An analytical construction of the SRB measures for Baker-type maps

For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle and Bowen showed the existence of an invariant measure (SRB measure) weakly attracting the temporal average of any initial distribution that is absolutely continuous with respect to the Lebesgue measure. Recently, the SRB measures were found to be related to the nonequilibrium stationary state distribution functions for thermostated or open systems. Inspite of the importance of these SRB measures, it is difficult to handle them analytically because they are often singular functions. In this article, for three kinds of Baker-type maps, the SRB measures are analytically constructed with the aid of a functional equation, which was proposed by de Rham in order to deal with a class of singular functions. We first briefly review the properties of singular functions including those of de Rham. Then, the Baker-type maps are described, one of which is nonconservative but time reversible, the second has a Cantor-like invariant set, and the third is a model of a simple chemical reaction R<-->I<-->P. For the second example, the cases with and without escape are considered. For the last example, we consider the reaction processes in a closed system and in an open system under a flux boundary condition. In all cases, we show that the evolution equation of the distribution functions partially integrated over the unstable direction is very similar to de Rham's functional equation and, employing this analogy, we explicitly construct the SRB measures. (c) 1998 American Institute of Physics.     

Observations concerning the treatment of long-range interactions in molecular dynamics simulations

Molecular dynamics simulations of pure water employing two different empirical water models have been used to study the effects of different methods for truncation of long-range interactions in molecular mechanics calculations. As has been observed previously in integral equation studies, “shifting” these interactions on an atom-by-atom basis was found to produce artificial structuring in the water and affect diffusion rates. In cases where some form of short-range truncation must be used, the ST2 switching function applied on a group-by-group basis was found to be the most realistic procedure. If atom-based shifting must be employed, a cutoff distance greater than or equal to 12.0 Å was found to be required to produce realistic results. © 1993 John Wiley & Sons, Inc.     

On the assumption of initial factorization in the master equation for weakly coupled systems I: General framework

We analyze the dynamics of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. In the weak-coupling (van Hove) limit, the dynamics can be properly described in terms of a master equation, but a consistent application of Nakajima-Zwanzig’s projection method requires that the reference (not necessarily equilibrium) state of the reservoir be endowed with the mixing property.     

Anomalous magnetic properties of tetraphenylporphinato Co(II) complex in the solid state

The α,β,γ,δ-tetraphenylporphinatocobalt(II) complex is found to exist in two distinct, but interconvertible, polycrystalline forms. The one with a tetragonal crystal symmetry (species B) gives the EPR spectrum which has been attributed to the low-spin electronic configuration of Co(II) ion in an axial crystal field. The other form (species A) having a triclinic crystal symmetry shows no easily detectable EPR signal even at liquid helium temperature.Magnetic susceptibility and magnetization meaurements demonstrated that the complex is paramagnetic in both forms, but the species (A) is characterized by ferromagnetic exchange coupling, while the species (B) behaves as a normal paramagnet.The experimental susceptibility versus 1/T curve can be reproduced quite well by using the Ising method. The g values thus obtained (g_| = 5.2,g_⊥ = 0) can not be explained by a low-spin electronic configuration, but are consistent with a high-spin ground state. Assigning a high-spin state to the species (A), the first such case in Co(II) porphine complexes, can not only explain the absence of EPR signal, but is also supported by the results of X-ray structural analyses.     

Spectral Properties of a Piecewise Linear Intermittent Map

For a piecewise linear intermittent map, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the Frobenius–Perron operator ^P are explicitly derived. The evolution of the averages are shown to be a superposition of the contributions from two simple eigenvalues 1 and _d (–1, 0), and a continuous spectrum on the unit interval [0,1] of ^P. Power-law decay of correlations are controlled by the continuous spectrum. Also the non-normalizable invariant measure in the non-stationary regime is shown to determine the strength of the power-law decay.     

Generalized spectral decomposition of the β-adic baker's transformation and intrinsic irreversibility

We construct a generalized spectral decomposition of the Frobenius-Perron operator of the β-adic baker's transformation using a general iterative operator method applicable in principle for any mixing dynamical system. The eigenvalues in the decomposition are related to the decay rates of the autocorrelation functions and have magnitudes less than one. We explicitly define appropriate generalized function spaces, which provide mathematical meaning to the formally obtained spectral decomposition. The unitary Frobenius-Perron evolution of densities, when extended to the generalized function spaces, splits into two semigroups, one decaying in the future and the other in the past. This split, which reflects the asymptotic evolution of the forward and backward K-partitions, shows the instrinsic irreversibility of the baker's transformation.     

Metallic ferromagnetism in the Hubbard model: a rigorous example

We present the first rigorous example of the Hubbard model in any dimension which exhibits metallic ferromagnetism. The model is a genuine Hubbard model with short-range hopping and on-site Coulomb repulsion, and has many single-electron bands. In the limit where the band gap and the Coulomb repulsion become infinite, we prove that the ground states are completely ferromagnetic and at the same time conducting.     

Formation of transient pairs of F and H centers at next nearest neighbor sites in alkali chloride crystals studied by the time delayed double excitation spectroscopy in picosecond range

Abstract

By making use of the time delayed double excitation spectroscopy, transient absorption spectra just after the excitation of self-trapped excitons (STE) from the lowest triplet state to higher excited states have been observed to find the transient F-H center pair [F-H]. Absorption bands due to transient [F-H] appeared as a doublet peaking at 2.70eV and 2.86eV (NaCl), at 2.25eV and 2.38eV (KCl) and at 1.97eV and 2.09eV (RbCl) at 108ps after the excitation. The ratio of peak heights between bands at low and high energy sides was 2:1 in all crystals. The results were tentatively understood by a recent theory for the STE by Song et al. (1987).     

Symmetry breaking in Heisenberg antiferromagnets

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies the existence of a symmetry breaking in the state obtained by applying an infinitesimal symmetry-breaking field. The theorem is most meaningful when applied to a class of quantum antiferromagnets where the existence of a long range order has been proved by the Dyson-Lieb-Simon method. We also present a related theorem for the ground states. It is an improvement of the theorem by Kaplan, Horsch and von der Linden. Our lower bounds on the spontaneous staggered magnetization in terms of the long range order parameter take into account the symmetry of the system properly, and are likely to be saturated in general models.