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Identifier

000378729

Title

Numerical studies of the stochastic, discrete, nonlinear Shcrodinger equation

Alternative Title

Αριθμητικές μελέτες πάνω στην στοχαστική, διακριτή, μη-γραμμική εξίσωση του Shcrodinger

Author

Joniald, Shena

Thesis advisor

Τσιρώνης, Γεώργιος

Abstract

We analyse properties of non-linear, stochastic dimer ( a system consisting of two lattice sites with stochastic energies) using the discrete, nonlinear, Schr¨odinger equation. The aim is to obtain a solution of such systems, mainly through numerical studies. Analytical studies has been taken only in the limiting case where the standard deviation is small enough and the correlation time quite large. With the advent of low stochastic effect, it seems that, with nonlinearity increasing, the mean value of the probability difference (for the particle to be at site 1 or 2) , is descending quickly, to an ”equilibrium” value. After the advent of strong stochastic processes, the main conclusion is just the following. The mean value of the probability difference , under stochastic processes and after an interval time , tends to zero. This situation takes place for any value of nonlinearity. The ”force” of nonlinearity tries to keep the system in an ”equilibrium” value. However, under stochastic processes constraint, the probability difference tends again to zero. With a large stochastic effect and without nonlinearity, the system behaves like sub-diffusion. The diffusion comes as a limiting case when the correlation time get large value. In contrast, if we put together, a low stochastic effect with nonlinearity, we obtain a hypertransport phenomenon. Again, the ballistic transport can be possible when nonlinearity approaches marginally the unit.

Language

English

Subject

DNLS

Diffusion

Dimer

Hypertransport

Διάχειση

Στοχαστικότητα

Υπερμεταφορά

Issue date

2013-03-15