Related papers: Berry's phase in noncommutative spaces
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space- space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons…
The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schr$\ddot{o}$dinger equations in the presence of a magnetic field on NC space…
The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schr$\ddot{o}$dinger equations on noncommutative(NC) space we obtain the Landau energy levels and the energy correction that is caused by…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
The paper aims to spell out the relevance of the Berry phase in view of the question what the minimal mathematical structure is that accounts for all observable quantum phenomena. The question is both of conceptual and of ontological…
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…
We show that Berry's geometrical (topological) phase for circular quantum dots with an odd number of electrons is equal to \pi and that eigenvalues of the orbital angular momentum run over half-integer values. The non-zero value of the…
In noncommutative space to maintain Bose-Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by…
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
The Berry phase is a fundamental concept in quantum mechanics with profound implications for understanding topological properties of quantum systems. This tutorial provides a comprehensive introduction to the Berry phase, beginning with the…
We propose a general scheme for the "logic" of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*-algebras, the non-commutative…
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner…
We introduce a pedagogical discussion on Bohmian mechanics and its physical implications in connection with the important role played by the quantum phase in the dynamics of quantum processes. In particular, we focus on phenomena such as…
Berry phase of simple harmonic oscillator is considered in a general representation. It is shown that, Berry phase which depends on the choice of representation can be defined under evolution of the half of period of the classical motions,…