Smorodinsky-Winternitz potentials: Coherent state approach

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 and the Kepler-Coulomb problem. In the first case we find the nonspreading 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 nonisotropic harmonic oscillators. All of these states evolve in physical-time. In the third case, the system is transformed into four oscillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two oscillators with the reflection symmetry and the parametrictime coherent states are constructed in two coordinate frames.     

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 state approach to the infra-red behaviour of non-abelian gauge theories

The infrared behaviour of matrix elements between coherent states of definite color is studied in non-abelian gauge theories. The matrix elements are shown to be finite to the lowest non-trivial order, and to all orders if the soft meson formula for real gluons holds to all orders. Factorization occurs in the fixed angle regime.     

Doorway state approach to optical potential scattering

We extend and apply the doorway state approach in the context of optical potential scattering. This entalls construction of doorway basis states for resolving the transition operator. We focus on analytic solutions to comparatively simple problems in optical potential scattering. Both low and high energy limits are considered, and absorptive interactions are treated; both on- and off-shell partial wave amplitudes are constructed. Further, the full scattering amplitude in the high energy limit is calculated directly in the doorway expansion. With our analytic results, it is possible to identify the physical parameters controlling convergence of the doorway expansion. The same parameters apply over the entire range of cases studied. These parameters are related simply to the target geometry and to the interaction strength. For interactions appropriate to hadron-nucleus scattering, convergence of both on- and off-shell amplitudes is very rapid.     

Coherent electron-hole BCS state: Study of dynamics

The first experimental study of the evolution of a coherent electron-hole (e-h) BCS-like state in bulk GaAs at room temperature is presented. We explicitly demonstrate that the total spontaneous emission from e-h pairs located within the conduction and valence bands approaches zero when the radiative recombination of the e-h BCS state occurs. This confirms that a vast majority of electrons and holes available are condensed at the very bottoms of the bands and form the BCS state. The average lifetime of this state is measured to be around 300 fs. We also show that the coherence of electrons and holes of the BCS state is preserved for a much longer time compared to the intraband relaxation time T₂.     

Coherent state polarons in quantum wells

We investigate the polaronic effects of an electron confined in a quantum well, which we describe through its algebraic properties using su(1,1), taking into account the electron-bulk longitudinal-optical phonon interaction. We construct the variational wave function as the direct product of an electronic part and a part describing coherent phonons generated by the Low–Lee–Pines transformation from the vacuum state. We use two explicit forms of coherent states, Perelomov and Barut-Girardello states, to represent the electronic part in the quantum well spectrum. Our results show that in a coherent state basis for electrons the basic polaron parameters such as the energy gap shift and effective mass are further enhanced compared to those obtained with the conventional sinusoidal form of the basis. The difference between the two types of quantum well coherent states appears in polaronic interactions in quantum wells. We extend the calculations in order to estimate polaron lifetimes for a variety of different material systems.     

三粒子Calogero-Sutherland模型的相干态

利用赝角动量算符方法求解三粒子CSM(Calogero-Sutherland Model)的类径向方程,给出本征态和相干态的解析表达式. 关键词： 三粒子Calogero-Sutherland模型 赝角动量算符方法 相干态     

Modified cell theory: Free volume distributions and the equation of state for D-dimensional hard sphere systems

A generalized cell model, using cells of different sizes, is applied to hard rods, disks and spheres. Structures is discussed in terms of free volumes. The derived equation of state is exact for rods. For disks and spheres it provides a good approximation in the dense fluid and solid state.     

Coherent state representations of nilpotent Lie groups

The coherent state representations of a connected and simply connected nilpotent Lie group are characterized in terms of the Kirillov correspondence, as being those irreducible unitary representations whose associated orbits under the coadjoint representation are linear varieties.     

Coherent state map quantization in a Hermitian-like setting

For vector bundles having an involution on the base space, Hermitian-like structures are defined in terms of such an involution. We prove a universality theorem for suitable self-involutive reproducing kernels on Hermitian-like vector bundles. This result relies on pullback operations involving the tautological bundle on the Grassmann manifold of a Hilbert space and exhibits the aforementioned reproducing kernels as pullbacks of universal reproducing kernels that live on the Hermitian-like tautological bundle. To this end we use a certain type of classifying morphisms, which are geometric versions of the coherent state maps from quantum theory. As a consequence of that theorem, we obtain some differential geometric properties of these reproducing kernels in this setting.     

