Non-perturbed System Research Articles

Direct momentum-space calculations for the resonant multiphoton processes of a hydrogen atom under intense laser pulses.

We present a momentum-space solution for the time-dependent Schr{umlt o}dinger equation of a realistic hydrogen atom in a strong laser pulse. The method can integrate the nonperturbative system to thousands of optical cycles, previously thought not yet feasible. A hydrogen atom under a 285-nm (4.357-eV), 97.5-TW/cm{sup 2} short pulse is found to produce two prominent photoelectron peaks above threshold, and significant intermediate bound-state resonance with the 4{ital p} state. With a 248-nm (5-eV) probe laser pulse that is ten times longer, the resonant structure is explored. {copyright} {ital 1996 The American Physical Society.}

Random perturbations of recursive sequences with an application to an epidemic model

We investigate the asymptotic sample path behaviour of a randomly perturbed discrete-time dynamical system. We consider the case where the trajectories of the non-perturbed dynamical system are attracted by a finite number of limit sets and characterize a case where this property remains valid for the perturbed dynamical system when the perturbation converges to zero. For this purpose, no further assumptions on the perturbation are needed and our main condition applies to the limit sets of the non-perturbed dynamical system. When the limit sets reduce to limit points we show that this main condition is more general than the usual assumption of the existence of a Lyapunov function for the non-perturbed dynamical system. An application to an epidemic model is given to illustrate our results.

Random perturbations of recursive sequences with an application to an epidemic model

We investigate the asymptotic sample path behaviour of a randomly perturbed discrete-time dynamical system. We consider the case where the trajectories of the non-perturbed dynamical system are attracted by a finite number of limit sets and characterize a case where this property remains valid for the perturbed dynamical system when the perturbation converges to zero. For this purpose, no further assumptions on the perturbation are needed and our main condition applies to the limit sets of the non-perturbed dynamical system. When the limit sets reduce to limit points we show that this main condition is more general than the usual assumption of the existence of a Lyapunov function for the non-perturbed dynamical system. An application to an epidemic model is given to illustrate our results.

About the calculation of the successive terms of the adiabatic invariant for slowly-time varying oscillatory systems

A practical method is constructed in order to obtain the adiabatic invariant of a Hamiltonian H( p, q, τ) (τ = εt, ε ⪡ 1), where some parameters vary slowly in time. Using the action-angle variables ( J, w) of the non-perturbed system (ε = 0) two successive time-dependent canonical transformations are used. The first few terms of the adiabatic series are calculated explicitly as a function of the terms H 0( J, τ) and H 1( J, w, τ) of the transformed Hamiltonian.

Electric field gradients of randomly disordered compounds.

The distribution of the electric-field-gradient tensor parameters is evaluated for a randomly disordered structure displaying an intrinsic local symmetry. The second-order symmetries of the nonperturbed system are defined by the two central parameters ${\ensuremath{\Delta}}_{0}$ and ${\ensuremath{\eta}}_{0}$; then the corresponding distribution in the disordered modification is governed by one order parameter $\ensuremath{\lambda}=\frac{{\ensuremath{\Delta}}_{0}}{\ensuremath{\sigma}}$ where ${\ensuremath{\sigma}}^{2}$ is the variance in the components of the perturbing tensor. An approximate analytical expression is proposed with the purpose of interpreting experimental data in terms of relevant structural parameters for compounds where the local symmetry is randomly disturbed, e.g., quasicrystals, amorphous alloys, or disordered rare-earth compounds with a symmetry lower than cubic. It should be emphasized that the intrinsic parameters characterizing the underlying symmetry (${\ensuremath{\Delta}}_{0},{\ensuremath{\eta}}_{0}$) are significantly different from the corresponding mean values of the distribution, as soon as the disorder becomes finite.

On the radius of convergence of Rayleigh-Schrodinger perturbative solutions for quantum oscillators in circular and spherical boxes

The energy eigenvalues of harmonic oscillators in circular and spherical boxes are obtained through the Rayleigh-Schrodinger perturbative expansion, taking the free particle in a box as the non-perturbed system. The perturbative series is shown to be convergent for small boxes, and an upper bound for the radius of convergence is established. Pade-approximant solutions are also constructed for boxes of any size. Numerical comparison with the exact eigenvalues-which are obtained by constructing and diagonalising the Hamiltonian in the basis of the eigenfunctions of the free particle in a box-corroborates the accuracy and range of validity of the approximate solutions, particularly the convergence and the radius of convergence of the perturbative series.

Physical basis of RF hyperthermia for cancer therapy (3). A non-perturbed and non-perturbing thermometer at RF heating.

A non-perturbing and non-perturbed thermometer system in RF field was developed. The probe is composed of (1) C-A thermocouple, wrapped by (2) the conductor, which encircles the C-A thermocouple, and also (3) the insulator of a low dielectric constant in the most outer layer. Production of noises and “ hot spots ” was prevented by coiling both a part of the cable of the probe and C-A thermocouple at the one of the two ends connected to a temperature monitor. It was pointed out that the RF current, which was rectified at the junction of the thermocouple, caused noises.

Reduction de systemes differentiels perturbes

One considers a perturbed ordinary differential system which is then reduced to the non-perturbed corresponding system; i.e. the existence of a global relation between the solutions of the two systems is established. From this it is easy to deduce the difference between two correspondent solutions, and the theorems of existence for particular solutions (periodic, quasiperiodic,…) or integral manifolds, of the initial system.