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}

}

Free Publicly Available Full Text

Publisher's Version of Record

Other availability

Cited by: 4 works

*Citation information provided by*

Web of Science

Web of Science

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

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

##
Functional theories of thermoelectric phenomena

journal, December 2016

- Eich, F. G.; Di Ventra, M.; Vignale, G.
- Journal of Physics: Condensed Matter, Vol. 29, Issue 6

##
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- $1/2$ 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

##
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