Related papers: Riemann-Silberstein geometric phase in 4D polariza…
We consider a problem of geometric phase generation in a system of two interacting bosons confined in a narrow ring potential with a localized defect. Geometric phase emerges from variation of parameters of the defect. Particle interaction…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Photon region (PR) in the strong gravitational field is defined as a compact region where photons can travel endlessly without going to infinity or disappearing at the event horizon. In Schwarzschild metric PR degenerates to the…
Geometric phase, which is acquired after a system undergoing cyclic evolution in the Hilbert space, is believed to be noise-resilient because it depends only on the global properties of the evolution path. Here, we report geometric control…
Focusing on the hole-doped two-dimensional systems of strongly correlated electrons, we examine geometric phases acquired by electronic wave functions as a result of polaron transport around a closed loop. For this study we apply the…
Conventional approaches for scattering manipulations rely on the technique of field expansions into spherical harmonics (electromagnetic multipoles), which nevertheless is non-generic (expansion coefficients depend on the position of the…
The relativistic quantum phase space (QPS) formalism extends classical phase space by incorporating both mean values and variance-covariance matrices of quantum states, thereby providing a unified setting where the uncertainty principle and…
4D cylindrical gravitational waves with aligned polarizations (Einstein-Rosen waves) are shown to be described by a weight 1/2 massive free field on the double cover of AdS_2. Thorn's C-energy is one of the sl(2,R) generators, the…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
The existence of Hopf fibrations S^{2N+1}/S^1 = CP^N and S^{4K+3}/S^3 = HP^K allows us to treat the Hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively $U(1)$ and $SU(2)$ fibers and…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
The topological phases of matter are characterized using the Berry phase, a geometrical phase, associated with the energy-momentum band structure. The quantization of the Berry phase, and the associated wavefunction polarization, manifest…
A geometrical study of supergravity defined on (1|1) complex superspace is presented. This approach is based on the introduction of generalized superprojective structures extending the notions of super Riemann geometry to a kind of super…
Generalized BMS (gBMS) is the Lie group of the asymptotic symmetries at null infinity, and is proposed to be a symmetry of the quantum S-matrix. Despite much progress in understanding the symplectic structure at null infinity consistent…
In a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to a…
The Euclidean dynamical symmetry hidden in the critical region of nuclear shape phase transitions is revealed by a novel algebraic F(5) description. With a nonlinear projection, it is shown that the dynamics in the critical region of the…
We introduce the set of framed convex polyhedra with N faces as the symplectic quotient C^2N//SU(2). A framed polyhedron is then parametrized by N spinors living in C^2 satisfying suitable closure constraints and defines a usual convex…
The generalization of photon spheres by considering the trajectories of massive particles leads to the definition of Massive Particle Surfaces (MPS). These surfaces are built with the trajectories of massive particles, and have a partial…
In this study, we investigate the polarization properties of gravitational waves within a torsionless spacetime framework, as described by the Palatini formalism. Our analysis uncovers the presence of two novel polarization modes, referred…
In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of…