Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of states

TL;DR

This paper applies the fast forward scheme to analyze a quantum gas in a rapidly expanding 1D cavity, deriving modified equations of state that include nonadiabatic effects related to the cavity's dynamics.

Contribution

It introduces a novel approach to incorporate nonadiabatic effects into quantum gas equations of state using the fast forward scheme, extending traditional thermodynamic relations.

Findings

Force includes nonadiabatic and adiabatic parts influenced by cavity dynamics.

Ratio of nonadiabatic to adiabatic contributions depends on wall type (soft or hard).

Conditions identified where nonadiabatic effects dominate, altering standard equations of state.

Abstract

With use of the scheme of fast forward which realizes quasi-static or adiabatic dynamics in shortened time scale, we investigate a thermally-isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size $L=L(t)$. In the fast-forward variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity ($\dot{L}$) and acceleration ($\ddot{L}$) of $L$ besides rapidly-changing state variables like effective temperature ($T$) and $L$ itself. The force is now a sum of nonadiabatic (NAD) and adiabatic contributions with the former caused by particles moving synchronously with kinetics of $L$ and the latter by ideal bulk particles insensitive to such a kinetics. The ratio of NAD and adiabatic contributions does not depend on the particle number ($N$) in the case of the soft-wall confinement, whereas such a ratio is controllable in the case of hard-wall confinement. We also reveal the condition when the NAD contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.