Quantum dynamics in a kicked square billiards

We study kicked particle dynamics in a rectangular quantum billiard. The kicking potential is chosen as localized at the center of the billiard. The exact solution for the time-dependent Schrödinger equation for a single kicking period is derived. Using this solution, the time-dependence of the average kinetic energy and probability density as a function of spatial coordinates are computed. Different regimes for trapping of the particle in kicking area are analyzed. It is found that depending of the values of kicking parameters, the average kinetic energy can be a periodic or a monotonically growing function of time or can be suppressed. Such behavior is explained in terms of particle trapping regimes. Wave packet dynamics are also studied. Keywords: quantum dynamics, billiard, Schrödinger equation. Received: 2 February 2015 State of the art and statement of the problem The study of particle dynamics in driven confined quantum systems is of practical importance for different newly emerging topics of nanoscale physics and nanotechnology. In fact, many nanoscale systems, materials and devices are subject to the influence of different external perturbations and environmental effects. The role of such effects in particle transport is relevant to the problem of tuning electronic, optic and acoustic properties of different nanoelectronic devices. Conversely, in confined quantum systems, particle dynamics also depend also on the geometry of the confinement boundaries. Due to these two facts driven confined systems have become an ideal testing ground for solving the problem of tunable particle transport in low-dimensional functional materials, such as quantum dots, wires networks etc. The most convenient tool for modeling of confined systems are so-called billiard geometries, or simply billiards. These are finite-size spatial domains with hard or soft walls providing confinement. Earlier, billiards were the subject of extensive study in nonlinear dynamics [1] and quantum chaos theory Later, quantum billiards have found effective application as models for quantum dots in nanoscale physic