The problem of a particle confined in a box with moving walls is studied, focusing on the case of small perturbations which do not alter the shape of the boundary (lq pantographyrq). The presence of resonant transitions involving the natural transiti
on frequencies of the system and the Fourier transform of the velocity of the walls of the box is brought to the light. The special case of a pantographic change of a circular box is analyzed in dept, also bringing to light the fact that the movement of the boundary cannot affect the angular momentum of the particle.
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.
Complete positivity of a class of maps generated by master equations derived beyond the secular approximation is discussed. The connection between such class of evolutions and physical properties of the system is analyzed in depth. It is also shown t
hat under suitable hypotheses a Zeno dynamics can be induced because of the high temperature of the bath.
We discuss the partitioning of the Hilbert space of a quantum system induced by the interaction with another system at thermal equilibrium, showing that the higher the temperature the more effective is the formation of Zeno subspaces. We show that ou
r analysis keeps its validity even in the case of interaction with a bosonic reservoir, provided appropriate limitations of the relevant bandwidth.
Repeated observations of a quantum system interacting with another one can drive the latter toward a particular quantum state, irrespectively of its initial condition, because of an {em effective non-unitary evolution}. If the target state is a pure
one, the degree of purity of the system approaches unity, even when the initial condition of the system is a mixed state. In this paper we study the behavior of the purity from the initial value to the final one, that is unity. Depending on the parameters, after a finite number of measurements, the purity exhibits oscillations, that brings about a lower purity than that of the initial state, which is a point to be taken care of in concrete applications.
A quantum system put in interaction with another one that is repeatedly measured is subject to a non-unitary dynamics, through which it is possible to extract subspaces. This key idea has been exploited to propose schemes aimed at the generation of p
ure quantum states (purification). All such schemes have so far been considered in the ideal situations of isolated systems. In this paper, we analyze the influence of non-negligible interactions with environment during the extraction process, with the scope of investigating the possibility of purifying the state of a system in spite of the sources of dissipation. A general framework is presented and a paradigmatic example consisting of two interacting spins immersed in a bosonic bath is studied. The effectiveness of the purification scheme is discussed in terms of purity for different values of the relevant parameters and in connection with the bath temperature.
