7 research outputs found
Free Energy of the Two-Matrix Model/dToda Tau-Function
We provide an integral formula for the free energy of the two-matrix model
with polynomial potentials of arbitrary degree (or formal power series). This
is known to coincide with the tau-function of the dispersionless
two--dimensional Toda hierarchy. The formula generalizes the case studied by
Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately
Takhtajan in the case of conformal maps of Jordan curves. Finally we generalize
the formula found in genus zero to the case of spectral curves of arbitrary
genus with certain fixed data.Comment: Ver 2: 18 pages added important formulas for higher genus spectral
curves, few typos removed (and few added). Ver 3: 19 pages (minor changes).
Typos removed, added appendix and improved exposition Ver 4: 19 pages, minor
corrections. Version submitted Ver 4; corrections prompted by referee and
accepted in Nuclear Phys.
Dibaryons as axially symmetric skyrmions
Dibaryons configurations are studied in the framework of the bound state
soliton model. A generalized axially symmetric ansatz is used to determine the
soliton background. We show that once the constraints imposed by the symmetries
of the lowest energy torus configuration are satisfied all spurious states are
removed from the dibaryon spectrum. In particular, we show that the lowest
allowed state in the channel carries the quantum numbers of the H
particle. We find that, within our approximations, this particle is slightly
bound in the model. We discuss, however, that vacuum effects neglected in the
present calculation are very likely to unbind the H.Comment: 24 pages, LaTeX, TAN-FNT-93-12 (it replaces old version which was
truncated
Perturbation Theory for the Rosenzweig-Porter Matrix Model
We study an ensemble of random matrices (the Rosenzweig-Porter model) which,
in contrast to the standard Gaussian ensemble, is not invariant under changes
of basis. We show that a rather complete understanding of its level
correlations can be obtained within the standard framework of diagrammatic
perturbation theory. The structure of the perturbation expansion allows for an
interpretation of the level structure on simple physical grounds, an aspect
that is missing in the exact analysis (T. Guhr, Phys. Rev. Lett. 76, 2258
(1996), T. Guhr and A. M\"uller-Groeling, cond-mat/9702113).Comment: to appear in PRE, 5 pages, REVTeX, 2 figures, postscrip
Spectroscopy with random and displaced random ensembles
Due to the time reversal invariance of the angular momentum operator J^2, the
average energies and variances at fixed J for random two-body Hamiltonians
exhibit odd-even-J staggering, that may be especially strong for J=0. It is
shown that upon ensemble averaging over random runs, this behaviour is
reflected in the yrast states. Displaced (attractive) random ensembles lead to
rotational spectra with strongly enhanced BE2 transitions for a certain class
of model spaces. It is explained how to generalize these results to other forms
of collectivity.Comment: 4 pages, 4 figure
Parametric S-matrix fluctuations in quantum theory of chaotic scattering
We study the effects of an arbitrary external perturbation in the statistical
properties of the S-matrix of quantum chaotic scattering systems in the limit
of isolated resonances. We derive, using supersymmetry, an exact
non-perturbative expression for the parameter dependent autocorrelator of two
S-matrix elements. Universality is obtained by appropriate rescaling of the
physical parameters. We propose this universal function as a new signature of
quantum chaos in open systems.Comment: 4 pages, 1 figure appended, written in REVTeX, Preprint OUTP-94-13S
(University of Oxford