Related papers: Resource Letter GPP-1: Geometric Phases in Physics
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the…
This Resource Letter treats the nascent discipline of physical eschatology, which deals with the future evolution of astrophysical objects, including the universe itself, and is thus both a counterpart and a complement to conventional…
This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for…
We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled…
The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.
This resource letter is designed to guide students, educators, and researchers through (some of) the literature on black holes. Both the physics and astrophysics of black holes are discussed. Breadth has been emphasized over depth, and…
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
Geometric phases are ubiquitous in physics; they act as memories of the transformation of a physical system. In optics, the most prominent examples are the Pancharatnam-Berry phase and the spin-redirection phase. Recent technological…
The geometric phase of a bi-particle model is discussed. For different initial states, especially when the initial state is pure or mixed, the geometric phase will show different properties. The relationship between the geometric phase and…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…