Thermal quasi-equilibrium states across Landau horizons in the effective gravity of superfluids

TL;DR

This paper explores the thermal behavior of quasiparticle horizons in superfluids with nonlinear dispersion, showing how they reach quasi-equilibrium states and shrink due to thermal effects analogous to Hawking radiation, without involving Planck-scale physics.

Contribution

It introduces a framework for understanding quasi-equilibrium states across Landau horizons considering nonlinear dispersion and relates thermal properties to low-energy corrections.

Findings

Quasi-equilibrium states are established at temperatures above Hawking temperature.

Nonlinear dispersion enables quasiparticle communication across the horizon.

Thermal properties depend on energy scales below the Planck energy.

Abstract

We give an account of the physical behaviour of a quasiparticle horizon due to non-Lorentz invariant modifications of the effective space-time experienced by the quasiparticles (``matter'') for high momenta. By introducing a ``relativistic'' conserved energy-momentum tensor, we derive quasi-equilibrium states of the fluid across the ``Landau'' quasiparticle horizon at temperatures well above the quantum Hawking temperature. Nonlinear dispersion of the quasiparticle energy spectrum is instrumental for quasiparticle communication and exchange across the horizon. It is responsible for the establishment of the local thermal equilibrium across the horizon with the Tolman temperature being inhomogeneous behind the horizon. The inhomogeneity causes relaxation of the quasi-equilibrium states due to scattering of thermal quasiparticles, which finally leads to a shrinking black hole horizon. This process serves as the classical thermal counterpart of the quantum effect of Hawking radiation and will allow for an observation of the properties of the horizon at temperatures well above the Hawking temperature. We discuss the thermal entropy related to the horizon. We find that only the first nonlinear correction to the energy spectrum is important for the thermal properties of the horizon. They are fully determined by an energy of order $E_{\rm Planck}(T/E_{\rm Planck})^{1/3}$, which is well below the Planck energy scale $E_{\rm Planck}$, so that Planck scale physics is not involved in determining thermal quantities related to the horizon.