The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a tim...

‎Einstein‎, ‎M"{o}bius‎, ‎and Proper Velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper Lorentz group in the real Minkowski space-time $bkR^{n,1}.$ Using the gyrolanguage we study their gyroharmonic analysis‎. ‎Although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them‎. ‎Our...

We propose a new time-scale modi cation method for high quality audio signals. Our approach strives to preserve pitch and timbre. In our method, the signal is represented as the sum of sinusoidal components and a residual (edges and noise). The decomposition is computed via a combined harmonic and wavelet representation. Time-scaling is performed on the harmonic components and residual componen...

TIME-VARYING PARAMETER IN A HARMONIC MODEL WITH MULTIPLE FUNDAMENTALS Rafael A. Irizarry Johns Hopkins University 615 N. Wolfe Street, Baltimore, Maryland 21205 [email protected], 410-614-5157, 410-955-0958 (fax) Abstract: Window-based estimates for stochastic harmonic regression models are useful for cases where harmonic parameters appear to be time-varying. Least squares estimates for harmon...

Extreme ultraviolet (XUV) single-order high harmonic pulses with 10(6) photons/pulse were separated from multiple harmonic orders by a time-compensated toroidal-grating monochromator consisting of a pair of toroidal gratings. The first grating separates the harmonic order and the second one compensates for the pulse-front tilt. The center photon energies were tunable between 42 and 23 eV. The s...

We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. Th...

The paper presents methods for instantaneous harmonic analysis with application to high-quality pitch, timbre, and time-scale modifications. The analysis technique is based on narrow-band filtering using special analysis filters with frequency-modulated impulse response. The main advantages of the technique are high accuracy of harmonic parameters estimation and adequate harmonic/noise separati...

Abstract For the Schrödinger flow from R × R to the 2-sphere S, it is not known if finite energy solutions can blow up in finite time. We study equivariant solutions whose energy is near the energy of the family of equivariant harmonic maps. We prove that such solutions remain close to the harmonic maps until the blow up time (if any), and that they blow up if and only if the length scale of th...

Plasma kinetics models which are commonly used to model rf discharges often produce electron energy distributions ~EEDs! averaged over the rf cycle. In doing so, the time dynamics of the EEDs are lost. In this article we describe a technique to recover these time dynamics by using an ‘‘on-the-fly’’ ~OTF! Monte Carlo method. The OTF method directly computes the harmonic content of the EEDs using...

Time-modulation (TM) arrays is implemented by using a set of radio-frequency switches in the beam forming network to modulate, by means of periodic pulse sequences to control the antenna radiation features. The on–off reconfiguration of the switches that can be easily implemented via software unavoidably generates harmonic radiations that can be suitably exploited for multiple channel communica...