Thermal conductivity in one-dimensional electronic fluids

D. B. Gutman, I. V. Protopopov, R. Samanta, A. D. Mirlin

Research output: Contribution to journalArticlepeer-review


We study thermal conductivity in one-dimensional electronic fluids combining kinetic [R. Samanta, I. V. Protopopov, A. D. Mirlin, and D. B. Gutman, Thermal transport in one-dimensional electronic fluid, Phys. Rev. Lett. 122, 206801 (2019)] and hydrodynamic [I. V. Protopopov, R. Samanta, A. D. Mirlin, and D. B. Gutman, Anomalous hydrodynamics in one-dimensional electronic fluid, Phys. Rev. Lett. 126, 256801 (2021)] theories. The kinetic approach is developed by partitioning the Hilbert space into bosonic and fermionic sectors. We focus on the regime where the long-living thermal excitations are fermions and compute thermal conductivity. From the kinetic theory standpoint, the fermionic part of thermal conductivity is normal, while the bosonic one is anomalous, that scales as ω-1/3 and thus dominates in the infrared limit. The multi-mode hydrodynamic theory is obtained by projecting the fermionic kinetic equation on the zero modes of its collision integral. On a bare level, both theories agree and the thermal conductivity computed in hydrodynamic theory matches the result of the kinetic equation. The interaction between hydrodynamic modes leads to renormalization and consequently to anomalous scaling of the transport coefficients. In a four-mode regime, all modes are ballistic and the anomaly manifests itself in Kardar-Parisi-Zhang-like broadening with asymmetric power-law tails. “Heads” and “tails” of the pulses contribute equally to thermal conductivity, leading to ω-1/3 scaling of heat conductivity. In the three-mode regime, the system is in the universality class of a classical viscous fluid [Herbert Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014); O. Narayan and S. Ramaswamy, Anomalous heat conduction in one-dimensional momentum-conserving systems, Phys. Rev. Lett. 89, 200601 (2002)].

Original languageEnglish
Pages (from-to)1358-1375
Number of pages18
JournalLow Temperature Physics
Issue number12
StatePublished - 1 Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 Author(s).


D. G. was supported by ISF-China 3119/19 and ISF 1355/20.

FundersFunder number
ISF-China3119/19, ISF 1355/20


    • Fermi-Bose duality
    • Kardar-Parisi-Zhang problem.
    • Luttinger liquid
    • electron hydrodynamics
    • thermal conductivity


    Dive into the research topics of 'Thermal conductivity in one-dimensional electronic fluids'. Together they form a unique fingerprint.

    Cite this