NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (2), P. 216–223
Quantum dynamics in a kicked square billiards
S. Rakhmanov – National University of Uzbekistan, Tashkent, Uzbekistan
D. Babajanov – Turin Polytechnic University in Tashkent, Tashkent, Uzbekistan
O. Karpova – National University of Uzbekistan; Turin Polytechnic University in Tashkent, Tashkent, Uzbekistan; firstname.lastname@example.org
F. Khoshimova – Navoi State Mining Institute, Navoiy, Uzbekistan
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 Schro¨dinger 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.