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Quantum dynamics of a hydrogen-like atom in a time-dependent box: Cooling, compressing and diffusive ionization in non-adiabatic regime

S. Rakhmanov, Davron U. Matrasulov, V. I. Matveev

Published Mar 15, 2017• 0 citations
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Abstract

We study quantum dynamics of one-electron atom confined in a spherical impenetrable box with time-dependent radius. The behavior of the atomic electron interacting with the moving walls of the box is analyzed by computing average binding energy, average force and pressure. Linearly extending, contracting and harmonically breathing boxes are considered in the non-adiabatic regime i.e. when the wall of the box moves with high velocities. It is shown that linearly extending box leads to de-excitation of the atom, while the rapidly contracting box causes the creation of very high pressure on the atom and transition of the atomic electron into the unbound state. In harmonically breathing box diffusive excitation of atomic electron and ionization may occur in analogy with that for atom in a microwave field.

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We study quantum dynamics of one-electron atom confined in a spherical impenetrable box with time-dependent radius. The behavior of the atomic electron interacting with the moving walls of the box is analyzed by computing average binding energy, average force and pressure. Linearly extending, contracting and harmonically breathing boxes are considered in the non-adiabatic regime i.e. when the wall of the box moves with high velocities. It is shown that linearly extending box leads to de-excitation of the atom, while the rapidly contracting box causes the creation of very high pressure on the atom and transition of the atomic electron into the unbound state. In harmonically breathing box diffusive excitation of atomic electron and ionization may occur in analogy with that for atom in a microwave field.
The quantum dynamics of a hydrogen-like atom confined in one-dimensional box with oscillating walls is studied.The description of the system is reduced to a one-dimensional Schrödinger equation for Coulomb potential with time-dependent boundary conditions, which is solved numerically.Using the obtained solution, the average kinetic energy and binding energies are calculated as a function of time.It is found that both the average kinetic energy and the binding energies are periodic in time with the period depending on the wall's oscillation parameters.The probability density is also analyzed as a function of time and coordinate.
We consider a Dirac particle in a spherical box with a time-dependent radius. Analytical and numerical solutions of the time-dependent Dirac equation with time-dependent boundary (Dirichlet) conditions are obtained. Using the obtained solutions, physically observable characteristics of the dynamical confinement, such as the average kinetic energy (as a function of time) and average quantum force acting on the particle by the moving wall, are calculated. The trembling motion is analysed by computing the average coordinate of the Dirac particle as a function of time. The absence of the geometric phase is shown by direct calculation.
The motion of a quantum particle in a time-dependent circular billiard is studied on the basis of the Schrödinger equation with time-dependent boundary conditions.The cases of monotonically expanding (contracting), non-harmonically, harmonically breathing circles the case when billiard wall suddenly disappears are explored in detail.The exact analytical solutions for monotonically expanding and contracting circles are obtained.For all cases, the time-dependence of the quantum average energy is calculated.It is found that for an harmonically breathing circle, the average energy is time-periodic in the adiabatic regime with the same period as that of the oscillation.For intermediate frequencies which are comparable with the initial frequency of the particle in unperturbed billiard, such periodicity is broken.However, for very high frequencies, the average energy once again becomes periodic.A qualitative analysis of the border between adiabatic and non-adiabatic regimes is provided.
Motivated by the recent discovery that a reflecting wall moving with a square-root-in-time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear-in-time and square-root-in-time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wave functions studied the square-root-in-time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear-in-time (constant box-wall velocity) expansion leaves a nonzero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root-in-time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root-in-time expansion.
Trajectories of a Bohmian particle confined in time-dependent cylindrical and spherical traps are computed for both contracting and expanding boxes. Quantum effective force is considered in arbitrary directions. It is seen that in contrast to the problem of a particle in an infinite rectangular box with one wall in motion, if particle initially is in an energy eigenstate of a tiny box the force is zero in all directions. Trajectories of a two-body system confined in the spherical trap are also computed for different statistics. Results of average separation of the particles confirm our expectation about the statistics.
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.