Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 27 min ago
Peer-reviewedCC BY-NC-ND 4.0Comptes Rendus. Physique

Phonon number relaxation in a 3D superfluid with a concave acoustic branch.

  • Yvan Castin
  • Mariia Tsimokha
Open at sourcePDFDOICite

Abstract

We consider the collisional evolution towards equilibrium of a spatially homogeneous and isotropic phonon gas of a three-dimensional superfluid with a concave acoustic excitation branch, at a non-zero but arbitrarily low temperature T. Three-phonon collisions 1ϕ↔ 2ϕ are forbidden by conservation of energy-momentum. Four-phonon collisions 2ϕ→ 2ϕ of Landau and Khalatnikov lead, after a time ∝ T−7, only to a partial thermal equilibrium, a Bose law of non-zero chemical potential for the phonons, because they conserve the total number of phonons. Relaxation towards complete thermochemical equilibrium is therefore ensured by the much slower five-phonon collisions 2ϕ↔ 3ϕ of Khalatnikov, in a time ∝ T−9. Using kinetic equations on the occupation numbers of the phonon modes and explicitly calculating the 2ϕ→ 3ϕ collisional amplitude with quantum hydrodynamics at low temperature, we determine the corresponding evolution of the fugacity zϕ of the phonon gas from the non-degenerate regime zϕ=0+ to complete equilibrium zϕ=1-. Using the conservation of total energy, we find that the fugacity varies with a non-integer power law ∝ t4/5 at short times and an exponential law at long times; the speed of change of entropy, always positive, is asymptotically proportional to the square of the speed of change of fugacity, (d/dt)Sϕ∝[(d/dt)zϕ]2, as Landau predicted for an arbitrarily slow adiabatic transformation. Our results bring to a close the study initiated by Khalatnikov in 1950 and could be experimentally verified in a gas of cold spin-1/2 fermionic atoms in the sector of the BEC-BCS crossover where the acoustic branch has a concave start, or in superfluid liquid helium-4 at sufficiently high pressure.

Related

  1. From Modal Memory to Topological Relaxation in a Driven Holographic Superfluid
    Yan Peng, Bo-Xuan Ge
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
  2. GaAs/AlAs Acoustic Nanocavities for Coherent GHz-THz Phonon Engineering
    S. Sandeep, E. R. Cardozo de Oliveira, E. Mehdi +1
    HALPreprintLicence not statedGeneral physicsHAL
  3. A material-agnostic platform to probe spin-phonon interactions using high-overtone bulk acoustic wave resonators
    Q. Greffe, A. Hugot, S. Zhang +6
    HALPreprintLicence not statedGeneral physicsHAL
  4. Acoustic damping limits superfluid helium as a thermal bath for mechanical resonators
    Yunhu Huang, Mehri Ebrahimi, Alireza Rashedi +1
    arXivPreprintCC BY 4.0Full textCondensed matterarXiv
  5. Exciton Coherence in CsPbBr3 Nanocrystals is Bounded by Phonon-Mediated Bright-Triplet Relaxation
    Tara Šverko, Annette J. Jones, Chantalle J. Krajewska +6
    arXivPreprintarXiv licenceFull textCondensed matterarXiv

Cite

BibTeXRIS
BibTeX
@article{castin2026phonon,
  title = {{Phonon number relaxation in a 3D superfluid with a concave acoustic branch.}},
  author = {Yvan Castin and Mariia Tsimokha},
  journal = {Comptes Rendus. Physique},
  year = {2026},
  month = oct,
  doi = {10.5802/crphys.292},
  eprint = {2604.18298},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05595595v2},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - JOUR
TI  - Phonon number relaxation in a 3D superfluid with a concave acoustic branch.
AU  - Yvan Castin
AU  - Mariia Tsimokha
PY  - 2026
DA  - 2026/10/14
JO  - Comptes Rendus. Physique
DO  - 10.5802/crphys.292
UR  - https://hal.science/hal-05595595v2
AB  - We consider the collisional evolution towards equilibrium of a spatially homogeneous and isotropic phonon gas of a three-dimensional superfluid with a concave acoustic excitation branch, at a non-zero but arbitrarily low temperature T. Three-phonon collisions 1ϕ↔ 2ϕ are forbidden by conservation of energy-momentum. Four-phonon collisions 2ϕ→ 2ϕ of Landau and Khalatnikov lead, after a time ∝ T^−7, only to a partial thermal equilibrium, a Bose law of non-zero chemical potential for the phonons, because they conserve the total number of phonons. Relaxation towards complete thermochemical equilibrium is therefore ensured by the much slower five-phonon collisions 2ϕ↔ 3ϕ of Khalatnikov, in a time ∝ T^−9. Using kinetic equations on the occupation numbers of the phonon modes and explicitly calculating the 2ϕ→ 3ϕ collisional amplitude with quantum hydrodynamics at low temperature, we determine the corresponding evolution of the fugacity z_ϕ of the phonon gas from the non-degenerate regime z_ϕ=0^+ to complete equilibrium z_ϕ=1^-. Using the conservation of total energy, we find that the fugacity varies with a non-integer power law ∝ t^4/5 at short times and an exponential law at long times; the speed of change of entropy, always positive, is asymptotically proportional to the square of the speed of change of fugacity, (d/dt)S_ϕ∝[(d/dt)z_ϕ]^2, as Landau predicted for an arbitrarily slow adiabatic transformation. Our results bring to a close the study initiated by Khalatnikov in 1950 and could be experimentally verified in a gas of cold spin-1/2 fermionic atoms in the sector of the BEC-BCS crossover where the acoustic branch has a concave start, or in superfluid liquid helium-4 at sufficiently high pressure.
SN  - 1631-0705
SN  - 1878-1535
ER  -