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Title: Propagation and attenuation of sound in one-dimensional quantum liquids

Abstract

At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies, the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid 4He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies, the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid, the entropy and density oscillations are strongly coupled and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to a single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves,more » similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat-diffusion mode. Lastly, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.« less

Authors:
 [1];  [2]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Univ. of Washington, Seattle, WA (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1483653
Alternate Identifier(s):
OSTI ID: 1479613
Grant/Contract Number:  
AC02-06CH11357; FG02-07ER46452
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 15; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Matveev, K. A., and Andreev, A. V. Propagation and attenuation of sound in one-dimensional quantum liquids. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.155441.
Matveev, K. A., & Andreev, A. V. Propagation and attenuation of sound in one-dimensional quantum liquids. United States. doi:10.1103/PhysRevB.98.155441.
Matveev, K. A., and Andreev, A. V. Mon . "Propagation and attenuation of sound in one-dimensional quantum liquids". United States. doi:10.1103/PhysRevB.98.155441.
@article{osti_1483653,
title = {Propagation and attenuation of sound in one-dimensional quantum liquids},
author = {Matveev, K. A. and Andreev, A. V.},
abstractNote = {At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies, the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid 4He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies, the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid, the entropy and density oscillations are strongly coupled and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to a single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat-diffusion mode. Lastly, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.},
doi = {10.1103/PhysRevB.98.155441},
journal = {Physical Review B},
issn = {2469-9950},
number = 15,
volume = 98,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
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