相关论文: Quantum particle on hyperboloid

We compare the respective efficiencies of three quantization methods (group theoretical, coherent state and geometric) by quantizing the dynamics of a free massive particle in two-dimensional de Sitter space. For each case we consider the…

We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…

Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a…

We consider the approach to gravity in which four-dimensional curved spacetime is represented by a surface in a flat Minkowski space of higher dimension. After a short overview of the ideas and results of such an approach we concentrate on…

We study the issue of description of spinning particle dynamics by means of recently proposed world sheet concept. A model of irreducible spinning particle in the $3d$ Minkowski space with two gauge symmetries is considered. The classical…

How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…

We consider the quantum dynamics of a charged particle in Euclidean space subjected to electric and magnetic fields under the presence of a potential that forces the particle to stay close to a compact surface. We prove that, as the…

This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…

We address a conceptual issue of reconciling the traditional canonical quantization framework of quantum theory with the spatially restricted quantum dynamics and the related spectral problems for confined and global observables of the…

Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…

Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is…

The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…

We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…

We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by…

We develop a Hamiltonian description of point particles in (2+1)-dimensions using connection and frame-field variables for general relativity. The topology of each spatial hypersurface is that of a punctured two-sphere with particles…

Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently…

Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…

Issues related to quantum entanglement in systems of indistinguishable particles, as discussed in the information theoretic approach, are extended to anyonic statistics. Local and non-local measurements discussed in this framework are…