טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentGurevich Evgeni
SubjectEffect of Correlations in Random Potential on the
Phenomenon of Localization
DepartmentDepartment of Physics
Supervisor Professor Emeritus Boris Shapiro
Full Thesis textFull thesis text - English Version


Abstract

    Various effects of correlation in random potential on the phenomenon of localization in one-dimensional (1D) disorder systems are investigated. First, weak disorder expansion for the inverse localization length in one-dimensional system with correlated disorder is developed using the ordered cumulant method of van-Kampen. This expansion is carried out explicitly for the first three perturbative orders. Then, this general expansion is applied to the specific model of "laser speckle potential", relevant to the experiments with cold atoms, where the disorder is proportional to the variations of the speckle pattern intensity.

    Disorder correlation affects not only the value of the localization length, but also the statistical properties of localization, and, in particular, the transmission distribution. We study effect of disorder correlations on the transmission statistics in a long but finite 1D system in terms of the generalized Lyapunov exponent and of the cumulants of the transmission logarithm.

    Another important characteristics of a system is the (reflection) Wigner delay time. First, we establish a relation between the statistics of delay times in one-channel reflection from a mesoscopic sample and the statistics of the eigenfunction intensities in its closed counterpart. Such relation was known previously for disordered systems where the random matrix theory and the non-linear σ-model are applicable, which excludes a strictly 1D geometry considered here. Obtained relation makes it possible to derive an intuitive estimation of the delay time distribution in finite and infinite system. For a finite system, this distribution has a log-normal tail, whose shape depends on the correlation properties of the disorder. Then, a weak disorder expansion for the delay time distribution in correlated disorder is developed using the ordered cumulant method of van-Kampen. The leading and the next to the leading terms are obtained explicitly. The leading term, both for finite and infinite systems, has the same functional form as for the white noise disorder. To this leading order, the only parameter of the distribution is the localization length corresponding to the considered model of disorder. The non-universal corrections to the delay time distribution appear in the next perturbative order. Our analytical studies are verified and supplemented with numerical simulation.