4,782 research outputs found
Geometric overconvergence of rational functions in unbounded domains
The basic aim of this paper is to study the phenomenon of overconvergence for rational functions converging geometrically on [0, + ∞)
One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions
Based on the spectral statistics obtained in numerical simulations on three
dimensional disordered systems within the tight--binding approximation, a new
superuniversal scaling relation is presented that allows us to collapse data
for the orthogonal, unitary and symplectic symmetry () onto a
single scaling curve. This relation provides a strong evidence for
one-parameter scaling existing in these systems which exhibit a second order
phase transition. As a result a possible one-parameter family of spacing
distribution functions, , is given for each symmetry class ,
where is the dimensionless conductance.Comment: 4 pages in PS including 3 figure
Generic spectral properties of right triangle billiards
This article presents a new method to calculate eigenvalues of right triangle
billiards. Its efficiency is comparable to the boundary integral method and
more recently developed variants. Its simplicity and explicitness however allow
new insight into the statistical properties of the spectra. We analyse
numerically the correlations in level sequences at high level numbers (>10^5)
for several examples of right triangle billiards. We find that the strength of
the correlations is closely related to the genus of the invariant surface of
the classical billiard flow. Surprisingly, the genus plays and important role
on the quantum level also. Based on this observation a mechanism is discussed,
which may explain the particular quantum-classical correspondence in right
triangle billiards. Though this class of systems is rather small, it contains
examples for integrable, pseudo integrable, and non integrable (ergodic,
mixing) dynamics, so that the results might be relevant in a more general
context.Comment: 18 pages, 8 eps-figures, revised: stylistic changes, improved
presentatio
Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition
The distribution of the correlation dimension in a power law band random
matrix model having critical, i.e. multifractal, eigenstates is numerically
investigated. It is shown that their probability distribution function has a
fixed point as the system size is varied exactly at a value obtained from the
scaling properties of the typical value of the inverse participation number.
Therefore the state-to-state fluctuation of the correlation dimension is
tightly linked to the scaling properties of the joint probability distribution
of the eigenstates.Comment: 4 pages, 5 figure
Scattering at the Anderson transition: Power--law banded random matrix model
We analyze the scattering properties of a periodic one-dimensional system at
criticality represented by the so-called power-law banded random matrix model
at the metal insulator transition. We focus on the scaling of Wigner delay
times and resonance widths . We found that the typical values of
and (calculated as the geometric mean) scale with the system
size as and , where is the information dimension and is the
correlation dimension of eigenfunctions of the corresponding closed system.Comment: 6 pages, 8 figure
Spectral Properties of the Chalker-Coddington Network
We numerically investigate the spectral statistics of pseudo-energies for the
unitary network operator U of the Chalker--Coddington network. The shape of the
level spacing distribution as well the scaling of its moments is compared to
known results for quantum Hall systems. We also discuss the influence of
multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J.
Phys. Soc. Jp
Second bound state of the positronium molecule and biexcitons
A new, hitherto unknown bound state of the positronium molecule, with orbital
angular momentum L=1 and negative parity is reported. This state is stable
against autodissociation even if the masses of the positive and negative
charges are not equal. The existence of a similar state in two-dimension has
also been investigated. The fact that the biexcitons have a second bound state
may help the better understanding of their binding mechanism.Comment: Latex, 8 pages, 2 Postscript figure
Global-Vector Representation of the Angular Motion of Few-Particle Systems II
The angular motion of a few-body system is described with global vectors
which depend on the positions of the particles. The previous study using a
single global vector is extended to make it possible to describe both natural
and unnatural parity states. Numerical examples include three- and four-nucleon
systems interacting via nucleon-nucleon potentials of AV8 type and a 3
system with a nonlocal potential. The results using the
explicitly correlated Gaussian basis with the global vectors are shown to be in
good agreement with those of other methods. A unique role of the unnatural
parity component, caused by the tensor force, is clarified in the state
of He. Two-particle correlation function is calculated in the coordinate
and momentum spaces to show different characteristics of the interactions
employed.Comment: 39 pages, 4 figure
Anomalously large critical regions in power-law random matrix ensembles
We investigate numerically the power-law random matrix ensembles.
Wavefunctions are fractal up to a characteristic length whose logarithm
diverges asymmetrically with different exponents, 1 in the localized phase and
0.5 in the extended phase. The characteristic length is so anomalously large
that for macroscopic samples there exists a finite critical region, in which
this length is larger than the system size. The Green's functions decrease with
distance as a power law with an exponent related to the correlation dimension.Comment: RevTex, 4 pages, 4 eps figures. Final version to be published in
Phys. Rev. Let
Wigner crystallization in a polarizable medium
We present a variational study of the 2D and 3D Wigner crystal phase of large
polarons. The method generalizes that introduced by S. Fratini,P.\
Qu{\'{e}}merais [Mod. Phys. Lett. B {\bf 12} 1003 (1998)]. We take into account
the Wigner crystal normal modes rather than a single mean frequency in the
minimization procedure of the variational free energy. We calculate the
renormalized modes of the crystal as well as the charge polarization
correlation function and polaron radius. The solid phase boundaries are
determined via a Lindemann criterion, suitably generalized to take into account
the classical-to-quantum cross-over.
In the weak electron-phonon coupling limit, the Wigner crystal parameters are
renormalized by the electron-phonon interaction leading to a stabilization of
the solid phase for low polarizability of the medium. Conversely, at
intermediate and strong coupling, the behavior of the system depends strongly
on the polarizability of the medium.
For weakly polarizable media, a density crossover occurs inside the solid
phase when the renormalized plasma frequency approaches the phonon frequency.
At low density, we have a renormalized polaron Wigner crystal, while at higher
densities the electron-phonon interaction is weakened irrespective of the {\it
bare} electron-phonon coupling.
For strongly polarizable media, the system behaves as a Lorentz lattice of
dipoles. The abrupt softening of the internal polaronic frequency predicted by
Fratini and Quemerais is observed near the actual melting point only at very
strong coupling, leading to a possible liquid polaronic phase for a wider range
of parameters.Comment: 24 pages, 13 figures v1.
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