Periodic-orbit theory of anderson localization on graphs

Prey-Predator System; Having Stable Periodic Orbit

The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant. On the other hand, for certain combin...

Periodic orbit theory and spectral statistics for scaling quantum graphs

The explicit solution to the spectral problem of quantum graphs found recently in [20], is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the distribution for the nearest neighbor separations, s n = k n − k n−1 , and the distribution of the spectral oscillations around the average, δk n = k n − ¯ k n .

Periodic Orbit Theory and Spectral Statistics for Quantum Graphs

Towards a New Proof of Anderson Localization

The wave function of a non-relativistic particle in a periodic potential admits oscillatory solutions, the Bloch waves. In the presence of a random noise contribution to the potential the wave function is localized. We outline a new proof of this Anderson localization phenomenon in one spatial dimension, extending the classical result to the case of a periodic background potential. The proof ma...