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arXiv:1309.0993 · Physica Scripta

Quantum effective force and Bohmian approach to time-dependent traps

S V Mousavi

Published Apr 23, 2014• 5 citations
arXivHTMLPDF

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.

DOI
10.1088/0031-8949/89/6/065003

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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.
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.
The Schrödinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though the particle is nowhere near the walls, it will be affected. It is shown that this force apart from a minus sign is equal to the expectation value of the gradient of the quantum potential for vanishing at the walls boundary condition. Variation of this force with time is studied. A selection of Bohmian trajectories of the confined particle is also computed.
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.