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

With use of the scheme of fast forward which realizes quasistatic or adiabatic dynamics in shortened timescale, we investigate a thermally isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size $L=L\left(t\right)$. 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.

Figure 1

(a) Quantum gas in soft-wall confinement; (b) quantum gas in hard-wall confinement. $L_0$ and $L\left(\mathrm{\Lambda }\right(t\left)\right)$ are the initial and time-dependent size of the expanding cavities, respectively. $F$ is the force due to the gas.