1,356 research outputs found
On the critical level-curvature distribution
The parametric motion of energy levels for non-interacting electrons at the
Anderson localization critical point is studied by computing the energy
level-curvatures for a quasiperiodic ring with twisted boundary conditions. We
find a critical distribution which has the universal random matrix theory form
for large level-curvatures corresponding to
quantum diffusion, although overall it is close to approximate log-normal
statistics corresponding to localization. The obtained hybrid distribution
resembles the critical distribution of the disordered Anderson model and makes
a connection to recent experimental data.Comment: 4 pages, 3 figure
Probability distribution of the conductance at the mobility edge
Distribution of the conductance P(g) at the critical point of the
metal-insulator transition is presented for three and four dimensional
orthogonal systems. The form of the distribution is discussed. Dimension
dependence of P(g) is proven. The limiting cases and are
discussed in detail and relation in the limit is proven.Comment: 4 pages, 3 .eps figure
Topology dependent quantities at the Anderson transition
The boundary condition dependence of the critical behavior for the three
dimensional Anderson transition is investigated. A strong dependence of the
scaling function and the critical conductance distribution on the boundary
conditions is found, while the critical disorder and critical exponent are
found to be independent of the boundary conditions
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
Spectral Properties of Three Dimensional Layered Quantum Hall Systems
We investigate the spectral statistics of a network model for a three
dimensional layered quantum Hall system numerically. The scaling of the
quantity is used to determine the critical exponent for
several interlayer coupling strengths. Furthermore, we determine the level
spacing distribution as well as the spectral compressibility at
criticality. We show that the tail of decays as with
and also numerically verify the equation
, where is the correlation dimension and the
spatial dimension.Comment: 4 pages, 5 figures submitted to J. Phys. Soc. Jp
Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition
The statistics of energy levels for a disordered conductor are considered in
the critical energy window near the mobility edge. It is shown that, if
critical wave functions are multifractal, the one-dimensional gas of levels on
the energy axis is ``compressible'', in the sense that the variance of the
level number in an interval is for .
The compressibility, , is given ``exactly'' in terms of the
multifractal exponent at the mobility edge in a -dimensional
system.Comment: 10 pages in REVTeX preprint format; to be published in JETP Letters,
199
Three-Dimensional Quantum Percolation Studied by Level Statistics
Three-dimensional quantum percolation problems are studied by analyzing
energy level statistics of electrons on maximally connected percolating
clusters. The quantum percolation threshold \pq, which is larger than the
classical percolation threshold \pc, becomes smaller when magnetic fields are
applied, i.e., \pq(B=0)>\pq(B\ne 0)>\pc. The critical exponents are found to
be consistent with the recently obtained values of the Anderson model,
supporting the conjecture that the quantum percolation is classified onto the
same universality classes of the Anderson transition. Novel critical level
statistics at the percolation threshold is also reported.Comment: to appear in the May issue of J. Phys. Soc. Jp
Temporary use of shape memory spinal rod in the treatment of scoliosis
NiTinol shape memory alloy is characterized by its malleability at low temperatures and its ability to return to a preconfigured shape above its activation temperature. This process can be utilized to assist in scoliosis correction. The goal of this retrospective study was to evaluate the clinical and radiographic results of intraoperative use of shape memory alloy rod in the correction of scoliosis. From May 2002 to September 2006, 38 scoliosis patients (ranging from 50° to 120°; 22 cases over 70°) who underwent shape memory alloy-assisted correction in our institute were reviewed. During the operation, a shape memory alloy rod served as a temporary correction tool. Following correction, the rod was replaced by a rigid rod. The mean blood loss at surgery was 680 ± 584 ml; the mean operative time was 278 ± 62 min. The major Cobb angle improved from an average 78.4° preoperatively to 24.3° postoperatively (total percent correction 71.4%). In 16 patients with a major curve <70° and flexibility of 52.7%, the deformity improved from 58.4° preoperatively to 12.3° postoperatively (percent correction, 78.9%). In 22 patients with a major curve >70° and flexibility of 25.6%, the deformity improved from 94.1° preoperatively to 30.1° postoperatively (percent correction, 68.1%). Only one case had a deep infection. There were no neurologic, vascular or correction-related complications such as screw pullout or metal fracture. The study shows that the intraoperative use of a shape memory rod is a safe and effective method to correct scoliosis
Multifractality and critical fluctuations at the Anderson transition
Critical fluctuations of wave functions and energy levels at the Anderson
transition are studied for the family of the critical power-law random banded
matrix ensembles. It is shown that the distribution functions of the inverse
participation ratios (IPR) are scale-invariant at the critical point,
with a power-law asymptotic tail. The IPR distribution, the multifractal
spectrum and the level statistics are calculated analytically in the limits of
weak and strong couplings, as well as numerically in the full range of
couplings.Comment: 14 pages, 13 eps figure
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