Application of the Asymptotic Taylor Expansion Method to Bistable Potentials

A recent method called asymptotic Taylor expansion (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.

DIFFUSION IN PERIODIC INTERACTING SYSTEMS: QUASI-ELASTIC SPECTRUM IN BISTABLE POTENTIALS

Mechanism of ion transport in periodic interacting systems is investigated by employing the Fokker–Planck approach. This is done through an investigation of the quasielastic peak in the dynamic structure factor S(q, ω). Its half width at half maximum (hwhm) exhibits an oscillatory behavior as a function of the scattering wave-vectors q, reflecting the role of correlations among diffusing particles. All calculations are performed at low temperature and at high friction limit.

ANOMALOUS RELAXATION IN NOISE-DRIVEN BISTABLE SYSTEMS

Relaxation dynamics for bistable oscillators driven by a periodic dichotomous noise process is described. The corresponding stochastic differential equation is a smooth flow between noise-switching events but the dynamics of the two-branched map induced by the transitions is a Markov process. Overdamped relaxation dynamics in harmonic and quartic bistable potentials are compared. Infrequent transitions produce cantor-set-like attractors. In the harmonic case the attractor is self-similar and the irreversible mass flow towards this attractor produces anomalous decay. However, for the quartic potential the map branches are sigmoidal functions and multiple transitions into the endpoints of the attractor also produce anomalous decay.