Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

In this paper we investigate the Gazeau–Klauder coherent states using a newly introduced diagonal ordering operation technique, in order to examine some of the properties of these coherent states. The results coincide with those obtained from other purely algebraic methods, but the calculations are greatly simplified. We apply the general theory to two cases of Gazeau–Klauder coherent states: pseudoharmonic as well as the Morse oscillators.     

Integrable spin–boson models descending from rational six-vertex models

We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain inhomogeneous rational vertex models combining bosonic and spin representations of SU(2)$\mathit{SU}(2)$, subject to non-diagonal toroidal and open boundary conditions. Only open boundary conditions are found to lead to integrable Hamiltonians combining both rotating and counter-rotating terms in the interaction. If the boundary matrices can be brought to triangular form simultaneously, the spectrum of the model can be obtained by means of the algebraic Bethe ansatz after a suitable gauge transformation; the corresponding Hamiltonians are found to be non-Hermitian. Alternatively, a certain quasi-classical limit of the transfer matrix is considered where Hermitian Hamiltonians are obtained as members of a family of commuting operators; their diagonalization, however, remains an unsolved problem.     

Is the Hamiltonian geometrical criterion for chaos always reliable?

It is found that the application of a newly developed geometrical criterion, in which negative eigenvalues of the associated matrix determined by the dynamical curvature of a conformal metric for a Hamiltonian system are used to identify the onset of local instability or chaos, is somewhat problematic in some circumstances. In fact, this criterion is neither necessary nor sufficient for the prediction of instability of orbits on a same energy hypersurface because it is not in good agreement with information on unstable or chaotic behavior given by the maximal Lyapunov exponent in general.     

L 2-exponential lower bounds to solutions of the Schrödinger equation

We study decay properties of solutions of the Schrödinger equation (–+V)=E. Typical of our results is one which shows that ifV=o(|x|^–1/2) at infinity or ifV is a homogeneousN-body potential (for example atomic or molecular), then ifE<0 and . We also construct examples to show that previous essential spectrum-dependent upper bounds can be far from optimal if is not the ground state.Research in partial fulfillment of the requirements for a Ph.D. degree at the University of VirginiaPartially supported by NSF grant MCS-81-01665Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr. 4240     

Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

A prolate γ-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in β collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the exact separation between the two Euler angles and the β variable, one arrives at a differential Schrödinger equation with a quartic anharmonic oscillator potential and a centrifugal-like barrier. The corresponding eigenvalue is approximated by an analytical formula depending only on a single parameter up to an overall scaling factor. The applicability of the model is discussed in connection to the existence interval of the free parameter, which is limited by the accuracy of the approximation, and by comparison with the predictions of the related X(3) and X(3)-β ² models. The model is applied to qualitatively describe the spectra for nine nuclei which exhibit near-vibrational features.     

Differential structure on the κ-Minkowski spacetime from twist

We study four-dimensional κ  -Minkowski spacetime constructed by the twist deformation of U(igl(4,R))$U(\mathit{igl}(4,R))$. We demonstrate that the differential structure of such twist-deformed κ-Minkowski spacetime is closed in four dimensions contrary to the construction of κ-Poincaré bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.     

Limits on decaying dark energy density models from the CMB temperature–redshift relation

The nature of the dark energy is still a mystery and several models have been proposed to explain it. Here we consider a phenomenological model for dark energy decay into photons and particles as proposed by Lima (Phys Rev D 54:2571, 1996). He studied the thermodynamic aspects of decaying dark energy models in particular in the case of a continuous photon creation and/or disruption. Following his approach, we derive a temperature redshift relation for the cosmic microwave background (CMB) which depends on the effective equation of state w _eff and on the “adiabatic index” γ. Comparing our relation with the data on the CMB temperature as a function of the redshift obtained from Sunyaev–Zel’dovich observations and at higher redshift from quasar absorption line spectra, we find w _eff = −0.97 ± 0.03, adopting for the adiabatic index γ = 4/3, in good agreement with current estimates and still compatible with w _eff = −1, implying that the dark energy content being constant in time.     

Cooperative emission from an ensemble of three-level Λ radiators in a cavity: An insight from the viewpoint of dynamics of nonlinear systems

Cooperative radiation emitted by an ensemble of three-level optical systems with a doublet in the ground state (Λ scheme), which is placed into a cyclic cavity, is studied theoretically. In contrast to the two-level model of emitters, this process with such a configuration of operating transitions may occur without population inversion in the whole, if the doublet is prepared at the initial instant in a superposition (coherent) state. In the ideal case of a Hamilton system, in which the cavity losses and relaxation in the radiator ensemble are disregarded, the conservation laws are derived, which allow a substantial reduction of the dimension of the phase space of the model (?¹¹ → ?⁵) and the application of methods of dynamics of nonlinear systems for analyzing the three-level superradiance under these conditions. The possibility of different (both quasiperiodic and chaotic) scenarios of the three-level superradiance is demonstrated on the basis of Poincaré’s mappings. Global bifurcation of the system upon a transition from the conventional superradiance regime to inversionless one is revealed. The effects of cavity losses, as well as homogeneous and inhomogeneous broadening in the system of radiators on the regularities found are also discussed.     

