Ph.D Thesis

Ph.D StudentKachman Tal
SubjectDynamics and Thermodynamics of Random Systems
DepartmentDepartment of Physics
Supervisors PROFESSOR EMERITUS Shmuel Fishman (Deceased)
PROF. Jeremy England
Full Thesis textFull thesis text - English Version


The thesis focused on various effects of randomness in statistical physics. In particular for this, a novel numerical method was implemented in order to solve the Schrödinger equation with a time dependent potential for extremely long time. It was applied to a quasiperiodic time dependent potential with an extremely large number of random Fourier components. It was demonstrated that it is much faster then the standard (split step) methods. Moreover there is a rigorous bound on the error. This was used to demonstrate that for some time dependent potentials, relevant for experiments in optics and atom optics, the correspondence principle holds and in particular the energy of the system in question does not grow indefinitely in spite of the external driving.

Another type of randomness was considered for systems that select a steady state far from equilibrium. Many patterns may be selected and may be found to be steady self consistently far from thermodynamic equilibrium. Such situations were simulated in the framework of a “toy model” and the statical distribution of the various results was found to agree with novel theories of non equilibrium statistical mechanics.