Related papers: The non-adiabatic classical geometric phase and it…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
This paper develops the tools of formal algebraic geometry in the setting of noncommutative manifolds, roughly ringed spaces locally modeled on the free associative algebra. We define a notion of noncommutative coordinate system, which is a…
The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
Let $\Lambda$ be a finite abelian group. A dynamical system with transformation group $\Lambda$ is a triple $(A,\Lambda,\alpha)$, consisting of a unital locally convex algebra $A$, the finite abelian group $\Lambda$ and a group homomorphism…
The effect due to the inter-subsystem coupling on the off-diagonal geometric phase in a composite system is investigated. We analyze the case where the system undergo an adiabatic evolution. Two coupled qubits driven by time-dependent…
We study the non-adiabatic dynamics of a typical symmetry-protected topological phase-the Haldane insulator phase with broken bond-centered inversion. By continuously breaking the middle chain, we find the gap closes at a critical point in…
We describe a classical thermodynamic model that reproduces the main features of the solid hydrogen phase diagram. In particular, we show how the general structure types that are found by electronic structure calculations and the quantum…
The possibility of realization of quantum gates by means of the non-adiabatic geometric phase is considered. It is shown that the non-adiabatic phase can be used for quantum gates realization as well as the adiabatic one.
The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to…
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
The classical dynamics of particles with (non-)abelian charges and spin moving on curved manifolds is established in the Poisson-Hamilton framework. Equations of motion are derived for the minimal quadratic Hamiltonian and some extensions…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
In a time-orbiting-potential magnetic trap the neutral atoms are confined by means of an inhomogeneous magnetic field superimposed to an uniform rotating one. We perform an analytic study of the atomic motion by taking into account the…
We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…