490 research outputs found
Wegner bounds for a two-particle tight binding model
We consider a quantum two-particle system on a d-dimensional lattice with
interaction and in presence of an IID external potential. We establish
Wegner-typer estimates for such a model. The main tool used is Stollmann's
lemma
Mott--Hubbard transition vs. Anderson localization of correlated, disordered electrons
The phase diagram of correlated, disordered electrons is calculated within
dynamical mean--field theory using the geometrically averaged (''typical'')
local density of states. Correlated metal, Mott insulator and Anderson
insulator phases, as well as coexistence and crossover regimes are identified.
The Mott and Anderson insulators are found to be continuously connected.Comment: 4 pages, 4 figure
Exploiting environmental resonances to enhance qubit quality factors
We discuss dephasing times for a two-level system (including bias) coupled to
a damped harmonic oscillator. This system is realized in measurements on
solid-state Josephson qubits. It can be mapped to a spin-boson model with a
spectral function with an approximately Lorentzian resonance. We diagonalize
the model by means of infinitesimal unitary transformations (flow equations),
and calculate correlation functions, dephasing rates, and qubit quality
factors. We find that these depend strongly on the environmental resonance
frequency ; in particular, quality factors can be enhanced
significantly by tuning to lie below the qubit frequency .Comment: 5 psges, 5 figure
Characterization of the Local Density of States Fluctuations near the Integer Quantum Hall Transition in a Quantum Dot Array
We present a calculation for the second moment of the local density of states
in a model of a two-dimensional quantum dot array near the quantum Hall
transition. The quantum dot array model is a realistic adaptation of the
lattice model for the quantum Hall transition in the two-dimensional electron
gas in an external magnetic field proposed by Ludwig, Fisher, Shankar and
Grinstein. We make use of a Dirac fermion representation for the Green
functions in the presence of fluctuations for the quantum dot energy levels. A
saddle-point approximation yields non-perturbative results for the first and
second moments of the local density of states, showing interesting fluctuation
behaviour near the quantum Hall transition. To our knowledge we discuss here
one of the first analytic characterizations of chaotic behaviour for a
two-dimensional mesoscopic structure. The connection with possible experimental
investigations of the local density of states in the quantum dot array
structures (by means of NMR Knight-shift or single-electron-tunneling
techniques) and our work is also established.Comment: 11 LaTeX pages, 1 postscript figure, to appear in Phys.Rev.
Localization Bounds for Multiparticle Systems
We consider the spectral and dynamical properties of quantum systems of
particles on the lattice , of arbitrary dimension, with a Hamiltonian
which in addition to the kinetic term includes a random potential with iid
values at the lattice sites and a finite-range interaction. Two basic
parameters of the model are the strength of the disorder and the strength of
the interparticle interaction. It is established here that for all there
are regimes of high disorder, and/or weak enough interactions, for which the
system exhibits spectral and dynamical localization. The localization is
expressed through bounds on the transition amplitudes, which are uniform in
time and decay exponentially in the Hausdorff distance in the configuration
space. The results are derived through the analysis of fractional moments of
the -particle Green function, and related bounds on the eigenfunction
correlators
Effective Model Formulation for Two Interacting Electrons in a Disordered Metal
We derive an analytical theory for two interacting electrons in a
--dimensional random potential. Our treatment is based on an effective
random matrix Hamiltonian. After mapping the problem on a nonlinear
model, we exploit similarities with the theory of disordered metals to identify
a scaling parameter, investigate the level correlation function, and study the
transport properties of the system. In agreement with recent numerical work we
find that pair propagation is subdiffusive and that the pair size grows
logarithmically with time.Comment: 4 pages, revtex, no figure
Distribution of level curvatures for the Anderson model at the localization-delocalization transition
We compute the distribution function of single-level curvatures, , for
a tight binding model with site disorder, on a cubic lattice. In metals
is very close to the predictions of the random-matrix theory (RMT). In
insulators has a logarithmically-normal form. At the Anderson
localization-delocalization transition fits very well the proposed novel
distribution with , which
approaches the RMT result for large and is non-analytical at small . We
ascribe such a non-analiticity to the spatial multifractality of the critical
wave functions.Comment: 4 ReVTeX pages and 4(.epsi)figures included in one uuencoded packag
Critical phenomena on scale-free networks: logarithmic corrections and scaling functions
In this paper, we address the logarithmic corrections to the leading power
laws that govern thermodynamic quantities as a second-order phase transition
point is approached. For phase transitions of spin systems on d-dimensional
lattices, such corrections appear at some marginal values of the order
parameter or space dimension. We present new scaling relations for these
exponents. We also consider a spin system on a scale-free network which
exhibits logarithmic corrections due to the specific network properties. To
this end, we analyze the phase behavior of a model with coupled order
parameters on a scale-free network and extract leading and logarithmic
correction-to-scaling exponents that determine its field- and temperature
behavior. Although both non-trivial sets of exponents emerge from the
correlations in the network structure rather than from the spin fluctuations
they fulfil the respective thermodynamic scaling relations. For the scale-free
networks the logarithmic corrections appear at marginal values of the node
degree distribution exponent. In addition we calculate scaling functions, which
also exhibit nontrivial dependence on intrinsic network properties.Comment: 15 pages, 4 figure
Fisher Renormalization for Logarithmic Corrections
For continuous phase transitions characterized by power-law divergences,
Fisher renormalization prescribes how to obtain the critical exponents for a
system under constraint from their ideal counterparts. In statistical
mechanics, such ideal behaviour at phase transitions is frequently modified by
multiplicative logarithmic corrections. Here, Fisher renormalization for the
exponents of these logarithms is developed in a general manner. As for the
leading exponents, Fisher renormalization at the logarithmic level is seen to
be involutory and the renormalized exponents obey the same scaling relations as
their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee
problem at their upper critical dimensions, where predictions for logarithmic
corrections are made.Comment: 10 pages, no figures. Version 2 has added reference
Information about the Integer Quantum Hall Transition Extracted from the Autocorrelation Function of Spectral Determinants
The Autocorrelation function of spectral determinants (ASD) is used to probe
the sensitivity of a two-dimensional disordered electron gas to the system's
size L.
For weak magnetic fields ASD is shown to depend only trivially on L, which is
a strong indication that all states are localized.
From nontrivial dependence of ASD on L for infinite L at a Hall conductance
of 1/2 e^2/h we deduce the existence of critical wave functions at this point,
as long as the disorder strength does not exceed a critical value.Comment: 4 pages, one citation correcte
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