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(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 (L[over ̇]) and acceleration (L[over ̈]) 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.
We introduce Khujakulov and Nakamura's scheme for the exact fast-forwarding of standard quantum dynamics for a charged particle. The idea allows the acceleration of both amplitude and phase of the wave function throughout the fast-forwarding time range. Firstly we shall apply the proposed method to 1-D free wave packet dynamics and obtain the electromagnetic field to ensure its rapid propagation and diffusion. Then we proceed to study 1-D quantum tunneling phenomenon, namely a rapid penetration of wave function through a delta-function type barrier. We elucidate the distribution of the tunneling current density to show the remarkable enhancement of the tunneling rate (tunneling power) due the fast-forwarding. We introduce two types of time-magnification factors and confirm the stability of fast-forward against the variation of such factors.
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