645 research outputs found

### Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents

Numerical studies of the Anderson transition are based on the finite-size
scaling analysis of the smallest positive Lyapunov exponent. We prove
numerically that the same scaling holds also for higher Lyapunov exponents.
This scaling supports the hypothesis of the one-parameter scaling of the
conductance distribution. From the collected numerical data for quasi one
dimensional systems up to the system size 24 x 24 x infinity we found the
critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < \nu <
1.54. Finite-size effects and the role of irrelevant scaling parameters are
discussed.Comment: 4 pages, 2 figure

### Ground state of a partially melted Wigner molecule

We consider three spinless fermions free to move on 2d square lattice with
periodic boundary conditions and interacting via a U/r Coulomb repulsion. When
the Coulomb energy to kinetic energy ratio r_s is large, a rigid Wigner
molecule is formed. As r_s decreases, we show that melting proceeds via an
intermediate regime where a floppy two particle molecule coexists with a
partially delocalized particle. A simple ansatz is given to describe the ground
state of this mesoscopic solid-liquid regime.Comment: to appear in Europhysics Letter

### Critical conductance of two-dimensional chiral systems with random magnetic flux

The zero temperature transport properties of two-dimensional lattice systems
with static random magnetic flux per plaquette and zero mean are investigated
numerically. We study the two-terminal conductance and its dependence on
energy, sample size, and magnetic flux strength. The influence of boundary
conditions and of the oddness of the number of sites in the transverse
direction is also studied. We confirm the existence of a critical chiral state
in the middle of the energy band and calculate the critical exponent nu=0.35
+/- 0.03 for the divergence of the localization length. The sample averaged
scale independent critical conductance _c turns out to be a function of the
amplitude of the flux fluctuations whereas the variance of the respective
conductance distributions appears to be universal. All electronic states
outside of the band center are found to be localized.Comment: to appear in Phys. Rev.

### Long-Range Energy-Level Interaction in Small Metallic Particles

We consider the energy level statistics of non-interacting electrons which
diffuse in a $d$-dimensional disordered metallic conductor of characteristic
Thouless energy $E_c.$ We assume that the level distribution can be written
as the Gibbs distribution of a classical one-dimensional gas of fictitious
particles with a pairwise additive interaction potential $f(\varepsilon ).$
We show that the interaction which is consistent with the known correlation
function of pairs of energy levels is a logarithmic repulsion for level
separations $\varepsilon <E_c,$ in agreement with Random Matrix Theory. When
$\varepsilon >E_c,$ $f(\varepsilon )$ vanishes as a power law in $\varepsilon /E_c$ with exponents $-{1 \over 2},-2,$ and $-{3 \over 2}$ for
$d=1,2,$ and 3, respectively. While for $d=1,2$ the energy-level
interaction is always repulsive, in three dimensions there is long-range level
attraction after the short-range logarithmic repulsion.Comment: Saclay-s93/014 Email: [email protected] [2017: missing
figure included

### A matrix ensemble with a preferential basis and its application to disordered metals and insulators

URL: http://www-spht.cea.fr/articles/s93/085The standard ensembles of the random matrix theory are invariant under change of basis. For non interacting electrons in disordered systems, this invariance is broken and deviations from the random matrix theory predictions occur, especially for strong disorder. We consider a generalization of the standard ensembles which includes a preferential basis and which gives rise to a ``screening'' of the logarithmic pairwise interaction between energy levels. In the unitary case, we recover a mathematically tractable distribution of energy levels first introduced by Gaudin. This simplified model provides a qualitative description of level statistics in the metal, insulator and at the mobility edge, which only depends on the dimensionless conductance $g$

### $h/2e$--Oscillations for Correlated Electron Pairs in Disordered Mesoscopic Rings

The full spectrum of two interacting electrons in a disordered mesoscopic
one--dimensional ring threaded by a magnetic flux is calculated numerically.
For ring sizes far exceeding the one--particle localization length $L_1$ we
find several $h/2e$--periodic states whose eigenfunctions exhibit a pairing
effect. This represents the first direct observation of interaction--assisted
coherent pair propagation, the pair being delocalized on the scale of the whole
ring.Comment: 4 pages, uuencoded PostScript, containing 5 figures

### Quantum Hall effects in layered disordered superconductors

Layered singlet paired superconductors with disorder and broken time reversal
symmetry are studied. The phase diagram demonstrates charge-spin separation in
transport. In terms of the average intergrain transmission and the interlayer
tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2
separated by a spin metal phase. We identify a spin metal-insulator
localization exponent as well as a spin conductivity exponent of ~0.9. In
presence of a Zeeman term an additional phase with spin Hall coefficient of 1
appears.Comment: 4 pages, 4 figure

### Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the
transfer-matrix approach to Anderson localization, in order to generate the
statistical distribution of electronic wavefunction amplitudes at arbitary
distances from the origin of $L^{d-1} \times \infty$ disordered systems. For
$d=1$ our approach is shown to reproduce exact diagonalization results
available in the literature. In $d=2$, where strips of width $L \leq 64$ sites
were used, attempted fits of gaussian (log-normal) forms to the wavefunction
amplitude distributions result in effective localization lengths growing with
distance, contrary to the prediction from single-parameter scaling theory. We
also show that the distributions possess a negative skewness $S$, which is
invariant under the usual histogram-collapse rescaling, and whose absolute
value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the
range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be
published

### Ericson fluctuations in an open, deterministic quantum system: theory meets experiment

We provide numerically exact photoexcitation cross sections of rubidium
Rydberg states in crossed, static electric and magnetic fields, in quantitative
agreement with recent experimental results. Their spectral backbone underpins a
clear transition towards the Ericson regime.Comment: 4 pages, 3 figures, 1 tabl

### Web-assisted tunneling in the kicked harmonic oscillator

We show that heating of harmonically trapped ions by periodic delta kicks is
dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these
values, quasienergy eigenstates localized on island structures undergo avoided
crossings with extended web-states.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. Let

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