Relaxation and Diffusion for the Kicked Rotor

The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase space densities in the chaotic component is calculated in presence of noise, and the limit of vanishing noise is taken is taken in the end of calculation. The relaxation rates (related to the Ruelle resonances) to the invariant equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. The global picture of relaxation to the equilibrium density in the chaotic component when the system is bounded and of diffusive behavior when it is unbounded is presented

Non-Collinear Magnetic Phases of a Triangular-Lattice Antiferromagnet and Doped CuFeO2_2

We obtain the non-collinear ground states of a triangular-lattice antiferromagnet with exchange interactions up to third nearest neighbors as a function of the single-ion anisotropy $D$. At a critical value of $D$, the collinear \uudd phase transforms into a complex non-collinear phase with odd-order harmonics of the fundamental ordering wavevector \vQ . The observed elastic peaks at 2\pi \vx -\vQ in both Al- and Ga- doped CuFeO$_2$ are explained by a "scalene" distortion of the triangular lattice produced by the repulsion of neighboring oxygen atoms.Comment: 4 pages 3 figures, accepted for publication by Phys. Rev. B Rapid communication

Diophantine approximation in Banach spaces

In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points