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Coherent structures versus chaotic behaviour in nonlinear complex systems
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Acronym: COSHANS
Number / Date of the contract: CEX-05-D11-09 / 03.10.2005
modul 1
Project Manager: Adrian Stefan Carstea
Partners: University of Craiova; West University Timisoara
Starting date / finishing date: 2005-10-03 / 2008-10-02
Project value: 1500000 RON
Abstract: The purpose of the present project is a basic research in the field of complex nonlinear systems, research which joins to the thematic area 11, with the aim to obtain advanced knowledges in this field, and also to explain some experimental data in specific problems.The project is oriented on the following directions:
Direction 1. The study of the integrability and coherent structures (solitons) in supersymmetric AKNS systems. We shall elaborate and develop specific techniques, especially the bilinearization method. The same method will be used to study the coherent structures in mixed systems of bosons and fermions, which generally are not integrable. Such systems are relevant for conducting polymers.
Direction 2 refers to the study of coherent structures in systems of interacting bosons. The modulational instability in a „cigar” shaped Bose-Einstein condensate in a longitudinal periodic field will be investigated. The situation of a condensate with two kind of bosons, as well as the possibility of a long range – short range resonance and the stochastic behaviour of the condensate near zero dispersion point will be analyzed. The previous results on the groups of coherent state type will be extended to more general situations of the semi-direct product of the many-dimensional Heisenberg group with the n-dimensional symplectic group.
Direction 3 tackles the study of quantum and classic discrete systems. We shall study a 2-D system of electrons in a transversal magnetic field, using Harper’s equation. A series of phenomena, specific for mezoscopic systems (including transport) will be analyzed. Using the specific methods of the discrete dynamical systems we shall perform a detailed study of genetic circuits for an arbitrary number of connected genes.
Direction 4 The integrability of several Hamiltonian systems and the chaotic dynamics of the nonintegrable ones, relevant to the plasma physics, will be investigated with the specific methods.The problem of quantum chaos will be discussed using the concept of the classical entropy of a quantum state introduced by us. The connection between Majorana representation for arbitrary spin and the entropy of a quantum state will be investigated. Using methods from the theory of stochastic systems and from the quantum mechanics of open systems the motion of particles in a asymptotic periodic potential (ratchet model), interacting with a non-equilibrium thermal bath, will be investigated in order to understand how a biological motor is running.

THE STAGES OF THE PROJECT AND DELIVERY DATES
1.  (2005-12-10)
2.  (2006-06-30)
3.  (2006-12-10)
4.  (2007-06-30)
5.  (2007-12-10)
6.  (2008-09-30)
RESULTS

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