Calculation of NMR Properties of Solitons in Superfluid 3He-A

Superfluid 3He-A has domain-wall-like structures, which are called solitons. We calculate numerically the structure of a splay soliton. We study the effect of solitons on the nuclear-magnetic-resonance spectrum by calculating the frequency shifts and the amplitudes of the soliton peaks for both longitudinal and transverse oscillations of magnetization. The effect of dissipation caused by normal-superfluid conversion and spin diffusion is calculated. The calculations are in good agreement with experiments, except a problem in the transverse resonance frequency of the splay soliton or in magnetic-field dependence of reduced resonance frequencies.Comment: 15 pages, 10 figures, updated to the published versio

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Statistical approach to nonhyperbolic chaotic systems

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Generalized Markov coarse graining and spectral decompositions of chaotic piecewise linear maps

Spectral decompositions of the evolution operator for probability densities are obtained for the most general one dimensional piecewise linear Markov maps and a large class of repellers. The eigenvalues obtained with respect to the space of functions piecewise analytic over the minimal Markov partition equal the reciprocals of the zeros of the Ruelle zeta functions. The logarithms of the zeros correspond to the decay rates of time correlation functions of analytic observables when the system is mixing. The space can also be extended to include piecewise analytic observables permitted to have discontinuities at the elements of any given periodic orbit(s), so that local behavior of observables can be considered. The new spectra associated with the extension are surprisingly simple and are related to the relative stability factors of the given orbit(s). Finally, arbitrarily slowly decaying periodic and aperiodic nonanalytic eigenmodes are constructed. © 1994 The American Physical Society.SCOPUS: ar.jinfo:eu-repo/semantics/publishe