Delocalization in infinite disordered two-dimensional lattices of different geometry

Spreading in disordered lattices with different nonlinearities

We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schrödinger equation with random on-site potentials —a nonlinear generalization of the Anderson model of localization. We use a nonlinear diffusion equation to describe the subdiffusive spreading. To confirm the self-similar nature of the evolution we characterize the peak structure...

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

Partial delocalization of two-component condensates in optical lattices

We study management of localized modes in two-component (spinor) Bose-Einstein condensates embedded in optical lattices by changing interspecies interactions. By numerical integration of the coupled Gross-Pitaevskii equations, we find three different regimes of the delocalizing transition: i) the partial delocalization when the chemical potential of one of the components collapses with a gap ed...

Quantum geometry of 3-dimensional lattices

We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices — lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable “ultra-local” Poisson bracket algebra defined on discrete 2D surfaces consisting of circular quadrilaterals. Quantization of this s...

The Geometry of Infinite-Dimensional Groups