On a geometrical property of the Bäcklund transformation of the sine-Gordon equation

We show how a solution of the Bäcklund transformation equations for the sine-Gordon equation determines an explicit isometry from the underlying surface to the upper half plane. We then use the action on the upper half to find explicitly the general solution of the equations.     

Integrating the geodesic equations in the Schwarzschild and Kerr space-times using Beltrami's “geometrical” method

We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired by the Hamilton-Jacobi method, is purely geometric. The application of this theorem to the Schwarzschild and Kerr metrics leads straightforwardly to the general solution of their geodesic equations. This way of dealing with the problem is, in our opinion, very much in keeping with the geometric spirit of general relativity. In fact, thanks to this theorem we can integrate the geodesic equations by a geometrical method and then verify that the classical conservation laws follow from these equations.     

Effective rank-five superstring models from CP3×CP3

We consider three-generation, rank-six superstring models based on the simplest known Calabi-Yau space. Assuming a breaking scale (to rank-five) M_B≳10¹⁶ GeV, as required by cosmology and other constraints, we describe the particle spectrum in a class of models in which the proton is stable and the neutrinos are massless. These models are effectively rank-five down to the weak scale O(100) GeV. We find that Higgs fields typically will have massess in excess of O(10⁶) GeV due to higher order non-renormalizable interactions, hence rendering the conventional spontaneous breakdown of the electroweak symmetries impossible.     

Are Kaluza-Klein models of the universe chaotic?

The generic behavior of vacuum inhomogeneous and spatially homogeneous Kaluza-Klein models is studied in the vicinity of the cosmological singularity. It is shown that, in space-time dimensions 11, the generalized Kasner solution, with monotonic power-law behavior of the spatial distances, becomes a general solution of the Einstein vacuum field equations and that, moreover, the chaotic oscillatory behavior disappears.On the other hand, the chaotic oscillatory behavior, absent in diagonal spatially homogeneous cosmological models in space-time dimensions between 5 and 10, can be reestablished when off-diagonal terms are included.     

Gradient models of the axion–photon coupling

We establish an extended version of the Einstein–Maxwell-axion model by introducing into the Lagrangian cross-terms, which contain the gradient four-vector of the pseudoscalar (axion) field in convolution with the Maxwell tensor. The gradient model of the axion–photon coupling is applied to cosmology: we analyze the Bianchi-I type Universe with an initial magnetic field, electric field induced by the axion–photon interaction, cosmological constant and dark matter, which is described in terms of the pseudoscalar (axion) field. Analytical, qualitative and numerical results are presented in detail for two distinguished epochs: first, for the early Universe with magnetic field domination; second, for the stage of late-time accelerated expansion.     

Photoconductivity derived from an exact modelling of the uncompensated one-donor model. III—problem of fitting the exact model with approximate models

Abstract

The paper is essentially devoted to a quantitative comparison of the exact (1D) model developed in Part I, with two approximate models indicated by Kittel (1D_a1) and by Van der Ziel (1D_a2). And this is made for identical values of their common parameters. This allows to show that models 1D and 1D_a1 generally present no suitable intervals for fitting. The model of Van der Ziel is more suited, for, a good fitting with the 1D model can be obtained, for relatively reduced G values, and for temperatures bounded upward by the characteristic temperature T ₀ defined previously. The role played by the sub-models, obtained after simplifying the 1D_ai model equations, is studied also.     

Effect of geometrical stress concentrators on the band formation and the serrated deformation in aluminum–magnesium alloys

The effect of holes on the band formation and the serrated deformation in planar specimens of aluminum–magnesium alloys AlMg5 and AlMg6 is studied by high-speed video filming of moving deformation bands. It is found that the concentration of an elastic field near a hole causes early nucleation of macrolocalized deformation bands and decreases the critical deformation of the first stress drop. Differences between the spatial–temporal patterns of deformation bands near holes under various deformation conditions are revealed.     

Painlevé test of the McKean and Carleman models

The Painlevé test of the system of nonlinear partial differential first-order equations u₁+u_k=k₁v²+k₂u²+k₃uv, v₁–v_x=–k₁v²–k₂u²–k₃uv is performed. The system includes the Carleman and McKean models which are caricatures of the Boltzmann equation. For k ₁=k ₂=0 the system describes the interaction of two waves u and v. The results of the Painlevé test are discussed in connection with whether or not the system is integrable. We also study in detail the constraint on (whose vanishing defines a noncharacteristic hypersurface S) which arises at the resonance.     

A comparison of two models of theρ-meson

A renormalization of the-propagator is presented. It is shown that if the-wave, isovector - amplitude is assumed to be dominated by this renormalized, many scattering parameters are predicted that agree well with experimental data. The model is compared with one presented by Tschang and Parkinson. It is shown that the predictions of the two models are the same, but that the renormalization model does not contain some of the theoretical problems of the Tschang and Parkinson scheme.Research partially supported by NSF Institutional Grant No. GU3220 and a grant from the Research Corporation.     

CP N−1 models beyond the leading order

We analyse the CP ^N?1 models in two and three dimensions. We discuss the effective potential, Greens functions and β functions to leading order. To non-leading order we formally evaluate and renormalise the effective potential. In three dimensions we also calculate the β function to \(0\left( {\frac{1}{N}} \right)\) . We show that it has a non-trivial fixed point which corresponds to a phase transition. This phenomenon persists beyond the leading order. The vacuum states are also unchanged by the nonleading order corrections.