27 research outputs found
Anderson localization on the Cayley tree : multifractal statistics of the transmission at criticality and off criticality
In contrast to finite dimensions where disordered systems display
multifractal statistics only at criticality, the tree geometry induces
multifractal statistics for disordered systems also off criticality. For the
Anderson tight-binding localization model defined on a tree of branching ratio
K=2 with generations, we consider the Miller-Derrida scattering geometry
[J. Stat. Phys. 75, 357 (1994)], where an incoming wire is attached to the root
of the tree, and where outcoming wires are attached to the leaves of
the tree. In terms of the transmission amplitudes , the total
Landauer transmission is , so that each channel
is characterized by the weight . We numerically measure the
typical multifractal singularity spectrum of these weights as a
function of the disorder strength and we obtain the following conclusions
for its left-termination point . In the delocalized phase ,
is strictly positive and is associated with a
moment index . At criticality, it vanishes and is
associated with the moment index . In the localized phase ,
is associated with some moment index . We discuss the
similarities with the exact results concerning the multifractal properties of
the Directed Polymer on the Cayley tree.Comment: v2=final version (16 pages
On the statistics of superlocalized states in self-affine disordered potentials
We investigate the statistics of eigenstates in a weak self-affine disordered
potential in one dimension, whose Gaussian fluctuations grow with distance with
a positive Hurst exponent . Typical eigenstates are superlocalized on
samples much larger than a well-defined crossover length, which diverges in the
weak-disorder regime. We present a parallel analytical investigation of the
statistics of these superlocalized states in the discrete and the continuum
formalisms. For the discrete tight-binding model, the effective localization
length decays logarithmically with the sample size, and the logarithm of the
transmission is marginally self-averaging. For the continuum Schr\"odinger
equation, the superlocalization phenomenon has more drastic effects. The
effective localization length decays as a power of the sample length, and the
logarithm of the transmission is fully non-self-averaging.Comment: 21 pages, 6 figure
Universality in quantum parametric correlations
We investigate the universality of correlation functions of chaotic and
disordered quantum systems as an external parameter is varied. A new, general
scaling procedure is introduced which makes the theory invariant under
reparametrizations. Under certain general conditions we show that this
procedure is unique. The approach is illustrated with the particular case of
the distribution of eigenvalue curvatures. We also derive a semiclassical
formula for the non-universal scaling factor, and give an explicit expression
valid for arbitrary deformations of a billiard system.Comment: LaTeX, 10 pages, 2 figures. Revised version, to appear in PR
Quadrupole Collective States in a Large Single-J Shell
We discuss the ability of the generator coordinate method (GCM) to select
collective states in microscopic calculations. The model studied is a
single- shell with hamiltonian containing the quadrupole-quadrupole
interaction. Quadrupole collective excitations are constructed by means of the
quadrupole single-particle operator. Lowest collective bands for =31/2 and
particle numbers =4,6,8,10,12, and are found. For lower values of ,
exact solutions are obtained and compared with the GCM results.Comment: submitted for publication in Phys. Rev. C, revtex, 28 pages, 15
PostScript figures available on request from [email protected], preprint
No. IFT/17/9
Self-Consistent Approximations for Superconductivity beyond the Bardeen-Cooper-Schrieffer Theory
We develop a concise self-consistent perturbation expansion for
superconductivity where all the pair processes are naturally incorporated
without drawing "anomalous" Feynman diagrams. This simplification results from
introducing an interaction vertex that is symmetric in the particle-hole
indices besides the ordinary space-spin coordinates. The formalism
automatically satisfies conservation laws, includes the Luttinger-Ward theory
as the normal-state limit, and reproduces the Bardeen-Cooper-Schrieffer theory
as the lowest-order approximation. It enables us to study the thermodynamic,
single-particle, two-particle, and dynamical properties of superconductors with
competing fluctuations based on a single functional of Green's
function in the Nambu space. Specifically, we derive closed equations
in the FLEX-S approximation, i.e., the fluctuation exchange approximation for
superconductivity with all the pair processes, which contains extra terms
besides those in the standard FLEX approximation.Comment: 14 pages, 6 figure
An SU(2) Analog of the Azbel--Hofstadter Hamiltonian
Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and
Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the
problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce
a modification of the tight binding Azbel--Hofstadter Hamiltonian that is a
specific spin-S Euler top and can be considered as its ``classical'' analog.
The eigenvalue problem for the proposed model, in the coherent state
representation, is described by the S-gap Lam\'e equation and, thus, is
completely solvable. We observe a striking similarity between the shapes of the
spectra of the two models for various values of the spin S.Comment: 19 pages, LaTeX, 4 PostScript figures. Relation between Cartan and
Cartesian deformation of SU(2) and numerical results added. Final version as
will appear in J. Phys. A: Math. Ge
Short-ranged RVB physics, quantum dimer models and Ising gauge theories
Quantum dimer models are believed to capture the essential physics of
antiferromagnetic phases dominated by short-ranged valence bond configurations.
We show that these models arise as particular limits of Ising (Z_2) gauge
theories, but that in these limits the system develops a larger local U(1)
invariance that has different consequences on different lattices. Conversely,
we note that the standard Z_2 gauge theory is a generalised quantum dimer
model, in which the particular relaxation of the hardcore constraint for the
dimers breaks the U(1) down to Z_2. These mappings indicate that at least one
realization of the Senthil-Fisher proposal for fractionalization is exactly the
short ranged resonating valence bond (RVB) scenario of Anderson and of
Kivelson, Rokhsar and Sethna. They also suggest that other realizations will
require the identification of a local low energy, Ising link variable {\it and}
a natural constraint. We also discuss the notion of topological order in Z_2
gauge theories and its connection to earlier ideas in RVB theory. We note that
this notion is not central to the experiment proposed by Senthil and Fisher to
detect vortices in the conjectured Z_2 gauge field.Comment: 17 pages, 4 postscript figures automatically include
Random-Matrix Theory of Quantum Transport
This is a comprehensive review of the random-matrix approach to the theory of
phase-coherent conduction in mesocopic systems. The theory is applied to a
variety of physical phenomena in quantum dots and disordered wires, including
universal conductance fluctuations, weak localization, Coulomb blockade,
sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and
giant conductance oscillations in a Josephson junction.Comment: 85 pages including 52 figures, to be published in Rev.Mod.Phy
The nuclear collective motion
Current developments in nuclear structure are discussed from a theoretical perspective. First, the progress in theoretical modeling of nuclei is reviewed. This is followed by the discussion of nuclear time scales, nuclear collective modes, and nuclear deformations. Some perspectives on nuclear structure research far from stability are given. Finally, interdisciplinary aspects of the nuclear many-body problem are outlined