Search results for "harmonic"
showing 10 items of 984 documents
Riccati-Padé quantization and oscillatorsV(r)=grα
1993
We develop an alternative construction of bound states based on matching the Riccati threshold and asymptotic expansions via their two-point Pad\'e interpolation. As a form of quantization it gives highly accurate eigenvalues and eigenfunctions.
Nonlinear collective oscillations of an ion cloud in a Paul trap
1997
In an experiment using a Paul trap, we create a ${\mathrm{H}}_{2}^{+}$ ion cloud by electron ionization of the background gas at ${10}^{\ensuremath{-}9}$-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the $r$ or $z$ direction, we observe a narrow resonance at some distance from the motional resonance center if the amplitude of the exciting field exceeds a threshold value. The threshold value decreases with increasing ion number. Since the narrow resonance does not shift with ion number, we interpret it as a collective resonance of the center of mass of the ion cloud. The resonance shape exhibits the typical form of a driven a…
Polarization of the Radiation Emitted in GaAs Semiconductors Driven by Far Infrared Fields
2010
The effects due to the mixing of two far infrared electric fields on the harmonic generation process in low doped GaAs bulks are studied by a three dimensional multivalleys Monte Carlo simulation. The conversion efficiency is calculated by using the appropriate Maxwell equation for the propagation of an electro-magnetic wave along a given direction in the medium. In particular, we focus our attention on the polarization of the generated harmonics, by comparing the polarization obtained from the mixing of an oscillating field with a static electric field with that obtained in the presence of two cyclostationary fields, having an integer ratio between the two frequencies. The findings show th…
Polarization of high harmonic generated spectra in H+2ion
2013
AbstractWe study the polarization of the harmonics generated by a homonuclear diatomic molecule in the presence of an intense, linearly polarized laser field. The polarization parameters of the emitted radiation are investigated as a function of the angle between the laser electric field and the molecular axis. The calculations are carried out by assuming a single active electron model with fixed nuclei; a two-dimensional model of the system is used. We find a different dependence of the parameters of the harmonics vs in the first or second half of the emitted spectrum. In particular, the differences are accentuated for , while for higher angles, until the perpendicular orientation, almost …
Harmonic Coupling of the Red Noise in X‐Ray Pulsars
1997
The power spectra of X-ray pulsars often show the presence of a red-noise component. This noise is produced by aperiodic variability believed to be associated with instabilities that seem to occur in accretion flows onto compact objects. In this paper we discuss how, independently of the details of the physical processes that generate these instabilities, a careful analysis of the power spectra can furnish some constraints on the distance from the stellar surface at which the sudden energy release associated with the instabilities occurs. In particular, any aperiodic variability coming from the accretion flow funneled toward the magnetic poles should be modulated at the pulsar spin period (…
From self-adjoint to non self-adjoint harmonic oscillators: physical consequences and mathematical pitfalls
2013
Using as a prototype example the harmonic oscillator we show how losing self-adjointness of the hamiltonian $H$ changes drastically the related functional structure. In particular, we show that even a small deviation from strict self-adjointness of $H$ produces two deep consequences, not well understood in the literature: first of all, the original orthonormal basis of $H$ splits into two families of biorthogonal vectors. These two families are complete but, contrarily to what often claimed for similar systems, none of them is a basis for the Hilbert space $\Hil$. Secondly, the so-called metric operator is unbounded, as well as its inverse. In the second part of the paper, after an extensio…
Physical Origin of Anharmonic Dynamics in Proteins: New Insights From Resolution-Dependent Neutron Scattering on Homomeric Polypeptides
2012
Neutron scattering reveals a complex dynamics in polypeptide chains, with two main onsets of anharmonicity whose physical origin and biological role are still debated. In this study the dynamics of strategically selected homomeric polypeptides is investigated with elastic neutron scattering using different energy resolutions and compared with that of a real protein. Our data spotlight the dependence of anharmonic transition temperatures and fluctuation amplitudes on energy resolution, which we quantitatively explain in terms of a two-site model for the protein-hydration water energy landscape. Experimental data strongly suggest that the protein dynamical transition is not a mere resolution …
The quantum relativistic harmonic oscillator: generalized Hermite polynomials
1991
A relativistic generalisation of the algebra of quantum operators for the harmonic oscillator is proposed. The wave functions are worked out explicitly in configuration space. Both the operator algebra and the wave functions have the appropriate c→∞ limit. This quantum dynamics involves an extra quantization condition mc2/ωℏ = 1, 32, 2, … of a topological character.
Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
2012
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory …
Berry phase in open quantum systems: a quantum Langevin equation approach
2007
The evolution of a two level system with a slowly varying Hamiltonian, modeled as s spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.