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

Abstract

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.

Fast forward approach to stochastic heat engine

“…The fast forward theory constitutes one of the promising ways of shortcuts to adiabaticity (STA) devoted to tailor excitations in nonadiabatic processes [17][18][19][20][21][22]. This theory revealed the nonequilibrium equation of states for the quantum gas under a rapid piston [23] and provided a simple protocol to accelerate the adiabatic quantum dynamics of spin clusters [24]. It is fascinating to investigate the fast forward of the heat engine which is classical and stochastic, find the fast-forward protocols, and investigate the power and efficiency of the engine.…”

Fast-forward scaling theory

“…Applying the idea of fast forward (FF) of adiabatic control of 1D confined systems, Babajanova, Matrasulov and Nakamura (BMN) [22] investigated the non-equilibrium equation of states of an ideal quantum gas (Fermi gas) confined to the rapidly dilating soft-wall and hard-wall cavities. BMN consider a Fermi gas of N noninteracting particles confined in the harmonic potential whose frequency is time-dependent and also the gas system in the hard-wall confinement.…”

“…Then, FFST was extended with great effect to charged particles [9][10][11][12], many-body [13] and discrete systems [14][15][16], tunneling [17,18] and Dirac dynamics [19,20]. Acceleration of classical adiabatic dynamics [21], role of FFST in non-equilibrium statistical mechanics [22,23] and various controls of cold atoms [5,[24][25][26] have been the subjects of researches. An approach encompassing quantum, classical and stochastic dynamics [27] and a semiclassical approach [28] were proposed.…”

Fast-forward approach to adiabatic quantum dynamics of regular spin clusters: Nature of geometry-dependent driving interactions

“…The fast-forward theory proposed by Masuda and Nakamura [7] was originally concerned with acceleration of general reference quantum dynamics. This theory was developed to accelerate the adiabatic quantum dynamics by introducing the large time-scaling factor in the quasiadiabatic dynamics guaranteed by regularization terms added to the reference Hamiltonian [8,9], and was then used to enhance the quantum tunneling power [13] and to construct the non-equilibrium equation of state under a rapid piston [14]. The relation between the fast-forward approach and other methods was rigorously investigated in [15].…”

“…added to the reference Hamiltonian [8,9], and was then used to enhance the quantum tunneling power [13] and to construct the non-equilibrium equation of state under a rapid piston [14]. The relation between the fast-forward approach and other methods was rigorously investigated in [15].…”