Band Distributions for Quantum Chaos on the Torus

Band distributions (BDs) are introduced describing quantization in a toral phase space. A BD is the uniform average of an eigenstate phase-space probability distribution over a band of toral boundary conditions. A general explicit expression for the Wigner BD is obtained. It is shown that the Wigner functions for {\em all} of the band eigenstates can be reproduced from the Wigner BD. Also, BDs are shown to be closer to classical distributions than eigenstate distributions. Generalized BDs, associated with sets of adjacent bands, are used to extend in a natural way the Chern-index characterization of the classical-quantum correspondence on the torus to arbitrary rational values of the scaled Planck constant.Comment: 12 REVTEX page

The heavy baryons in the nonperturbative string approach

We present some piloting calculations of the short-range correlation coefficients for the light and heavy baryons and masses of the doubly heavy baryons $\Xi_{QQ'}$ and $\Omega_{QQ'}$ ($Q,Q'=c,b$) in the framework of the simple approximation within the nonperturbative QCD approach.Comment: 21 pages; to appear in Phys. Atom. Nuc

Wigner Functions and Separability for Finite Systems

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of dimension p^n where p is a prime number. With this limitation it is possible to define a phase space and Wigner functions in close analogy to the continuous case. That is, we use a phase space that is a direct sum of n two-dimensional vector spaces each containing p^2 points. This is in contrast to the more usual choice of a two-dimensional phase space containing p^(2n) points. A useful aspect of this approach is that we can relate complete separability of density matrices and their Wigner functions in a natural way. We discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd. Special attention is required for two qubits (p=2) and our technique fails to establish the separability property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of the A matrices has been adde

Multicomplementary operators via finite Fourier transform

A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.Comment: 15 pages, no figure

Heavy Baryon Specroscopy from the Lattice

The results of an exploratory lattice study of heavy baryon spectroscopy are presented. We have computed the full spectrum of the eight baryons containing a single heavy quark, on a $24^3\times 48$ lattice at $\beta=6.2$, using an $O(a)$-improved fermion action. We discuss the lattice baryon operators and give a method for isolating the contributions of the spin doublets $(\Sigma,\Sigma^*)$, $(\Xi',\Xi^*)$ and $(\Omega,\Omega^*)$ to the correlation function of the relevant operator. We compare our results with the available experimental data and find good agreement in both the charm and the beauty sectors, despite the long extrapolation in the heavy quark mass needed in the latter case. We also predict the masses of several undiscovered baryons. We compute the \Lambda-\mbox{pseudoscalar meson} and $\Sigma-\Lambda$ mass splittings. Our results, which have errors in the range $10-30\%$, are in good agreement with the experimental numbers. For the $\Sigma^*-\Sigma$ mass splitting, we find results considerably smaller than the experimental values for both the charm and the beauty baryons, although in the latter case the experimental results are still preliminary. This is also the case for the lattice results for the hyperfine splitting for the heavy mesons.Comment: 31 pages LaTex, with postscript figures include

Observation of Two Narrow States Decaying into Ξc+γ\Xi_{c}^{+}\gamma and Ξc0γ\Xi_{c}^{0}\gamma

We report the first observation of two narrow charmed strange baryons decaying to $\Xi_c^+\gamma$ and $\Xi_c^0\gamma$, respectively, using data from the CLEO II detector at CESR. We interpret the observed signals as the $\Xi_c^{+\prime}(c{su})$ and $\Xi_c^{0\prime}(c{sd})$, the symmetric partners of the well-established antisymmetric $\Xi_c^+(c[su])$ and $\Xi_c^0(c[sd])$. The mass differences $M(\Xi_c^{+\prime})-M(\Xi_c^+)$ and $M(\Xi_c^{0\prime})-M(\Xi_c^0)$ are measured to be $107.8\pm 1.7\pm 2.5$ and $107.0\pm 1.4\pm 2.5 MeV/c^2$, respectively.Comment: 11 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Particle Content of the Nonlinear Sigma Model with Theta-Term: a Lattice Model Investigation

Using new as well as known results on dimerized quantum spin chains with frustration, we are able to infer some properties on the low-energy spectrum of the O(3) Nonlinear Sigma Model with a topological theta-term. In particular, for sufficiently strong coupling, we find a range of values of theta where a singlet bound state is stable under the triplet continuum. On the basis of these results, we propose a new renormalization group flow diagram for the Nonlinear Sigma Model with theta-term.Comment: 10 pages, 5 figures .eps, iopart format, submitted to JSTA

SU(3) Predictions for Weak Decays of Doubly Heavy Baryons -- including SU(3) breaking terms

We find expressions for the weak decay amplitudes of baryons containing two b quarks (or one b and one c quark -- many relationship are the same) in terms of unknown reduced matrix elements. This project was originally motivated by the request of the FNAL Run II b Physics Workshop organizers for a guide to experimentalists in their search for as yet unobserved hadrons. We include an analysis of linear SU(3) breaking terms in addition to relationships generated by unbroken SU(3) symmetry, and relate these to expressions in terms of the complete set of possible reduced matrix elements.Comment: 49 page

Percolation thresholds in chemical disordered excitable media

The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the light-sensitive Belousov-Zhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed, which depend on the relative wave transmittances of the two-state medium considered