Thermal Casimir effect in a classical liquid in a quasi-periodically identified conical spacetime

TL;DR

This paper investigates the thermal Casimir effect in a classical liquid influenced by the topology of a conical spacetime and quasi-periodic boundary conditions, deriving analytic expressions for fluctuations and thermodynamic quantities.

Contribution

It provides the first analytic expressions for quantum fluctuations and thermodynamics of a liquid in conical spacetime with quasi-periodic conditions, considering finite temperature effects.

Findings

Derived closed-form expressions for thermal Hadamard function and density fluctuations.

Analyzed low and high-temperature limits for different spacetime topologies.

Explored effects of conical defects and boundary conditions on thermodynamic properties.

Abstract

In this paper, we study the finite-temperature quantum fluctuation of a classical liquid induced by the topology of an effective conical spacetime, as well as by a quasi-periodic boundary condition. The conical spacetime could be either a disclination or a cosmic string. In this context, we consider a phonon field representing quantum excitations of the liquid density, which obeys an effective Klein- Gordon equation with the sound velocity replaced by the light velocity. We obtain closed analytic expressions for the thermal Hadamard function, and consequently, the renormalized mean square density fluctuation of the liquid along with thermodynamics quantities such as internal energy, free energy, total energy, and entropy densities. We also discuss the limiting cases, including low and high-temperature regimes, and the situations in which there are only either the conical spacetime or quasi-periodicity.