Quantum phases for a generalized harmonic oscillator

An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.      

All-optical measurement of high-harmonic amplitudes and phases in aligned molecules

We report a new all-optical approach to measuring the phase and amplitude of high-harmonic emission from aligned molecules. We combine the transient grating technique with a continuous rotation of the molecular alignment axis and develop an analytical model that enables the simultaneous determination of phases and amplitudes. Measurements in N(2) molecules are shown to be in qualitative agreement with the results of ab initio quantum scattering calculations.     

Theoretical investigation of amplitudes and phases in exciton reflection spectra

The phase difference Δ between the p and s component of light reflected from a semiconductor in the spectral region of the 1-S exciton is theoretically investigated. The exciton polariton theory used leads to a very good agreement with experimental spectra. No additional assumptions, such as ABC (additional boundary condition) or dead layer are necessary.     

Dual amplitudes of baryonium interaction

It is shown that the interaction of the M₀^J-baryonium can be described by Brower-Goddard dual amplitudes with n=3, where n is the dimension of “Koba-Nielsen” variables.     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999     

Unitarity bounds for multiparticle interaction amplitudes

A regular method of asymptotical estimations for multiparticle interaction amplitudes is constructed. The method gives a generalization of the well-known Froissart result to the multiparticle case.     

q-Anharmonic oscillator with quartic interaction

The first order perturbative correction to the energy levels of a boson realization of aq-oscillator due to a quartic term in the potential energy is evaluated. We also discuss the statistical mechanics ofq-anharmonic oscillators in the case where the parameterq deviates slightly from unity.     

Measurement of phases and amplitudes of AWG by fitting interference intensities

We measured the phases and amplitudes of an arrayed waveguide grating (AWG) by fitting interference intensities via a frequency domain method. The intensities were recorded as a function of the laser frequency in an interferometer containing the AWG. We fit the theoretical intensity profile to the recorded data via the Monte-Carlo method after filtering out the low-frequency noise. The phases and amplitudes are the parameters in the fitting process, and hence, the values are determined from the final fit. The variations in the measured phase values with the change in the initial condition of the Monte-Carlo process were less than $0.1^\circ $ . The variations in the measured amplitude values were negligible. In order to verify our measurement, we calculated the transmission spectrum of the AWG using the measured phases and amplitudes and compared it with a directly measured spectrum. The calculated and measured spectrums are in good agreement with each other.     

An extended interaction oscillator based on a complex resonatorstructure

We report experimental investigation of a novel scheme for efficient interaction between a linear electron beam and an electromagnetic wave in a complex extended interaction structure. The structure of interest consists of a high R/Q, five-gap, coupled-cavity resonator that incorporates a coaxial section of a quarter plasma wavelength placed between the first and second cavities. In the coaxial section, beam and wave propagate in separate channels. The first cavity, strongly coupled to the other cavities through the wave channel of the coaxial section, serves as a buncher cavity. An inner channel running through the center conductor of the coaxial section provides a cutoff drift space for ballistic bunching of electrons, an effect that is shown to significantly enhance the interaction efficiency. Oscillation power of 2.2 kW at 16.6 GHz was demonstrated with an interaction efficiency of 30%. The total efficiency was further increased to 41% by incorporation of a two-stage depressed collector     

Baryon-baryon and baryon-antibaryon interaction amplitudes in the spin-momentum operator expansion method

Partial-wave scattering amplitudes in baryon-baryon and baryon-antibaryon collisions and amplitudes for the production and decay of baryon resonances are constructed in the framework of the spin-momentum operator expansion method. The approach is relativistically invariant and it allows us to perform combined analyses of different reactions imposing analyticity and unitarity directly. The role of final-state interactions (triangle and box diagrams) is discussed.     

Mode interaction in a spatially inhomogeneous laser

In this paper the influence of spatial matter inhomogeneities on laser action is investigated theoretically. The calculations are based on nonlinear laser theory for the amplitudes of the empty-cavity modes. The nonlinear mode interactions like mode suppression or phase locking are modified by spatial inhomogeneities. There also arises a linear coupling among the cavity modes in general leading to monochromatically oscillating states which are superpositions of the empty-cavity eigenfunctions.     

The interaction of resonances in a weakly nonlinear oscillator with a quasiperiodic excitation

Conditions for chaos onset due to the interaction of resonances in a weakly nonlinear oscillator with a quasiperiodic excitation are investigated. The focus is made on the interaction of the 1:1 resonance with that of 1:m, where m is an arbitrary integer number. Analytical conditions of the chaos arising are obtained through the combined application of the averaging procedure and Melnikov's technique. The comparison study of these conditions with those following from standard Chirikov's approach is provided. (c) 1997 American Institute of Physics.     

The interaction of a quantum mechanical oscillator with gravitational radiation

Within the framework of the linearized field equations of gravitation, the interaction operators between a quantum mechanical system and an external gravitational field are derived from the general-covariant Klein-Gordon and Dirac equation. In the case of linearly polarized plane gravitational waves the transition probabilities for absorption and induced and spontaneous emission of gravitational radiation by a quantum mechanical harmonic oscillator are calculated with the help of the time-dependent perturbation method. The results coincide with the classical ones according to the correspondence principle.     

Computer simulations of the interaction between a heavy charge and a classical harmonic oscillator

The interaction of a heavy, point-like charge with a classical electron harmonically bound to a positive, heavy nucleus was simulated. Attention was focused on the stopping of the moving charge. Although most results in this paper can be explained within the framework of Bohr's and more recent theoretical studies, discrepancies do appear. The stopping number ( L ) does not seem to be a universal function of \xi = mv_{0}^{3}/(Z_{1}e^{2}\omega) as was previously proposed. Actually, L seems to be also a function of the amplitude A , the oscillator frequency \omega and the sign of the ion charge. For \xi \ll 1 , and provided the ion is positively charged, simulations yield L 's which are greater than theoretical predictions. This seems to be caused by the fact that, during the collision, the electron is first virtually captured by the ion and released later in a higher energy state. In the high velocity regime, a partition rule similar to that which holds for a quantum harmonic oscillator seems to also hold for the classical counterpart. However, instead of the quantum equipartition a two-third partition rule appears to hold in the classical case.     

Determination of the amplitudes and phases of the scattering matrix upon photodissociation of molecules

The photodissociation of RbI molecules via the second excited state under the action of circularly polarized radiation with a wavelength of 266 nm is studied. By using sub-Doppler Faraday spectroscopy, the angular distributions of the orientation of spins of Rb(5²S_1/2) atoms formed are studied and the anisotropy parameters describing these angular distributions are determined. Based on the anisotropy parameters, the ratio between the amplitudes of the inelastic scattering matrix elements corresponding to the two possible photodissociation channels is determined to be r_Ω=1/r_Ω=0=0.71±0.15, while the phase difference for these matrix elements is found to amount to Δφ = 173° ± 29°.     

Barut equation for the particle-antiparticle system with a Dirac oscillator interaction

Barut showed us how it is possible to get a Poincaré invariant n-body equation with a single time. Starting from the Barut equation for n-free particles, we show how to generalize it when they interact through Dirac oscillators with different frequencies. We then particularize the problem to n=2 and consider the particle-antiparticle system whose frequencies are respectively and –. We indicate how the resulting equation can be solved by perturbation theory, though the spectrum and its comparison with that of the mesons will be given in another publication.Member of El Colegio Nacional and El Sistema Nacional de Investigadores.Fellow of El Sistema Nacional de Investigadores (México).