Ph.D Student | Rahav Saar |
---|---|

Subject | Billiards in Atom Optics |

Department | Department of Physics |

Supervisor | Professor Emeritus Shmuel Fishman (Deceased) |

Several topics related to the
implementation of billiards, where the walls are formed by rapidly moving light
beams and the particles are cold atoms, are studied. The classical and quantum
dynamics in a high frequency field are found to be described by an effective
time independent Hamiltonian. It is calculated in a systematic expansion in the
inverse of the frequency (ω) to order ω^{-4}. The work is an
extension of the classical result for the Kapitza pendulum, which was
calculated in the past to order ω^{-2}. The analysis makes use of
an implementation of the method of separation of time scales and of a quantum
gauge transformation in the framework of Floquet theory. The effective time
independent Hamiltonian enables one to explore the dynamics in presence of
rapidly oscillating fields, in the framework of theories that were developed
for systems with time independent Hamiltonians. The spectral properties of
integrable billiards with localized perturbations are studied. The statistics
of energy levels of a rectangular billiard, which is perturbed by a strong
localized potential, are studied analytically and numerically, when this
perturbation is at the center or at a typical position. The form factor, that
is the Fourier transform of the energy-energy correlation function, is
calculated analytically, in the framework of the semiclassical geometrical
theory of diffraction, and numerically. Contributions of classical orbits that
are non diagonal are calculated and are found to be essential. The resulting
statistics is intermediate between those of integrable and chaotic systems.