7,968 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, , for small values of
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 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
where for odd ,
for even not divisible by 3, and for even
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, where is the
fractional part of the flux through the rectangle when and it is symmetric with respect to the line when . The comparison of these results with numerical
calculations of the form factor is discussed in detail. The above values of
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
Continuum Singularities of a Mean Field Theory of Collisions
Consider a complex energy for a -particle Hamiltonian and let
be any wave packet accounting for any channel flux. The time independent
mean field (TIMF) approximation of the inhomogeneous, linear equation
consists in replacing by a product or Slater
determinant of single particle states This results, under the
Schwinger variational principle, into self consistent TIMF equations
in single particle space. The method is a
generalization of the Hartree-Fock (HF) replacement of the -body homogeneous
linear equation by single particle HF diagonalizations
We show how, despite strong nonlinearities in this mean
field method, threshold singularities of the {\it inhomogeneous} TIMF equations
are linked to solutions of the {\it homogeneous} HF equations.Comment: 21 pages, 14 figure
Distinguishing humans from computers in the game of go: a complex network approach
We compare complex networks built from the game of go and obtained from
databases of human-played games with those obtained from computer-played games.
Our investigations show that statistical features of the human-based networks
and the computer-based networks differ, and that these differences can be
statistically significant on a relatively small number of games using specific
estimators. We show that the deterministic or stochastic nature of the computer
algorithm playing the game can also be distinguished from these quantities.
This can be seen as tool to implement a Turing-like test for go simulators.Comment: 7 pages, 6 figure
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
Antisymmetrization of a Mean Field Calculation of the T-Matrix
The usual definition of the prior(post) interaction between
projectile and target (resp. ejectile and residual target) being contradictory
with full antisymmetrization between nucleons, an explicit antisymmetrization
projector must be included in the definition of the transition
operator, We derive the
suitably antisymmetrized mean field equations leading to a non perturbative
estimate of . The theory is illustrated by a calculation of forward
- scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14
A preliminary numerical simulation of bora wind with a limited area model of atmospheric circulation
One case of bora that burst out on the 4th of January 1995 has been simulated with a regional atmospheric model (RAMS). This was a typical bora with a stationary cyclone that remained over southern Adriatic Sea during the whole
episode of bora. Some common features of bora such as upstream acceleration, strong descent within bora layer and turbulent zone just downstream of the mountain have been demonstrated by the model simulation. The simulation of the
bora wind speed and direction showed good agreement with the observation in Trieste (Italy)
Direct probing of band-structure Berry phase in diluted magnetic semiconductors
We report on experimental evidence of the Berry phase accumulated by the
charge carrier wave function in single-domain nanowires made from a
(Ga,Mn)(As,P) diluted ferromagnetic semiconductor layer. Its signature on the
mesoscopic transport measurements is revealed as unusual patterns in the
magnetoconductance, that are clearly distinguished from the universal
conductance fluctuations. We show that these patterns appear in a magnetic
field region where the magnetization rotates coherently and are related to a
change in the band-structure Berry phase as the magnetization direction
changes. They should be thus considered as a band structure Berry phase
fingerprint of the effective magnetic monopoles in the momentum space. We argue
that this is an efficient method to vary the band structure in a controlled way
and to probe it directly. Hence, (Ga,Mn)As appears to be a very interesting
test bench for new concepts based on this geometrical phase.Comment: 7 pages, 6 figure
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