Projection of Markov Measures May Be Gibbsian

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Hölder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.     

Traveling patterns in cellular automata

A method to identify the invariant subsets of bi-infinite configurations of cellular automata that propagate rigidly with a constant velocity nu is described. Causal traveling configurations, propagating at speeds not greater than the automaton range, mid R:numid R:相似文献   

Non-Born-Oppenheimer treatment of the H2 Hookean molecule

We show that the exact non-Born-Oppenheimer Schrodinger equation for the Hookean diatomic molecule H2 (a two-proton, two-electron system where the electron-proton interaction is harmonic while the proton-proton and electron-electron interactions are Coulombic) can be decoupled into equations describing the relative motion of the electrons, the relative motion of nuclei, the motion of a collective mode representing a three-dimensional harmonic oscillator, and the motion of a free particle expressed as a linear combination of the individual center-of-mass coordinates of the nuclei and electrons. Analytic solutions to the relative motion of electrons can be readily obtained for the given values of the harmonic coupling constant. However, exact analytic solutions to the equation for the relative motion of the nuclei cannot be obtained simultaneously due to the fact that the harmonic constants in these two equations are coupled. For this reason, we present for the relative nuclear motion approximate analytic wave functions, one of them obtained variationally and the other by a series solution where the coefficients are determined recursively. We also explore a variational solution to the Taylor-series expansion of the nuclear interaction potential. Properties of the electronic and nuclear intracule densities are examined at different values of the coupling constant. An interesting result of the present non-Born-Oppenheimer treatment of this harmonic model is the fact that the relative nuclear motion occurs in a highly correlated regime. This leads in a natural way to a spatial localization of the nuclei akin to Wigner electronic crystallization.