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-dimensi
onal 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.
We reconsider the effect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in different spatial regions
. We explicitly show that if the spin measurements are performed in disjoint spatial regions then there are no constraints on the structure of the reduced state of the system. This implies that the statistics of identical particles has no role from the point of view of separability and entanglement when the measurements are spatially separated. We extend the treatment to the case of n particles and show the connection with some recent criteria for separability based on subalgebras of observables.
