910 research outputs found
Geometry of random interactions
It is argued that spectral features of quantal systems with random
interactions can be given a geometric interpretation. This conjecture is
investigated in the context of two simple models: a system of randomly
interacting d bosons and one of randomly interacting fermions in a j=7/2 shell.
In both examples the probability for a given state to become the ground state
is shown to be related to a geometric property of a polygon or polyhedron which
is entirely determined by particle number, shell size, and symmetry character
of the states. Extensions to more general situations are discussed
Regular spectra in the vibron model with random interactions
The phenomenom of emerging regular spectral features from random interactions
is addressed in the context of the vibron model. A mean-field analysis links
different regions of the parameter space with definite geometric shapes. The
results that are, to a large extent, obtained in closed analytic form, provide
a clear and transparent interpretation of the high degree of order that has
been observed in numerical studies.Comment: 19 pages, 8 figures, 2 tables. Physical Review C, in pres
Angular momentum I ground state probabilities of boson systems interacting by random interactions
In this paper we report our systematic calculations of angular momentum
ground state probabilities () of boson systems with spin in the
presence of random two-body interactions. It is found that the P(0) dominance
is usually not true for a system with an odd number of bosons, while it is
valid for an even number of bosons, which indicates that the P(0) dominance is
partly connected to the even number of identical particles. It is also noticed
that the 's of bosons with spin do not follow the 1/N (,
referring to the number of independent two-body matrix elements) relation. The
properties of the 's obtained in boson systems with spin are
discussed.Comment: 8 pages and 3 figure
Generic Rotation in a Collective SD Nucleon-Pair Subspace
Low-lying collective states involving many nucleons interacting by a random
ensemble of two-body interactions (TBRE) are investigated in a collective
SD-pair subspace, with the collective pairs defined dynamically from the
two-nucleon system. It is found that in this truncated pair subspace collective
vibrations arise naturally for a general TBRE hamiltonian whereas collective
rotations do not. A hamiltonian restricted to include only a few randomly
generated separable terms is able to produce collective rotational behavior, as
long as it includes a reasonably strong quadrupole-quadrupole component.
Similar results arise in the full shell model space. These results suggest that
the structure of the hamiltonian is key to producing generic collective
rotation.Comment: 11 pages, 5 figure
Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states
In this paper, we discuss the angular momentum distribution in the ground
states of many-body systems interacting via a two-body random ensemble.
Beginning with a few simple examples, a simple approach to predict P(I)'s,
angular momenta I ground state (g.s.) probabilities, of a few solvable cases,
such as fermions in a small single-j shell and d boson systems, is given. This
method is generalized to predict P(I)'s of more complicated cases, such as even
or odd number of fermions in a large single-j shell or a many-j shell, d-boson,
sd-boson or sdg-boson systems, etc. By this method we are able to tell which
interactions are essential to produce a sizable P(I) in a many-body system. The
g.s. probability of maximum angular momentum is discussed. An
argument on the microscopic foundation of our approach, and certain matrix
elements which are useful to understand the observed regularities, are also
given or addressed in detail. The low seniority chain of 0 g.s. by using the
same set of two-body interactions is confirmed but it is noted that
contribution to the total 0 g.s. probability beyond this chain may be more
important for even fermions in a single-j shell. Preliminary results by taking
a displaced two-body random ensemble are presented for the I g.s.
probabilities.Comment: 39 pages and 8 figure
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
Spin Structure of Many-Body Systems with Two-Body Random Interactions
We investigate the spin structure of many-fermion systems with a
spin-conserving two-body random interaction. We find a strong dominance of
spin-0 ground states and considerable correlations between energies and wave
functions of low-lying states with different spin, but no indication of
pairing. The spectral densities exhibit spin-dependent shapes and widths, and
depend on the relative strengths of the spin-0 and spin-1 couplings in the
two-body random matrix. The spin structure of low-lying states can largely be
explained analytically.Comment: 10 pages, including 3 figure
Baryons in O(4) and Vibron Model
The structure of the reported excitation spectra of the light unflavored
baryons is described in terms of multi-spin valued Lorentz group
representations of the so called Rarita-Schwinger (RS) type (K/2, K/2)* [(1/
2,0)+ (0,1/2)] with K=1,3, and 5. We first motivate legitimacy of such pattern
as fundamental fields as they emerge in the decomposition of triple fermion
constructs into Lorentz representations. We then study the baryon realization
of RS fields as composite systems by means of the quark version of the U(4)
symmetric diatomic rovibron model. In using the U(4)/ O(4)/ O(3)/ O(2)
reduction chain, we are able to reproduce quantum numbers and mass splittings
of the above resonance assemblies. We present the essentials of the four
dimensional angular momentum algebra and construct electromagnetic tensor
operators. The predictive power of the model is illustrated by ratios of
reduced probabilities concerning electric de-excitations of various resonances
to the nucleon.Comment: Phys. Rev. D (in press, 2001
Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
The embedded ensembles were introduced by Mon and French as physically more
plausible stochastic models of many--body systems governed by one--and
two--body interactions than provided by standard random--matrix theory. We
review several approaches aimed at determining the spectral density, the
spectral fluctuation properties, and the ergodic properties of these ensembles:
moments methods, numerical simulations, the replica trick, the eigenvector
decomposition of the matrix of second moments and supersymmetry, the binary
correlation approximation, and the study of correlations between matrix
elements.Comment: Final version. 29 pages, 4 ps figures, uses iopart.st
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