Finite linewidths and "forbidden" three-phonon interactions

Anthony J Leggett, D. Ter Haar

Research output: Contribution to journalArticle

Abstract

We have used thermodynamic perturbation theory to study the effect of the finite energy spread of phonon excitations upon the possibility of three-phonon interactions which could not otherwise conserve energy. It is shown that a proper treatment of this effect is equivalent to a consideration of higher order processes in which the interacting phonons occur in virtual intermediate states, but that such processes cannot in general be adequately taken into account simply by assigning a lifetime to one or more of the interacting phonons. It is also shown that the higher order terms of conventional perturbation theory should be modified, whether or not the three-phonon process is energetically allowed; if it is, these modified terms should be substituted for the three-phonon contribution rather than added to it. We give a qualitative discussion of applications to liquid helium II and to dielectric solids.

Original languageEnglish (US)
JournalPhysical Review
Volume139
Issue number3A
DOIs
StatePublished - Dec 1 1965

Fingerprint

phonons
perturbation theory
liquid helium
interactions
life (durability)
thermodynamics
energy
excitation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Finite linewidths and "forbidden" three-phonon interactions. / Leggett, Anthony J; Haar, D. Ter.

In: Physical Review, Vol. 139, No. 3A, 01.12.1965.

Research output: Contribution to journalArticle

@article{5cae3a8ec10c498db40a8e3018f56930,
title = "Finite linewidths and {"}forbidden{"} three-phonon interactions",
abstract = "We have used thermodynamic perturbation theory to study the effect of the finite energy spread of phonon excitations upon the possibility of three-phonon interactions which could not otherwise conserve energy. It is shown that a proper treatment of this effect is equivalent to a consideration of higher order processes in which the interacting phonons occur in virtual intermediate states, but that such processes cannot in general be adequately taken into account simply by assigning a lifetime to one or more of the interacting phonons. It is also shown that the higher order terms of conventional perturbation theory should be modified, whether or not the three-phonon process is energetically allowed; if it is, these modified terms should be substituted for the three-phonon contribution rather than added to it. We give a qualitative discussion of applications to liquid helium II and to dielectric solids.",
author = "Leggett, {Anthony J} and Haar, {D. Ter}",
year = "1965",
month = "12",
day = "1",
doi = "10.1103/PhysRev.139.A779",
language = "English (US)",
volume = "139",
journal = "Physical Review",
issn = "0031-899X",
publisher = "American Institute of Physics Publising LLC",
number = "3A",

}

TY - JOUR

T1 - Finite linewidths and "forbidden" three-phonon interactions

AU - Leggett, Anthony J

AU - Haar, D. Ter

PY - 1965/12/1

Y1 - 1965/12/1

N2 - We have used thermodynamic perturbation theory to study the effect of the finite energy spread of phonon excitations upon the possibility of three-phonon interactions which could not otherwise conserve energy. It is shown that a proper treatment of this effect is equivalent to a consideration of higher order processes in which the interacting phonons occur in virtual intermediate states, but that such processes cannot in general be adequately taken into account simply by assigning a lifetime to one or more of the interacting phonons. It is also shown that the higher order terms of conventional perturbation theory should be modified, whether or not the three-phonon process is energetically allowed; if it is, these modified terms should be substituted for the three-phonon contribution rather than added to it. We give a qualitative discussion of applications to liquid helium II and to dielectric solids.

AB - We have used thermodynamic perturbation theory to study the effect of the finite energy spread of phonon excitations upon the possibility of three-phonon interactions which could not otherwise conserve energy. It is shown that a proper treatment of this effect is equivalent to a consideration of higher order processes in which the interacting phonons occur in virtual intermediate states, but that such processes cannot in general be adequately taken into account simply by assigning a lifetime to one or more of the interacting phonons. It is also shown that the higher order terms of conventional perturbation theory should be modified, whether or not the three-phonon process is energetically allowed; if it is, these modified terms should be substituted for the three-phonon contribution rather than added to it. We give a qualitative discussion of applications to liquid helium II and to dielectric solids.

UR - http://www.scopus.com/inward/record.url?scp=28844444297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28844444297&partnerID=8YFLogxK

U2 - 10.1103/PhysRev.139.A779

DO - 10.1103/PhysRev.139.A779

M3 - Article

AN - SCOPUS:28844444297

VL - 139

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 3A

ER -