1,383 research outputs found

### Integrable random matrix ensembles

We propose new classes of random matrix ensembles whose statistical
properties are intermediate between statistics of Wigner-Dyson random matrices
and Poisson statistics. The construction is based on integrable N-body
classical systems with a random distribution of momenta and coordinates of the
particles. The Lax matrices of these systems yield random matrix ensembles
whose joint distribution of eigenvalues can be calculated analytically thanks
to integrability of the underlying system. Formulas for spacing distributions
and level compressibility are obtained for various instances of such ensembles.Comment: 32 pages, 8 figure

### Periodic orbits contribution to the 2-point correlation form factor for pseudo-integrable systems

The 2-point correlation form factor, $K_2(\tau)$, for small values of $\tau$
is computed analytically for typical examples of pseudo-integrable systems.
This is done by explicit calculation of periodic orbit contributions in the
diagonal approximation. The following cases are considered: (i) plane billiards
in the form of right triangles with one angle $\pi/n$ and (ii) rectangular
billiards with the Aharonov-Bohm flux line. In the first model, using the
properties of the Veech structure, it is shown that
$K_2(0)=(n+\epsilon(n))/(3(n-2))$ where $\epsilon(n)=0$ for odd $n$,
$\epsilon(n)=2$ for even $n$ not divisible by 3, and $\epsilon(n)=6$ for even
$n$ divisible by 3. For completeness we also recall informally the main
features of the Veech construction. In the second model the answer depends on
arithmetical properties of ratios of flux line coordinates to the corresponding
sides of the rectangle. When these ratios are non-commensurable irrational
numbers, $K_2(0)=1-3\bar{\alpha}+4\bar{\alpha}^2$ where $\bar{\alpha}$ is the
fractional part of the flux through the rectangle when $0\le \bar{\alpha}\le
1/2$ and it is symmetric with respect to the line $\bar{\alpha}=1/2$ when $1/2
\le \bar{\alpha}\le 1$. The comparison of these results with numerical
calculations of the form factor is discussed in detail. The above values of
$K_2(0)$ differ from all known examples of spectral statistics, thus confirming
analytically the peculiarities of statistical properties of the energy levels
in pseudo-integrable systems.Comment: 61 pages, 13 figures. Submitted to Communications in Mathematical
Physics, 200

### Distance matrices and isometric embeddings

We review the relations between distance matrices and isometric embeddings
and give simple proofs that distance matrices defined on euclidean and
spherical spaces have all eigenvalues except one non-negative. Several
generalizations are discussed.Comment: 17 page

### Short-range plasma model for intermediate spectral statistics

We propose a plasma model for spectral statistics displaying level repulsion
without long-range spectral rigidity, i.e. statistics intermediate between
random matrix and Poisson statistics similar to the ones found numerically at
the critical point of the Anderson metal-insulator transition in disordered
systems and in certain dynamical systems. The model emerges from Dysons
one-dimensional gas corresponding to the eigenvalue distribution of the
classical random matrix ensembles by restricting the logarithmic pair
interaction to a finite number $k$ of nearest neighbors. We calculate
analytically the spacing distributions and the two-level statistics. In
particular we show that the number variance has the asymptotic form
$\Sigma^2(L)\sim\chi L$ for large $L$ and the nearest-neighbor distribution
decreases exponentially when $s\to \infty$, $P(s)\sim\exp (-\Lambda s)$ with
$\Lambda=1/\chi=k\beta+1$, where $\beta$ is the inverse temperature of the gas
($\beta=$1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class
respectively). In the simplest case of $k=\beta=1$, the model leads to the
so-called Semi-Poisson statistics characterized by particular simple
correlation functions e.g. $P(s)=4s\exp(-2s)$. Furthermore we investigate the
spectral statistics of several pseudointegrable quantum billiards numerically
and compare them to the Semi-Poisson statistics.Comment: 24 pages, 4 figure

### Dual methods and approximation concepts in structural synthesis

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins

### ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included

### SPECTRAL PROPERTIES OF BILLIARDS AND QUANTUM CHAOS

The first 800 eigenvalues of the stadium billiard have been evaluated numerically. It is shown that the four spectra obtained (corresponding to the four types of symmetry of the wave function) exhibit the fluctuation properties of the Gaussian Orthogonal Ensemble of Random Matrices. This reinforces the belief that these fluctuation properties are characteristic of quantum chaotic systems

### Random matrix ensembles associated with Lax matrices

A method to generate new classes of random matrix ensembles is proposed.
Random matrices from these ensembles are Lax matrices of classically integrable
systems with a certain distribution of momenta and coordinates. The existence
of an integrable structure permits to calculate the joint distribution of
eigenvalues for these matrices analytically. Spectral statistics of these
ensembles are quite unusual and in many cases give rigorously new examples of
intermediate statistics

### NEUROSPORA BIBLIOGRAPHY

Every attempt has been made to insure that the citations appear exactly as they do in the original publication. Entries for which the original could not be obtained for verification are indicated by (-)

### Neurospora Bibliography - 1993

Neurospora Bibliography - 1993 - Every attempt has been made to insure that the citations appear exactly as they do in the original publication

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