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Peer-reviewedCC BY 4.0SciPost Physics

Quantum fluctuations in hydrodynamics and quantum long-time tails

  • Akash Jain1
  1. 1University of Oxford
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Abstract

We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in \hbar ℏ . The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.

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Cite

BibTeXRIS
BibTeX
@article{jain2026quantum,
  title = {{Quantum fluctuations in hydrodynamics and quantum long-time tails}},
  author = {Akash Jain},
  journal = {SciPost Physics},
  year = {2026},
  month = oct,
  doi = {10.21468/scipostphys.21.4.083},
  url = {https://scipost.org/10.21468/SciPostPhys.21.4.083},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Quantum fluctuations in hydrodynamics and quantum long-time tails
AU  - Akash Jain
PY  - 2026
DA  - 2026/10/01
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.4.083
UR  - https://scipost.org/10.21468/SciPostPhys.21.4.083
AB  - We construct a quantum Schwinger-Keldysh (SK) effective field theory for the diffusive hydrodynamics of a conserved scalar field. Quantum corrections within the SK framework are guided by fluctuation-dissipation relations, enforced via a dynamical Kubo-Martin-Schwinger (KMS) symmetry. We find that the KMS symmetry necessarily generates fluctuation contributions in the SK effective action at all orders in the noise field, thereby giving rise to intrinsically non-Gaussian noise. We use our results to compute one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a quantum generalization of hydrodynamic long-time tails. Our results apply at arbitrarily high orders in \hbar ℏ . The one-loop results for retarded correlation functions have been expressed in terms of a family of polynomials. We also provide a closed-form expression for the one-loop results at leading order in the wavevector expansion.
SN  - 2542-4653
ER  -