相关论文: Geometric Phases
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…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
We investigate the level surfaces of geometric measure of quantum discord, and provide a pictorial interpretation of geometric discord for Bell-diagonal states. We have observed its nonanalytic behavior under decoherence employing this…
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.
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
Geometric phases of scattering states in a ring geometry are studied based on a variant of the adiabatic theorem. Three time scales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a…
We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of…
This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…
Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed…
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…
The derivation of the phase transition in the model of Ga\'zdzicki and Gorenstein is generalized and simplified by using a geometrical construction.
Some aspects of the multidimensional soliton geometry are considered.