Universal correlations of one-dimensional interacting electrons in the gas phase

We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics of correlation functions at small temperatures, in the presence of a magnetic field.Comment: 4 pages, Revte

Role of Large Gluonic Excitation Energy for Narrow Width of Penta-Quark Baryons in QCD String Theory

We study the narrow decay width of low-lying penta-quark baryons in the QCD string theoryin terms of gluonic excitations. In the QCD string theory, the penta-quark baryon decays via a gluonic-excited state of a baryon and meson system, where a pair of Y-shaped junction and anti-junction is created. Since lattice QCD shows that the lowest gluonic-excitation energy takes a large value of about 1 GeV, the decay of the penta-quark baryon near the threshold is considered as a quantum tunneling process via a highly-excited state (a gluonic-excited state) in the QCD string theory. This mechanism strongly suppresses the decay and leads to an extremely narrow decay width of the penta-quark system.Comment: Talk given at International Conference on the Structure of Baryons (Baryons 04) October 25 - 29, 2004, Ecole Polytechnique, Palaiseau, Franc

Bayesian definition of random sequences with respect to conditional probabilities

We study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider four variants of conditional random sequences with respect to the conditional distributions: two of them are defined by ML-randomness on Bayes models and the others are defined by blind tests for conditional distributions. We consider a weak criterion for conditional ML-randomness and show that only variants of ML-randomness on Bayes models satisfy the criterion. We show that these four variants of conditional randomness are identical when the conditional probability measure is computable and the posterior distribution converges weakly to almost all parameters. We compare ML-randomness on Bayes models with randomness for uniformly computable parametric models. It is known that two computable probability measures are orthogonal if and only if their ML-random sets are disjoint. We extend these results for uniformly computable parametric models. Finally, we present an algorithmic solution to a classical problem in Bayes statistics, i.e.~the posterior distributions converge weakly to almost all parameters if and only if the posterior distributions converge weakly to all ML-random parameters.Comment: revised versio

Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain

Recently a new integral equation describing the thermodynamics of the 1D Heisenberg model was discovered by Takahashi. Using the integral equation we have succeeded in obtaining the high temperature expansion of the specific heat and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than those obtained so far by the standard methods such as the linked-cluster algorithm. Our results will be useful to examine various approximation methods to extrapolate the high temperature expansion to the low temperature region.Comment: 5 pages, 4 figures, 2 table