M.Sc Student | Rivkind Alexandr |
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Subject | Some Rigorous Bounds for the Anderson Model and Their Applications |

Department | Department of Physics |

Supervisor | Professor Emeritus Shmuel Fishman (Deceased) |

Full Thesis text |

Exploration of the nonlinear
Schrödinger equation (NLSE) with a random potential motivated studies of
some properties of the linear model. The main focus of the present work is on
rigorous analysis of the properties of the spectrum of a finite chain with a
random potential. It is shown that the spacing between eigenvalues of the
discrete one dimensional Hamiltonian with arbitrary potentials which are
bounded, and with Dirichlet or Neumann Boundary Conditions is bounded away from
zero. An explicit lower bound, given by *Ce ^{-bN}*, where