Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

HCN laser scattering on the JIPP T-IIU tokamak

A 4-channel HCN laser scattering system has been developed and applied to the JIPP T-IIU tokamak. Main aim of this system is to study microturbulence excited in the plasma, especially in the high power ICRF heating experiment. The observed density fluctuations are in a frequency range of the electron diamagnetic drift wave and have broad frequency spectra. The main part of the wavenumber is found to satisfy the condition of . In the heating experiments, deterioration of the energy confinement time is observed, and the density fluctuation level increases with the increase of the heating power.     

Exclusive semi-leptonic decays of bottom mesons in the spectator quark model

We calculate the exclusive semileptonic bottom meson decays \(B \to D(D*) + l^ - + \bar v_l \) in the spectator quark model. The helicity structure of the mesonic current transitionsB→D(D ^*) is matched to the helicity structure of the free quark current transitionsb→c at minimum momentum transferq ²=0. The results are continued toq ²≠=0 by pole-dominated form factors. Our results are compared to recent calculations that use quark model dynamics at maximum momentum transferq _max ² = (M ₁ ?M ₂)². We find agreement atq _max ² . Atq ²=0 there are significant differences between the predictions of the two approaches leading to marked differences in the predictions for the shape of the lepton energy spectrum, the shape of theq ²-distribution, and the helicity composition of the transition measurable in the angular distributions of the decaysD ^*→Dπ and \(W_{virtual}^ - \to l^ - + \bar v_l \) .     

Magnetic excitations in the quasi one-dimensional antiferromagnetic singlet groundstate system CsFeBr3

We have measured the magnetic excitations in CsFeBr₃ along the chain direction (z-axis) and perpendicular to it by inelastic neutron scattering. The measured dispersion curves can be reproduced by the formula $$\omega ^2 (q) = A^2 - 8A[J\cos (\pi q_c ) + J'\gamma (2\pi q_ \bot )]R(T)$$ which is very different from dispersion relations for usual 1 D antiferromagnets, because of the singlet groundstate of this system. The large value of the anisotropy energyA/k=29.8±0.5 K, which is independent of temperature, causes the singlet groundstate. The intra-and inter-chain exchange parameters areJ/k=?3.2±0.15K andJ'/k=?0.32±0.02 K determined atT=1.4 K. At 1.4 K the renormalisation factor is taken to beR(T)=1. AtT=30 K the value forR(T) was found to be 0.5±0.1 keepingJ andJ' unchanged. The excitations at (1/3 1/31) show soft mode behaviour but no phase transition. The observed intensities are interpreted by a heuristic model for the eigenvectors in the excited state including antiferro-as well as ferromagnetic configurations of the fluctuations.