相关论文: Bargmann Invariants and Geometric Phases - a Gener…

It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…

We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

We present a picture of Lagrangean mechanics, free of some unnatural features (such as complete divergences). As a byproduct, a completely natural U(1)-bundle over the phase space appears. The correspondence between classical and quantum…

Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior…

Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $GL_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using…

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…

We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a self-dual manner as a principal bundle frame resolution and a dual…

We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the…

We show the explicit expression of the geometric phase for $n$-partite Gaussian states. In our analysis, the covariance matrix can be obtained as a boundary term of the geometric phase.

We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.

We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…

Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…

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…

A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative…

We outline a new model in which generalised uncertainty relations are obtained without modified commutation relations. While existing models introduce modified phase space volumes for the canonical degrees of freedom, we introduce new…

The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…

Given a curve in quantum spin state space, we inquire what is the relation between its geometry and the geometric phase accumulated along it. Motivated by Mukunda and Simon's result that geodesics (in the standard Fubini-Study metric) do…

Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…

The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…