A one year collaboration of the proposed researcher with the Italian Host is planned in order to develop general theoretical approaches to boundary driven nonlinear transport phenomena and tunneling processes and to seek for applications in various realist ic nonlinear physical systems. In particular, this proposal intends to generalize the transmission hysteresis effect, that we discovered in Fermi-Pasta-Ulam lattices, by predicting the conditions for the realization of similar effects in optical waveguide arrays, ferromagnetic and antiferromagnetic spin chains, quantum Hall bilayers, etc., leading to possible technological advances in the creation of novel switching devices. Moreover, we propose to continue the ongoing work on the theoretical investigations of quantum tunnelling effects in optical systems. Specifically, based on our discovery of a Landau-Zener tunneling effect in waveguide arrays caused by a step in the refractive index, we propose to examine the same effect in the case of Bose-Einstein cond ensates in optical lattices (since both waveguide arrays and Bose-Einstein condensates are described by the Schroedinger equation) as well as in Bragg gratings, considering both adiabatic and nonadiabatic regimes. The training objective of the present prop osal is to acquire analytical skills that will allow to deal with exactly solvable equations and, on the other hand, to gain additional knowledge of realistic physical systems in laboratory experiments. The completion of the project activities is planned d uring the return phase at the Host Institution in Georgia (home country of the researcher). In particular, the establishment of a competitive research team is planned, which will work on the possible technological applications of the discovered effects in priority scientific areas in Georgia.
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