A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes

We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for continuity which is also known to be necessary. Using an isomorphism theorem of Eisenbaum and Kaspi which relates Markov local times and permanental processes, we obtain a general sufficient condition for the joint continuity of local times.Comment: Published in at http://dx.doi.org/10.1214/12-AOP744 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Liquid-vapour asymmetry in pure fluids: A Monte Carlo simulation study

Monte Carlo simulations within the grand canonical ensemble are used to obtain the joint distribution of density and energy fluctuations $p_L(\rho,u)$ for two model fluids: a decorated lattice gas and a polymer system. In the near critical region the form of $p_L(\rho,u)$ is analysed using a mixed field finite-size-scaling theory that takes account of liquid-vapour asymmetry. Field mixing transformations are performed that map $p_L(\rho,u)$ onto the joint distribution of critical scaling operators \ptMEstar\ appropriate to the Ising fixed point. Carrying out this procedure permits a very accurate determination of the critical point parameters. By forming various projections of \ptMEstar , the full universal finite-size spectrum of the critical density and energy distributions of fluids is also obtained. In the sub-critical coexistence region, an examination is made of the influence of field mixing on the asymmetry of the density distribution.Comment: 19 pages Latex, 15 Figures available on request. Report Number #IP-94.15

Permanental Vectors

A permanental vector is a generalization of a vector with components that are squares of the components of a Gaussian vector, in the sense that the matrix that appears in the Laplace transform of the vector of Gaussian squares is not required to be either symmetric or positive definite. In addition the power of the determinant in the Laplace transform of the vector of Gaussian squares, which is -1/2, is allowed to be any number less than zero. It was not at all clear what vectors are permanental vectors. In this paper we characterize all permanental vectors in $R^{3}_{+}$ and give applications to permanental vectors in $R^{n}_{+}$ and to the study of permanental processes

Accurate Measurements of the Chemical Potential of Polymeric Systems by Monte-Carlo Simulation

We present a new Monte-Carlo method for estimating the chemical potential of model polymer systems. The method is based upon the gradual insertion of a penetrable `ghost' polymer into the system and is effective for large chain lengths and at high densities. Insertion of the ghost chain is facilitated by use of an expanded ensemble in which weighted transitions are permitted between states characterising the strength of the excluded volume and thermal interactions experienced by the ghost chain. We discuss the implementation and optimisation of the method within the framework of the bond fluctuation model, and demonstrate its precision by a calculation of the finite-size corrections to the chemical potential.Comment: 12 pages Latex, Report Number #IP-94.12

An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state

A theory is described for the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pressures. The theory is implemented using a simplified description which treats the transition state as loose. The two principal features of the theory are a phase space partitioning of the transition states of the two exit channels after formation of the energetic molecule and a small (ca. 15%) decrease in the effective density of states, rho [a "non-Rice–Ramsperger–Kassel–Marcus (RRKM) effect"], for the symmetric ozone isotopomers [B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 (1999)]. This decrease is in addition to the usual statistical factor of 2 for symmetric molecules. Experimentally, the scrambled systems show a "mass-independent" effect for the enrichments delta (for trace) and E (for heavily) enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled systems show a strongly mass-dependent behavior. The contrasting behavior of scrambled and unscrambled systems is described theoretically using a "phase space" partitioning factor. In scrambled systems an energetic asymmetric ozone isotopomer is accessed from both entrance channels and, as shown in paper I, the partitioning factor becomes unity throughout. In unscrambled systems, access to an asymmetric ozone is only from one entrance channel, and differences in zero-point energies and other properties, such as the centrifugal potential, determine the relative contributions (the partitioning factors) of the two exit channels to the lifetime of the resulting energetic ozone molecule. They are responsible for the large differences in individual recombination rate constants at low pressures. While the decrease in rho for symmetric systems is attributed to a small non-RRKM effect eta, these calculated results are independent of the exact origin of the decrease. The calculated "mass-independent" enrichments, delta and E, in scrambled systems are relatively insensitive to the transition state (TS), because of the absence of the partitioning factor in their case (for a fixed non-RRKM eta). They are compared with the data at room temperature. Calculated results for the ratios of individual isotopomeric rate constants for the strongly mass-independent behavior for unscrambled systems are quite sensitive to the nature of the TS because of the partitioning effect. The current data are available only at room temperature but the loose TS is valid only at low temperatures. Accordingly, the results calculated for the latter at 140 K represent a prediction, for any given eta. At present, a comparison of the 140 K results can be made only with room temperature data. They show the same trends as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate for room temperature

An intramolecular theory of the mass-independent isotope effect for ozone. I

An intramolecular theory of the unusual mass-independent isotope effect for ozone formation and dissociation is described. The experiments include the enrichment factor, its dependence on the ambient pressure, the ratio of the formation rates of symmetric and asymmetric ozone isotopomers, the enrichment of ozone formed from heavily enriched oxygen isotopes, the comparison of that enrichment to that when the heavy isotopes are present in trace amounts, the isotopic exchange rate constant, and the large mass-dependent effect when individual rate constants are measured, in contrast with the mass-independent effect observed for scrambled mixtures. To explain the results it is suggested that apart from the usual symmetry number ratio of a factor of 2, the asymmetric ozone isotopomers have a larger density of reactive (coupled) quantum states, compared with that for the symmetric isotopomers (about 10%), due to being more "RRKM-like" (Rice–Ramsperger–Kessel–Marcus): Symmetry restricts the number of intramolecular resonances and coupling terms in the Hamiltonian which are responsible for making the motion increasingly chaotic and, thereby, increasingly statistical. As a result the behavior occurs regardless of whether the nuclei are bosons (16O, 18O) or fermions (17O). Two alternative mechanisms are also considered, one invoking excited electronic states and the other invoking symmetry control in the entrance channel. Arguments against each are given. An expression is given relating the mass-independent rates of the scrambled systems to the mass-dependent rates of the unscrambled ones, and the role played by a partitioning term in the latter is described. Different definitions for the enrichment factor for heavily enriched isotopic systems are also considered. In the present paper attention is focused on setting up theoretical expressions and discussing relationships. They provide a basis for future detailed calculations