Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

The Elliptic Billiard: Subtleties of Separability

Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem can be solved. A geometric picture is given revealing why levels of a separable system cross. It is shown that the repulsions found by Ayant and Arvieu are computational effects and that the method used by Traiber et al. is related to the present picture which explains the crossings they find. An asymptotic formula for the energy-levels is derived and it is found that the statistical quantities of the spectrum P(s) and \Delta(L) have the form expected for an integrable system.Comment: 10 pages, LaTeX, 3 Figures (postscript). Submitted to European Journal of Physic

Metastable states in glassy systems

Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs to cast them in a form involving states with finite lifetimes. Starting from elementary examples and using results of Gaveau and Schulman, we propose a simple expression for the configurational entropy and revisit the question of taking flat averages over metastable states. The construction is applicable to finite dimensional systems, and we explicitly show that for simple mean-field glass models it recovers, justifies and generalises the known results. The calculation emphasises the appearance of new dynamical order parameters.Comment: 4 fig., 20 pages, revtex; added references and minor change

An Intersecting Loop Model as a Solvable Super Spin Chain

In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical regime, we conjecture that the central charge is $c=q-1$ for $q$ integer $< 2$. Low-lying excitations are examined, supporting a superdiffusive behavior for $q=1$. We argue that these systems are interesting examples of integrable lattice models realizing $c \leq 0$ conformal field theories.Comment: latex file, 7 page

Excited Charmed Mesons: Observations, Analyses and Puzzles

We review the status of recently observed positive parity charmed resonances, both in the non-strange and in the strange sector. We describe the experimental findings, the main theoretical analyses and the open problems deserving further investigations.Comment: LaTeX, 25 pages, 5 figures. Invited revie

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of Statistical Physic

Modelling Dynamic Conditional Correlations in WTI Oil Forward and Futures Returns

This paper estimates the dynamic conditional correlations in the returns on WTI oil one-month forward prices, and one-, three-, six-, and twelve-month futures prices, using recently developed multivariate conditional volatility models. The dynamic correlations enable a determination of whether the forward and various futures returns are substitutes or complements, which are crucial for deciding whether or not to hedge against unforeseen circumstances. The models are estimated using daily data on WTI oil forward and futures prices, and their associated returns, from 3 January 1985 to 16 January 2004. At the univariate level, the estimates are statistically significant, with the occasional asymmetric effect in which negative shocks have a greater impact on volatility than positive shocks. In all cases, both the short- and long-run persistence of shocks are statistically significant. Among the five returns, there are ten conditional correlations, with the highest estimate of constant conditional correlation being 0.975 between the volatilities of the three-month and six-month futures returns, and the lowest being 0.656 between the volatilities of the forward and twelve-month futures returns. The dynamic conditional correlations can vary dramatically, being negative in four of ten cases and being close to zero in another five cases. Only in the case of the dynamic volatilities of the three-month and six-month futures returns is the range of variation relatively narrow, namely (0.832, 0.996). Thus, in general, the dynamic volatilities in the returns in the WTI oil forward and future prices can be either independent or interdependent over time