Quantum instability for a wave packet kicked periodically by a quadratic potential

Roy J. Glauber

V. E. Eshniyazov, Davron U. Matrasulov, Jambul Yusupov

We study quantum dynamics of a kicked relativistic spin-half particle in a one dimensional box. Time-dependence of the average kinetic energy and evolution of the wave packet are explored. Kicking potential is introduced as the Lorentz-scalar, i.e., through the mass-term in the Dirac equation. It is found that depending on the values of the kicking parameters E(t) can be periodic, monotonically growing and non-periodic function of time. Particle transport in the system is studied by considering spatio-temporal evolution of the Gaussian wave packet.Splitting of the packet into two symmetric parts and restoration of the profile of the packet is found.

Claude M. Dion, A. Hashemloo, G. Rahali

S. Rakhmanov, Doniyor Babajanov, O. Karpova +1 more

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.

Jean-Louis Basdevant, Jean Dalibard

K. N. Alekseev, D. S. Priimak

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos.