Showing papers on "Coherent states in mathematical physics published in 1993"

Coherent states on a circle and quantum interference.

Abstract: As a generalization of the optical Schrodinger cats, discrete sets of coherent states are considered on a circle in the a plane. It is shown that simple superpositions of Schrodinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state

N-dimensional affine Weyl-Heisenberg wavelets

Abstract: n-dimensional coherent states systems generated by translations, modulations, rotations and dilations are described. Starting from unitary irreducible representations of the n-dimensional affine Weyl-Heisenberg group, which are not square-integrable, one is led to consider systems of coherent states labeled by the elements of quotients of the original group. Such systems can yield a resolution of the identity, and then be used as alternatives to usual wavelet or windowed Fourier analysis. When the quotient space is the phase space of the representation, different embeddings of it into the group provide different descriptions of the phase space.

Coherent states for the quantum complex plane

Abstract: The coherent states for the quantum complex plane are introduced. It is demonstrated that the Bargmann representation corresponding to these states involves both the standard integral with respect to the Gaussian measure and the Berezin integral over Grassmann variables. The quantum generalizations of many constructions developed for classical coherent states are described.

On Coherent States and q-Deformed Algebras

Abstract: We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to provide a path integral formalism allowing to study a modified form of q-classical mechanics, to probe some geometrical consequences of the q-deformation and finally to construct Bargmann complex analytic realizations for some quantum algebras.

Coherent States, Dynamics and Semiclassical Limit on Quantum Groups

Abstract: Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to $q$-deformation as a $q$-Weyl quantization and a relavence of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.

The general form of the microscopic coherent boson states

Abstract: Recently the classical coherent states on the photonic C ∗-Weyl algebra have been classified. Non-classical coherence occurs only for states which are normal with respect to the Fock representation of the CCR. Here, the Fock-normal (=microscopic) coherent states are characterized completely. It suffices to consider Fock coherence only on the one-mode Weyl algebra W ( C ). The smoothness and coherence properties of a regular state on W ( C ) are expressed by the diagonal elements of the associated density matrix. With a Kolmogorov decomposition the off-diagonal matrix elements are replaced by a unique sequence of normalized vectors in a Hilbert space, which leads to the GNS representation and to a construction procedure for the whole set of all (microscopic) coherent states of arbitrary order. The variety of non-classical fully coherent states on W ( C ) is shown to be much larger than the one for classical fully coherent states. Moreover, it is proved that there exist (non-classical) elements of the extreme boundary of the weak ∗ -compact, convex set of fully coherent states, which are not pure states.

GLAUBER COHERENT STATE q-DEFORMED QUANTUM OSCILLATOR

Abstract: By making use of the Fock States of the q-deformed quantum oscillator which possesses the symmetry of quantum group, we construct the Glauber coherent state of the q-deformed quantum oscillator (the q-Glauber coherent state ㄧα>q). We discuss the of completeness properties, particle number distribution, oscillator strength distribution and the minimal uncertainty principle of the q-Glauber coherent states, and point out that the coherent degree of the q-Glauber coherent state can be described by the parameter q.

Coherent neutron fields and the Lie algebra sl(2,R)

Abstract: The application of Glauber's definition (1963) of quantum coherence allows the introduction of neutron fields of partial coherence under the assumption that the complete occupation number space is a direct product of Fermi subspaces. Excitations are described by 'collective' creation and annihilation operators which span an algebra isomorphic to the sl(2,R) algebra. The associated coherent states are of partial coherence and the finite dimensional representation of the su(2,R) algebra is not regularly coherent. In contrast, the transition to an infinite dimensional representation space results in regular coherent properties of the field. This is demonstrated using the representation space of the su(1,1) algebra which has a real isomorphism to the sl(2,R) algebra. The coherent states calculated from Glauber's condition for coherence are completely coherent, and are, moreover, identical to those found by Barut and Girardello (1971) in starting from a far more abstract argument.