Quantum-Classical correspondence in nonlinear multidimensional systems: enhanced di usion through soliton wave-particles

الموضوعات

علوم تطبيقية وتكنولوجية

الملخص

Quantum chaos has emerged in the half of the last century with the notoriousproblem of scattering of heavy nuclei. Since then, theoreticians have developed powerfultechniques to approach disordered quantum systems. In the late 70's, Casatiand Chirikov initiated a new field of research by studying the quantum counterpartof classical problems that are known to exhibit chaos. Among the several quantum-classical chaotic systems studied, the kicked rotor stimulated a lot of enthusiasm inthe scientific community due to its equivalence to the Anderson tight binding model.This equivalence allows one to map the random Anderson model into a set of fullydeterministic equations, making the theoretical analysis of Anderson localization considerablysimpler. In the one-dimensional linear regime, it is known that Andersonlocalization always prevents the diffusion of the momentum. On the other hand, forhigher dimensions it was demonstrated that for certain conditions of the disorder parameter,Anderson localized modes can be inhibited, allowing then a phase transitionfrom localized (insulating) to delocalized (metallic) states. In this thesis we will numerically and theoretically investigate the properties ofa multidimensional quantum kicked rotor in a nonlinear medium. The presence ofnonlinearity is particularly interesting as it raises the possibility of having solitonwaves as eigenfunctions of the systems. We keep the generality of our approachby using an adjustable diffusive nonlinearity, which can describe several physicalphenomena.By means of Variational Calculus we develop a chaotic map which fully describesthe soliton dynamics. The analysis of such a map shows a rich physical scenario thatevidences the wave-particle behavior of a soliton. Through the nonlinearity, we tracea correspondence between quantum and classical mechanics, which has no equivalentin linearized systems.Matter waves experiments provide an ideal environment for studying Andersonlocalization, as the interactions in these systems can be easily controlled by Feshbachresonance techniques. In the end of this thesis, we propose an experimental realizationof the kicked rotor in a dipolar Bose Einstein Condensate.

روابط وملفات

التعريف والنوع

رقم الوثيقة

0d35246a-0726-497f-9408-b3af7fa46ba1

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

1700843_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"أندريا فراتالوتشي","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"دانيلو سيموس برامبيلا","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

Quantum-Classical correspondence in nonlinear multidimensional systems: enhanced di usion through soliton wave-particles

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Anderson Localization , Quantum Chaos , Solitons , Variational

إشراف وإعداد

الإشراف

أندريا فراتالوتشي

الإعداد

دانيلو سيموس برامبيلا

الاقتباسات الببليوغرافية