Coherent state evolution in a Raman dispersion process

By using the technique of integration within an ordered product of operators, we derive the evolution of an initial coherent state in a Raman dispersion process.     

S-Matrix formalism for particles interacting with phonon fields: Coherent state representation

We apply the quasiparticle picture to the interaction between a fermion and a boson field using a coherent states representation of theS matrix. Its matrix elements between single particle states are explicitly evaluated in terms of a path integral. The method is extended to include dispersion in the excitation spectrum and applied to the case of a metal with electron-hole symmetry. Its relation with perturbation theory is discussed and the second order perturbative result for polarons in insulators is recovered.     

Coherent potential approximation for strong-coupling superconducting transition-metal alloys

Within the coherent potential approximation (CPA) a theory for strong-coupling superconducting transition-metal alloys is developed. The configurational dependence of the selfenergy-part is discussed and, in analogy to McMillan, an expression forT _c is derived for a singles band as well as for anΓ′₂₅-band. The electron-phonon coupling constantλ occuring in this expression depends explicitly on: the average component density of states,N _A (0) andN _B (0), the electron-phonon matrix elements of the components, the difference of the atomic energy levels,δ, and the phonon Green's function at zero frequency. In the limit of the pure metal this expression reduces to that developed by Appel and Kohn. It is shown that the change of the phonon density of states in an alloy due to the atomic mass differences — which is very complicated — does not influence the value ofλ.     

Quasinormal modes of D-dimensional de Sitter spacetime

We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in D-dimensional de Sitter spacetime (D ≥ 4). We also study the quasinormal modes of a real massive scalar field and compare our results with those of other references.     

Coherent state embeddings, polar divisors and Cauchy formulas

For arbitrary quantizable compact Kähler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realized via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vectors on the manifold with the corresponding scalar products on projective space (Cauchy formulas), two-point, three-point and more generally cyclic m-point functions are discussed. The three-point function is related to the shape invariant of geodesic triangles in projective space.     

Coherent state path integral methods and central limit theorem

We consider a coherent state path integral expression originating for example after path integration over a second interacting system and by using a method based on the use of the central limit theorem on the phase of the path integral representation, we extract under certain conditions a closed form for the propagator.     

类氢原子的相干态

用赝角动量算符方法直接求解球坐标下束缚态类氢原子的径向方程.给出本征态的解析表达式,其中归一化问题比较特殊,需要格外细致;最后给出相应的相干态. 关键词： 类氢原子径向方程 赝角动量算符方法 本征值谱 相干态     

Coherent state approach to the cross-collisional effects in the population dynamics of a two-mode Bose–Einstein condensate

We reanalyze the non-linear population dynamics of a Bose–Einstein condensate (BEC) in a double well trap considering a semiclassical approach based on a time dependent variational principle applied to coherent states associated to SU(2) group. Employing a two-mode local approximation and hard sphere type interaction, we show in the Schwinger’s pseudo-spin language the occurrence of a fixed point bifurcation that originates a separatrix of motion on a sphere. This separatrix corresponds to the borderline between two dynamical regimes of Josephson oscillations and mesoscopic self-trapping. We also consider the effects of interaction between particles in different wells, known as cross-collisions. Such terms are usually neglected for traps sufficiently far apart, but recently it has been shown that they contribute to the effective tunneling constant with a factor growing linearly with the particle number. This effect changes considerably the effective tunneling of the system for sufficiently large number of trapped atoms, in perfect accord with experimental data. Finally, we identify analytically the transition parameter associated to the bifurcation in the generalized phase space of the model with cross-collision terms, and show how the dynamical regime depends on the initial conditions of the system and the collisional parameters values.     

Coherent approach to analysis of modulated optical radiation

A method is proposed for determining the modulation parameters of optical radiation that does not require wide-band photodetectors for modulation at high and microwave frequencies. The method is based on measurement of the time coherence of optical radiation containing a modulation signal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 25–28, April, 1930.