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We examine fluctuations of vorticity excited by an external random force in two-dimensional fluid in the presence of a strong external shear flow. The problem is motivated by the analysis of big coherent vortices appearing as a consequence…
We combine a DEM simulation with a stochastic process to model the movement of spherical particles in a turbulent channel flow. With this model we investigate the mixing properties of two species of particles flowing through the channel. We…
Level and wavefunction statistics have been studied for two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between - (1/2) Phi_0 and (1/2)…
We study billiards in plane domains, with a perpendicular magnetic field and a potential. We give some results on periodic orbits, KAM tori and adiabatic invariants. We also prove the existence of bound states in a related scattering…
We compute the frequency spectrum of turbulent superfluid vortex density fluctuations and obtain the same Kolmogorov scaling which has been observed in a recent experiment in Helium-4. We show that the scaling can be interpreted in terms of…
In the mixed state of type II superconductors, vortices penetrate the sample and form a correlated system due to the screening of supercurrents around them. Interestingly, we can study this correlated system as a function of density and…
Classical transport in a doubly connected polygonal billiard, i.e. the annulus square billiard, is considered. Dynamical properties of the billiard flow with a fixed initial direction are analyzed by means of the moments of arbitrary order…
We firstly study the Navier-Stokes equation for the motion of a passive particle with harmonic, viscous, perturbative forces, subject to an exponentially correlated Gaussian force. Secondly, from the Fokker-Planck equation in an…
In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic…
Quantised vortices are remarkable manifestations on a macroscopic scale of the coherent nature of quantum fluids, and the study of their properties is of fundamental importance for the understanding of this peculiar state of matter.…
We formulate a simple additivity principle allowing to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal densities from the knowledge of its first two…
The integrals of motion for a cylindrically symmetric stationary vortex are obtained in a covariant description of a mixture of interacting superconductors, superfluids and normal fluids. The relevant integrated stress-energy coefficients…
The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into regions of oscillatory and rotational motion. The classical…
We study the stability and structure of vortices emerging in two-dimensional quantum dots in high magnetic fields. Our results obtained with exact diagonalization and density-functional calculations show that vortex structures can be found…
A method to derive the charge current density and its quantum mechanical correlation from the scattering matrix is discussed for quantum scattering systems described by a time-dependent Hamiltonian operator. The current density and charge…
Eigenstates and energy levels of a square quantum billiard in a magnetic field, or with an Aharonov-Bohm flux line, are found in quasiclassical approximation, that is, for high enough energy. Explicit formulas for the energy levels and…
Following recent work of Chernov, Markarian, and Zhang, it is known that the billiard map for dispersing billiards with zero angle cusps has slow decay of correlations with rate 1/n. Since the collisions inside a cusp occur in quick…
In the hard core limit, interacting vortices in planar type II superconductors can be modeled as non-interacting one dimensional fermions propagating in imaginary time. We use this analogy to derive analytical expressions for the…
We define a new class of plane billiards - the `pensive billiard' - in which the billiard ball travels along the boundary for some distance depending on the incidence angle before reflecting, while preserving the billiard rule of equality…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…