846 research outputs found
Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions
Using a fermionic renormalization group approach we analyse a model where the
electrons diffusing on a quantum dot interact via Fermi-liquid interactions.
Describing the single-particle states by Random Matrix Theory, we find that
interactions can induce phase transitions (or crossovers for finite systems) to
regimes where fluctuations and collective effects dominate at low energies.
Implications for experiments and numerical work on quantum dots are discussed.Comment: 4 pages, 1 figure; version to appear in Phys Rev Letter
Linear Increments with Non-monotone Missing Data and Measurement Error.
Linear increments (LI) are used to analyse repeated outcome data with missing values. Previously, two LI methods have been proposed, one allowing non-monotone missingness but not independent measurement error and one allowing independent measurement error but only monotone missingness. In both, it was suggested that the expected increment could depend on current outcome. We show that LI can allow non-monotone missingness and either independent measurement error of unknown variance or dependence of expected increment on current outcome but not both. A popular alternative to LI is a multivariate normal model ignoring the missingness pattern. This gives consistent estimation when data are normally distributed and missing at random (MAR). We clarify the relation between MAR and the assumptions of LI and show that for continuous outcomes multivariate normal estimators are also consistent under (non-MAR and non-normal) assumptions not much stronger than those of LI. Moreover, when missingness is non-monotone, they are typically more efficient
Ground-state energy and spin in disordered quantum dots
We investigate the ground-state energy and spin of disordered quantum dots
using spin-density-functional theory. Fluctuations of addition energies
(Coulomb-blockade peak spacings) do not scale with average addition energy but
remain proportional to level spacing. With increasing interaction strength, the
even-odd alternation of addition energies disappears, and the probability of
non-minimal spin increases, but never exceeds 50%. Within a two-orbital model,
we show that the off-diagonal Coulomb matrix elements help stabilize a ground
state of minimal spin.Comment: 10 pages, 2 figure
Discrete charging of metallic grains: Statistics of addition spectra
We analyze the statistics of electrostatic energies (and their differences)
for a quantum dot system composed of a finite number of electron islands
(metallic grains) with random capacitance-inductance matrix , for which the
total charge is discrete, (where is the charge of an electron and
is an integer). The analysis is based on a generalized charging model,
where the electrons are distributed among the grains such that the
electrostatic energy E(N) is minimal. Its second difference (inverse
compressibility) represents the spacing between
adjacent Coulomb blockade peaks appearing when the conductance of the quantum
dot is plotted against gate voltage. The statistics of this quantity has been
the focus of experimental and theoretical investigations during the last two
decades. We provide an algorithm for calculating the distribution function
corresponding to and show that this function is piecewise
polynomial.Comment: 21 pages, no figures, mathematical nomenclature (except for Abstract
and Introduction
Orthogonality Catastrophe in Parametric Random Matrices
We study the orthogonality catastrophe due to a parametric change of the
single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian
is modeled by a suitable random matrix ensemble. We show that the overlap
between the original and the parametrically modified many-body ground states,
, taken as Slater determinants, decreases like , where is
the number of electrons in the systems, is a numerical constant of the
order of one, and is the deformation measured in units of the typical
distance between anticrossings. We show that the statistical fluctuations of
are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure
Integrable model for interacting electrons in metallic grains
We find an integrable generalization of the BCS model with non-uniform
Coulomb and pairing interaction. The Hamiltonian is integrable by construction
since it is a functional of commuting operators; these operators, which
therefore are constants of motion of the model, contain the anisotropic Gaudin
Hamiltonians. The exact solution is obtained diagonalizing them by means of
Bethe Ansatz. Uniform pairing and Coulomb interaction are obtained as the
``isotropic limit'' of the Gaudin Hamiltonians. We discuss possible
applications of this model to a single grain and to a system of few interacting
grains.Comment: 4 pages, revtex. Revised version to be published in Phys. Rev. Let
An efficient Fredholm method for calculation of highly excited states of billiards
A numerically efficient Fredholm formulation of the billiard problem is
presented. The standard solution in the framework of the boundary integral
method in terms of a search for roots of a secular determinant is reviewed
first. We next reformulate the singularity condition in terms of a flow in the
space of an auxiliary one-parameter family of eigenproblems and argue that the
eigenvalues and eigenfunctions are analytic functions within a certain domain.
Based on this analytic behavior we present a numerical algorithm to compute a
range of billiard eigenvalues and associated eigenvectors by only two
diagonalizations.Comment: 15 pages, 10 figures; included systematic study of accuracy with 2
new figures, movie to Fig. 4,
http://www.quantumchaos.de/Media/0703030media.av
Kidney after extrarenal transplantation - the impact of Alemtuzumab induction: 1582 (Abstract)
Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations
We study a model of interacting fermions in a disordered potential, which is
assumed to generate uniformly fluctuating interaction matrix elements. We show
that the ground state magnetization is systematically decreased by off-diagonal
fluctuations of the interaction matrix elements. This effect is neglected in
the Stoner picture of itinerant ferromagnetism in which the ground-state
magnetization is simply determined by the balance between ferromagnetic
exchange and kinetic energy, and increasing the interaction strength always
favors ferromagnetism. The physical origin of the demagnetizing effect of
interaction fluctuations is the larger number of final states available for
interaction-induced scattering in the lower spin sectors of the Hilbert space.
We analyze the energetic role played by these fluctuations in the limits of
small and large interaction . In the small limit we do second-order
perturbation theory and identify explicitly transitions which are allowed for
minimal spin and forbidden for higher spin. These transitions then on average
lower the energy of the minimal spin ground state with respect to higher spin.
For large interactions we amplify on our earlier work [Ph. Jacquod and A.D.
Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is
favored due to a larger broadening of the many-body density of states in the
low-spin sectors. Numerical results are presented in both limits.Comment: 35 pages, 24 figures - final, shortened version, to appear in
Physical Review
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