M.Sc Student | Roman Kreiserman |
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Subject | Wavepackets in Dynamically-Evolving Disordered Potentials |

Department | Department of Physics |

Supervisor | ? 18? Segev Mordechai |

Full Thesis text |

My M.Sc. thesis research focuses on the analytical and numerical study of
propagation of wavepackets in dynamically-evolving disordered potentials.** **I
will present a new approach developed to describe and explain the interaction
of waves with dynamically fluctuating disordered potential. The idea is to
represent the disordered potential as a multi-frequency phase grating, where
each frequency is accompanied by a random phase term. When a test wavepacket is
launched into the disordered potential, the diffraction pattern at the exit of
the lattice can be explained as a multiple scattering events from the net
effect of these phase gratings.

In our spectral wave theory, we distinguish between two regimes. For low potential energies, i.e. potential with slow dynamics, the interaction between the wavepacket and the disorder is dominated by conservation of momentum (phase matching). Momentum conservation in (transverse direction) is due to the grating momentum, with inherent momentum conservation in (longitudinal direction) due to phase matching. On the other hand at high energies, for fast fluctuations in the disordered potential, it seems that the interaction does not conserve momentum (phase mismatch) momentarily. Here, momentum is being conserved in (transverse direction) due to the grating momentum, while the phase mismatch is compensated by the presence of many longitudinal spectral components of the disordered potential. From simple considerations of momentum conservation and small angle assumption (using the paraxial approximation), we can extract the analytical prediction for the width of spectrum of the waves at saturation in the limit of weak disordered potential. Hereby we are able to demonstrate the profound difference between the regime of slow dynamics (Bragg regime) and the regime of fast dynamics (Raman-Nath regime).

** **We test the spectral theory by solving numerically the paraxial
wave equation and comparing the dynamics of waves to the dynamics of classical
Newtonian particles in a one dimensional potential that is random both in space
and in time. We find that, in the case of a dynamic disordered potential with
high energies, both the waves and the particles exhibit the same global
behavior, conforming on the Correspondence Principle. Nonetheless, we test our
analytical predictions in some physical scenarios (such as Bragg resonances,
spectral tunneling etc.) and show features of distinct wave character, that
cannot be predicted by any particle theory, since such theories can give
estimates and equivalences between the dynamics of waves and particles only at
the major observables.