Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the 'pantographic' case (same shape of the box through the entire process) and the case with deformation.

Anzà, F., Martino, S., Messina, A., Militello, B. (2015). Dynamics of a particle confined in a two-dimensional dilating and deforming domain. PHYSICA SCRIPTA, 90(7), 074062-1-074062-10 [10.1088/0031-8949/90/7/074062].

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

MESSINA, Antonino
;
MILITELLO, Benedetto
2015-01-01

Abstract

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the 'pantographic' case (same shape of the box through the entire process) and the case with deformation.
2015
Settore FIS/03 - Fisica Della Materia
Settore FIS/02 - Fisica Teorica, Modelli E Metodi Matematici
Anzà, F., Martino, S., Messina, A., Militello, B. (2015). Dynamics of a particle confined in a two-dimensional dilating and deforming domain. PHYSICA SCRIPTA, 90(7), 074062-1-074062-10 [10.1088/0031-8949/90/7/074062].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/168669
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