Analysis of the Accuracy of Prediction of the Celestial Pole Motion

VLBI observations carried out by global networks provide the most accurate values of the precession-nutation angles determining the position of the celestial pole; as a rule, these results become available two to four weeks after the observations. Therefore, numerous applications, such as satellite navigation systems, operational determination of Universal Time, and space navigation, use predictions of the coordinates of the celestial pole. In connection with this, the accuracy of predictions of the precession- nutation angles based on observational data obtained over the last three years is analyzed for the first time, using three empiric nutation models---namely, those developed at the US Naval Observatory, the Paris Observatory, and the Pulkovo Observatory. This analysis shows that the last model has the best of accuracy in predicting the coordinates of the celestial pole. The rms error for a one-month prediction proposed by this model is below 100 microarcsecond.Comment: 13 p

Higher order approximation of isochrons

Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction of a single oscillator, one needs to obtain the gradient of the phase function, which essentially provides a linear approximation of isochrons. In this paper, we extend the method for obtaining partial derivatives of the phase function to arbitrary order, providing higher order approximations of isochrons. In particular, our method in order 2 can be applied to the study of dynamics of a stable oscillator subjected to stochastic perturbations, a topic that will be discussed in a future paper. We use the Stuart-Landau oscillator to illustrate the method in order 2

High resolution infrared absorption spectra, crystal field, and relaxation processes in CsCdBr_3:Pr^3+

High resolution low-temperature absorption spectra of 0.2% Pr^3+ doped CsCdBr_3 were measured in the spectral region 2000--7000 cm-1. Positions and widths of the crystal field levels within the 3H5, 3H4, 3F2, and 3F3 multiplets of the Pr^3+ main center have been determined. Hyperfine structure of several spectral lines has been found. Crystal field calculations were carried out in the framework of the semiphenomenological exchange charge model (ECM). Parameters of the ECM were determined by fitting to the measured total splittings of the 3H4 and 3H6 multiplets and to the observed in this work hyperfine splittings of the crystal field levels. One- and two-phonon relaxation rates were calculated using the phonon Green's functions of the perfect (CsCdBr_3) and locally perturbed (impurity dimer centers in CsCdBr_3:Pr^3+) crystal lattice. Comparison with the measured linewidths confirmed an essential redistribution of the phonon density of states in CsCdBr_3 crystals doped with rare-earth ions.Comment: 16 pages, 5 tables, 3 figure

Optical evidence for symmetry changes above the Neel temperature in KCuF3

We report on optical measurements of the 1D Heisenberg antiferromagnet KCuF3. The crystal-field excitations of the Cu2+ ions have been observed and their temperature dependence can be understood in terms of magnetic and exchange-induced dipole mechanisms and vibronic interactions. Above T_N we observe a new temperature scale T_S characterized by the emergence of narrow absorption features that correlate with changes of the orbital ordering as observed by Paolasini et al. [Phys. Rev. Lett. 88, 106403 (2002)]. The appearance of these optical transitions provides evidence for a symmetry change above the Neel temperature that affects the orbital ordering and paves the way for the antiferromagnetic ordering.Comment: 4 pages, 2 figure

The Classical Schrodinger's Equation

A non perturbative numerical method for determining the discrete spectra is deduced from the classical analogue of the Schrodinger's equation. The energy eigenvalues coincide with the bifurcation parameters for the classical orbits.Comment: UUEncoded Postscript, 18 pages, 4 figures inserted in tex

f-Oscillators and Nonlinear Coherent States

The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.Comment: Latex, 32 pages, accepted by Physica Script

Coherent States of SU(l,1)SU(l,1) groups

This work can be considered as a continuation of our previous one (J.Phys., 26 (1993) 313), in which an explicit form of coherent states (CS) for all SU(N) groups was constructed by means of representations on polynomials. Here we extend that approach to any SU(l,1) group and construct explicitly corresponding CS. The CS are parametrized by dots of a coset space, which is, in that particular case, the open complex ball $CD^{l}$. This space together with the projective space $CP^{l}$, which parametrizes CS of the SU(l+1) group, exhausts all complex spaces of constant curvature. Thus, both sets of CS provide a possibility for an explicit analysis of the quantization problem on all the spaces of constant curvature.Comment: 22 pages, to be published in "Journal of Physics A

Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator

The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time dependent harmonic oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example

Orthogonal localized wave functions of an electron in a magnetic field

We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.Comment: RevTex, 18 pages, 5 ps fi