We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.

A Fokker-Planck equation is derived for the energy distribution of atoms in a three-dimensional harmonic trap with fluctuations in the spring constant and the equilibrium position. Using this model, we predict trap lifetimes based on the measurable noise spectra of the fluctuations. The energy distributions evolve into a single eigenmode where the apparent temperature of the distribution remain...

The vibrational partition function of ethane is calculated in the temperature range of 200-600 K using well-converged energy levels that were calculated by vibrational configuration interaction, and the results are compared to the harmonic oscillator partition function. This provides the first test of the harmonic oscillator approximation for a molecule with more than five atoms. The absolute f...

9.1 Harmonic Oscillator 9.1.1 Classical harmonic oscillator and h.o. model 9.1.2 Oscillator Hamiltonian: Position and momentum operators 9.1.3 Position representation 9.1.4 Heisenberg picture 9.1.5 Schrödinger picture 9.2 Uncertainty relationships 9.3 Coherent States 9.3.1 Expansion in terms of number states 9.3.2 Non-Orthogonality 9.3.3 Uncertainty relationships 9.3.4 X-representation 9.4 Phon...

In this paper, we study the bubbling phenomena of weak solution sequences of a class of degenerate quasilinear elliptic systems of m-harmonic type. We prove that, under appropriate conditions, the energy is preserved during the bubbling process. The results apply to m-harmonic maps from a manifold Ω to a homogeneous space, and to m-harmonic maps with constant volumes, and also to certain Palais...

We present and evaluate here an Harmonic + Noise Model (HNM) for speech synthesis. The noise part is represented by an autoregressive model whose output is pitch-synchronously modulated in energy. The harmonic part of the signal is represented by a sum of harmonic sinusoids. This paper compares different methods for separating these two components. We then evaluate different models for the anal...

We study high-order harmonic generation at a high pumping energy using a long focal length lens. We identify different saturation regimes of the harmonic emission, revealing the interplay between phase matching, absorption, and laser defocusing. In the optimal conditions, high conversion efficiencies are obtained, resulting in an increase of at least one order of magnitude of the harmonic energ...

In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...

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...

High harmonic generation in solids presents the possibility for bringing attosecond techniques to semiconductors and a simple source for frequency comb spectroscopy in the vacuum ultraviolet. We generate up to the seventh harmonic of a Tm fiber laser by focusing in silicon or zinc oxide. The harmonics are strong and stable, with no indication of material damage. Calculations show the potential ...