Related papers: Geodesics in Information Geometry : Classical and …
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
At low temperature a thermodynamic system undergoes a phase transition when a physical parameter passes through a singularity point of the free energy, corresponding to formation of a new order. At high temperature the thermal fluctuations…
We study the geodesic motion in a space-time describing a swirling universe. We show that the geodesic equations can be fully decoupled in the Hamilton-Jacobi formalism leading to an additional constant of motion. The analytical solutions…
In this paper we argue that one-way quantum computation can be seen as a form of phase transition with the available information about the solution of the computation being the order parameter. We draw a number of striking analogies between…
We define an evolution of multiple particles on a discrete manifold $G$. Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move deterministically and reversibly on the frame bundle $P$ of…
We obtain the ground-state energy level and associated geometric phase in the Dicke model analytically by means of the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The non-adiabatic…
We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of…
We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with…
We consider geodesics motion in a particular Kundt type III spacetime in which Einstein-Yang-Mills equations admit solutions. On a particular surface as constraint we project the geodesics into the (x,y) plane and treat the problem as a…
Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties…
In this research, we investigate the quantum and classical phase transitions of the Dirac particles in a homogeneously magnetized curved rotating 2+1 dimensional spacetime. We consider the intricate relationship between geometry and quantum…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Within the Geometry of Interaction (GoI) paradigm, we present a setting that enables qualitative differences between classical and quantum processes to be explored. The key construction is the physical interpretation/realization of the…
We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The…
The geometric phase is of fundamental interest and plays an important role in quantum information processing. However, the definition and calculation of this phase for open systems remains a problem due to the lack of agreement on…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…