Coherent states of nonstationary soliton potentials

With the help of a nonstationary Darboux transformation, we have obtained a system of coherent states for the potential which is a solution of the Kadomtsev-Petviashvili equation. We have determined the measure realizing expansion of unity with respect to these states. We have constructed a holomorphic representation of the state vectors and the ladder operators for the discrete basis of the Hilbert space of solutions of the Schrödinger equation.     

Coherent states for Smorodinsky-Winternitz potentials

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.      

Coherent states as extreme energy states

A class of states obtained by extremizing the energy of a system under certain conditions is introduced and their properties are compared with those of the coherent states. Conditions under which these states move without change of shape and follow the classical path are investigated.     

Coherent soliton pattern formation in a fiber laser

We report the observation of bound states of 350 pulses in a ring fiber laser mode locked by nonlinear rotation of the polarization. The phenomenon is described theoretically using a multiscale approach to the gain dynamics; the fast evolution of a small excess of gain is responsible for the stabilization of a periodic pattern, while the slow evolution of the mean value of gain explains the finite length of the quasiperiodic soliton train.     

Coherent states in optics

An approach has been developed with the use of coherent states for constructing wavelets based on spiral light beams.     

Coherent states of theq-Weyl algebra

New coherent states of theq-Weyl algebraAA –qA A = 1,0 <q < 1, are constructed. They are defined as eigenstates of the operatorA which is the lowering operator for nonhighest weight representations describing positive energy states. Depending on whether the positive spectrum is discrete or continuous, these coherent states are related either to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of theq-Weyl algebra whenA A d²/dx² is used for illustrations.On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia.     

Coherent states,phase states,and condensed states

We study phase properties of generalized coherent states obtained from usual Fock coherent states by adapting classical methods of statistical mechanics, in particular, the well-known procedure of thermodynamical limit. Moreover, we show that there exists a close connection between these states and the states describing boson systems with condensation properties.     

Coherent states and symmetric spaces

Properties of system of the coherent states related to representations of the class I of principal series of the motion groups of symmetric spaces of rank 1 have been studied. It has been proved that such states are given by horospherical kernels and are the generalization of the plane waves for the case of symmetric spaces.     

Coherent states and squeezed states of realq-deformed quantum oscillators

A detailed physical characterisation of the coherent states and squeezed states of a realq-deformed oscillator is attempted. The squeezing andq-squeezing behaviours are illustrated by three different model Hamiltonians, namely i) Batemann Hamiltonian ii) harmonic oscillator with time dependent mass and frequency and iii) a system with constant mass and time-dependent frequency.     

Coherent states and coordinate-free quantization

The usual quantization procedures interpret canonical transformations in an active way linking them with unitary transformations, while the quantization procedure offered by coherent states completely separates classical canonical transformations and unitary operator transformations. By exploiting this property, along with a physically motivated shadow metric, it is seen how to realize the quantization process in as coordinate-free a form as holds in classical mechanics.     

Coherent states and partition function

The concept of coherent states for arbitrary Lie group is suggested as a tool for explicitly obtaining an integral representation of the partition function, whenever the Hamiltonian has a dynamical group. Two examples are thoroughly discussed: the case of the nilpotent group of Weyl related to a generic many-body problem with two-body interactions, and the case of SU(1, 1)() relevant for a superfluid system.     

Coherent states and induced representations

A generalization of the notion of coherent states is given. The following one-to-one correspondences are pointed out: (1) between covariant overcomplete systems of coherent states and a class of covariant semi-spectral measures; (2) between covariant semispectral measures and unitary irreducible subrepresentations of induced representations of Lie groups; (3) between unitary irreducible representations of Lie groups with covariant overcomplete systems of coherent states and unitary irreducible subrepresentations of induced representations, whose representation spaces are reproducing kernel Hilbert spaces.     

Coherent states with elliptical polarization

Coherent states of the two-dimensional harmonic oscillator are constructed as superpositions of energy and angular momentum eigenstates. It is shown that these states are Gaussian wave-packets moving along a classical trajectory, with a well-defined elliptical polarization. They are coherent correlated states with respect to the usual Cartesian position and momentum operators. A set of creation and annihilation operators is defined in polar coordinates, and it is shown that these same states are precisely coherent states with respect to such operators.     

Coherent states and uncertainty relations

The most general form of the minimality-preserving Hamiltonians is found and the uncertainty products ΔqΔp are calculated for some quadratic quantum systems     

Coherent states and geometric quantization

Based on the concept of generalized coherent states, a theory of mechanical systems is formulated in a way which naturally exhibits the mutual relation of classical and quantum aspects of physical phenomena.This work was supported in part by The Swedish Institute     

Coherent states in geometric quantization

In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to collect some recent results. We begin by recalling the basic constructions of geometric quantization in both the Kähler and non-Kähler cases. We then study the reproducing kernels associated to the quantum Hilbert spaces and use them to define symplectic coherent states. The rest of the paper is dedicated to the properties of symplectic coherent states and the corresponding Berezin–Toeplitz quantization. Specifically, we study overcompleteness, symplectic analogues of the basic properties of Bargmann’s weighted analytic function spaces, and the ‘maximally classical’ behavior of symplectic coherent states. We also find explicit formulas for symplectic coherent states on compact Riemann surfaces.     

Coherent states of theq-canonical commutation relations

For theq-deformed canonical commutation relationsa(f)a (g)=(1-q)f,g 1+qa (g)a(f) forf, g in some Hilbert space we consider representations generated from a vector satisfyinga(f)=<f, >, where . We show that such a representation exists if and only if 1. Moreover, for <1 these representations are unitarily equivalent to the Fock representation (obtained for =0). On the other hand representations obtained for different unit vectors are disjoint. We show that the universal C^*-algebra for the relations has a largest proper, closed, two-sided ideal. The quotient by this ideal is a naturalq-analogue of the Cuntz algebra (obtained forq=0). We discuss the conjecture that, ford<, this analogue should, in fact, be equal to the Cuntz algebra itself. In the limiting casesq=±1 we determine all irreducible representations of the relations, and characterize those which can be obtained via coherent states.Supported in part by the NSF(USA), and NATO Available by anonymous FTPfrom nostrom.physik.Uni-Osnabrueck.DE