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The development of theoretical methods for analysis of driven systems


This project aims to develop theoretical methods for the study of physical systems driven by regular and stochastic fields. The systems driven by regular fields are modelled by an over-damped particle or a chain of under-damped particles that interact also with random or ratchet potentials and with constant or alternating external force fields. Such model systems represent numerous physical systems far from equilibrium and adequately describe their evolution. The main objectives of this part of the investigation are to formulate an appropriate thermodynamic theory of deterministically driven systems and to study the features of chaotic transport and current reversal in deterministic ratchets, which arise from inter-particle interactions. To achieve these goals, a concept of the system effective temperature and a criterion for chaotic transport will be developed.

The stochastically driven systems considered in the project include two-dimensional ensembles of dipolar interacting magnetic nanoparticles driven by thermal fluctuations, and model systems driven by multiplicative Levy white noise. To describe the magnetic relaxation in nanoparticle ensembles, a novel, two-step mean-field approximation scheme will be developed that operates with two different mean fields and takes into account the correlation effects, in contrast to the conventional mean-field approximation. To describe the statistical properties of noisy systems with strong fluctuations, a new class of Langevin equations with multiplicative Levy white noise will be introduced and the corresponding generalized Fokker-Planck equation will be derived and solved for particular cases. The methods developed during the project will be applied to the study of the steady-state properties of disordered ionic chains driven by an alternating electric field, chaotic transport of interacting charged particles, thermally activated magnetic relaxation in nanoparticle ensembles, and anomalous phenomena in noisy systems.

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