Quantum effective force and Bohmian approach to time-dependent traps

Abstract

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. Computations show that there are situations for which distance between bosons is greater than the fermions. However, results of average separation of the particles confirm our expectation about the statistics.

Strong and weak single particle nonlocality induced by time-dependent boundary conditions

“…In this paper we distinguish between a strong form and and a weak form of nonlocality. We first show that there is no strong nonlocality, in the sense that moving walls have no effect on the dynamics of a localized quantum state placed far from the wall as claimed (but never proved) in previous works [12][13][14][15][16][17][18]. We then show that for quantum states extended over the well extension, the system displays a weak form of nonlocality: moving walls generate instantaneously a current density in the central region of the box.…”

“…The particle in a box with moving walls has also been the prime example in the investigations of possible nonlocal effects induced by time-dependent boundary conditions. It was initially suggested by Greenberger [12], and subsequently mentioned by several authors, eg [13][14][15][16][17][18], that time-dependent boundary conditions could give rise to a genuine form of nonlocality: a particle at rest and localized in the center of the box, remaining far from the moving walls, would nevertheless be physically displaced by the changing boundary conditions induced by the walls motion.…”

Schrödinger Equation for a Non-Relativistic Particle in a Gravitational Field confined by Two Vibrating Mirrors

“…Soon thereafter the quantum mechanical version emerged in the area of quantum chaos. Another line of studies concerning this quantum mechanical system involves non-locality induced by the moving wall on a localized state [13][14][15][16][17][18][19][20] (for a recent disproof of this conjecture see [21].) Still another context of this system concerns chirped frequency excitations of quantum states, which were proposed in [22].…”

Resonant Transitions Due to Changing Boundaries

“…Several other works appeared, dealing with specific box shapes [44,45], aimed at giving proper mathematical treatment of the Schrödinger problem in the presence of moving boundaries [46], and exploring the raise of correlations between different particles confined in the same time-dependent potential [47]. Very recently, some works reporting on the numerical resolution of the dynamics of a particle confined in a one-dimensional box with moving walls has appeared [48,49].…”