21 research outputs found
Dynamics of a particle confined in a two-dimensional dilating and deforming domain
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 all
the process) and the case with deformation.Comment: 13 pages, 2 figure