Some Aspects of the Generalized Uncertainty Principle Theoretical Development and Applications

الموضوعات

علوم بحتة وطبيعية

الملخص

This thesis investigates some consequences arising from the modification of Heisen-berg’s Uncertainty Principle (HUP), postulated in quantum theory to introduce limitvalues in the position and momentum uncertainties. In this context, the HUP is re-placed by the so-called Generalized Uncertainty Principle (GUP). Firstly, by focusingon the fundamental physical aspect, we present the arguments of different hypothesessuggesting the existence of upper and lower bounds of some measurable quantities,as well as the related GUPs that have been proposed based on these hypotheses. Wefocus in particular on three GUPs: the one leading to the existence of a minimallength (suggested in various frameworks, such as quantized space-time theory, stringtheory and black hole physics), the GUP incorporating a minimal length and a maxi-mal momentum (emerging in doubly special relativity) and the GUP with a maximallength (predicted in cosmology). The formalism of deformed quantum mechanics,which occurs from these GUPs, is studied exhaustively in the second chapter. Es-pecially, we exhibit the modified commutation relations of position and momentumoperators, the corresponding Hilbert space representations and the scalar productdefinition. Moreover, some theoretical developments are discussed by summarizingmost important works in the literature.We consider furthermore some applications in statistical physics by focusing onthe recent maximal-length GUP. In fact, three systems are investigated, namely,an ideal gas, an ensemble of harmonic oscillators and a relativistic gas. In thisframework, the thermodynamic properties of these systems are studied within thecanonical ensemble via the quantum and semiclassical approaches. The comparisonwith the results obtained in the context of the minimal-length GUPs indicates thatthe maximum length may induce new effects, which become important at high tem-peratures and for large volumes. In particular, a modified equation of state for idealgases emerges in the scope of this new formalism. By analyzing some experimentaldata, we argue that the maximal length might be viewed as a macroscopic scaleassociated with the system under study.

روابط وملفات

التعريف والنوع

رقم الوثيقة

0afc69de-6f46-4fe3-b0d8-74e2402bacdc

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

2185518_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"Djamil Bouaziz","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Salaheddine Bensalem","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

French

المصدر والدورية

اسم المصدر

Some Aspects of the Generalized Uncertainty Principle Theoretical Development and Applications

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Generalized uncertainty principle, modified dispersion relation, max- imal length, minimal length, ideal gas, harmonic oscillator, relativistic gas, partition function, equation of state

إشراف وإعداد

الإشراف

Djamil Bouaziz

الإعداد

Salaheddine Bensalem

الاقتباسات الببليوغرافية