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Uncertain dynamical systems: A differential game approach
A class of dynamical systems in a conflict situation is formulated and discussed, and the formulation is applied to the study of an important class of systems in the presence of uncertainty. The uncertainty is deterministic and the only assumption is that its value belongs to a known compact set. Asymptotic stability is fully discussed with application to variable structure and model reference control systems
Full counting statistics of Luttinger liquid conductor
Non-equilibrium bosonization technique is used to study current fluctuations
of interacting electrons in a single-channel quantum wire representing a
Luttinger liquid (LL) conductor. An exact expression for the full counting
statistics of the transmitted charge is derived. It is given by Fredholm
determinant of the counting operator with a time dependent scattering phase.
The result has a form of counting statistics of non-interacting particles with
fractional charges, induced by scattering off the boundaries between the LL
wire and the non-interacting leads.Comment: 5 pages, 2 figure
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