Effect Of Time-dependent Perturbation Research Articles

Electron Transport and Time-Dependent Perturbation in a Two-Dimensional Symplectic System

Electron transport in a two-dimensional symplectic system with time-dependent perturbations is investigated numerically by the equation of motion method. The effect of time-dependent perturbations on the conductivity is examined in the critical regime as well as in the metallic regime. The universal correction to the conductivity, which is consistent with the weak localization theory, is indeed observed in the metallic regime. In the critical regime, it is found that the dependence of the conductivity on the frequency of perturbations can be described by the one-parameter scaling.

Time-Dependent Perturbation in Two-Dimensional Disordered Symplectic Systems: Dephasing and Scaling

The effect of time-dependent perturbations on transport phenomena in disordered systems has been studied in various context, such as the destruction of localization, the suppression of the interference effect, and the effect of temperature. In general, timedependent perturbations destroy the phase coherence. In fact, a numerical study of the dephasing effect by a time-dependent perturbation in two-dimensional disordered systems has been performed by Nakanishi et al. They have investigated the effect of the timedependent on-site potential oscillating with a frequency ω and demonstrated that the ω-dependent correction to the conductivity takes an universal form in the metallic regime. In the present work, we study a different type of time-dependent perturbation, namely the timedependent transfer-integrals. It is expected that this type of perturbation is more representative for the effect of temperature. We consider a two-dimensional disordered system with spin-orbit interaction, which belongs to the symplectic universality class. The system exhibits the Anderson transition even in two dimensions. We numerically evaluate the conductivity as a function of the frequency of the perturbation using the equation of motion method. In the metallic regime, it is examined whether the universal ω-dependent correction to the conductivity can be observed also for the present type of perturbation. For the critical regime, we find that the frequency dependence of the conductivity can be described by the one-parameter scaling. The model we adopt is the Ando model extend to the case where transfer-integrals oscillate with a frequency ω. The Hamiltonian is given by

Characteristic multipliers for assessing stability of electrical power systems

Characteristic multipliers (CM) of the Mathieu equation are the equivalent of eigenvalues of a linearized nonlinear differential equation. Oscillations will be stable when the real part of CMs is less than unity. The characteristic of an oscillation will change if the real part of CMs have magnitude greater than unity. In this letter, the investigation is directed to the effect of changes in CM on the stability of power systems. The significant role of nonlinearity is demonstrated by finding CM for the nontrivial single-machine system. The nonautonomous form of the Mathieu equation obtained models the effect of time dependent perturbations at the quasi-infinite bus.

Ionization and scattering for short-lived potentials

We consider perturbations of a model quantum system consisting of a single bound state and continuum radiation modes. In many problems involving the interaction of matter and radiation, one is interested in the effect of time-dependent perturbations. A time-dependent perturbation will couple the bound and continuum modes causing ‘radiative transitions’. Using techniques of time-dependent resonance theory, developed in earlier work on resonances in linear and nonlinear Hamiltonian dispersive systems, we develop the scattering theory of short-lived (\( (\mathcal{O}(t^{ - 1 - {\varepsilon }} ))\)(t−1−ε)) spatially localized perturbations. For weak pertubations, we compute (to second order) the ionization probability, the probability of transition from the bound state to the continuum states. These results can also be interpreted as a calculation, in the paraxial approximation, of the energy loss resulting from wave propagation in a waveguide in the presence of a localized defect.

A soluble model for time dependent perturbations of an unstable quantum system

We show that a time dependent addition to the coupling constant of the Lee-Friedrichs model results in an exactly soluble model for the effect of time dependent perturbations of an unstable quantum system. For a perturbation of a single frequency, a shift in the position of the original Lee-Friedrichs pole, and the emergence of a harmonically associated sequence of other poles, are obtained by iteration of the exact difference equations for the reduced resolvent. In lowest order, line broadening can be seen directly in the structure of the shifted pole position. If the time dependence contains modulation, e.g., with two commensurate frequencies, we show that there are contributions which could lead to line narrowing as well.