Related papers: Smooth Loops, Generalized Coherent States and Geom…
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…
A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization.
Within the framework of thermofield dynamics, we construct a thermalized coherent thermal state, which is a general type of the coherent state with the thermal effects and can be presumably produced experimentally. The wavefunction and the…
Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view…
Multipartite generalizations of spin coherent states are introduced and analyzed. These are the spin analogues of multimode optical coherent states as used in continuous variable quantum information, but generalized to possess full spin…
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…
Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.
The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As…
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…
A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The…
In the first half we show an interesting relation between coherent states and the Bell states in the case of spin 1/2, which was suggested by Fivel. In the latter half we treat generalized coherent states and try to generalize this relation…
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following…
We present a possible construction of coherent states on the unit circle as configuration space. In our approach the phase space is the product Z x S^1. Because of the duality of canonical coordinates and momenta, i.e. the angular variable…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical…
Coupled cluster theory in the standard formulation is unable to correctly describe conical intersections among states of the same symmetry. This limitation has restricted the practical application of an otherwise highly accurate electronic…
It is shown that the general relativity has a one-parameter compact symmetry and this symmetry is analogous to the phase symmetry of quantum mechanics
A dynamical algebra ${\cal A}_q$, englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the…
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…
The main objective of the paper is to unveil an adequate mathematics hidden behind entanglement, that is Geometric Invariant Theory. More specifically relation between these two subjects can be described by the following theses. (i) Total…