909 research outputs found
An exact-diagonalization study of rare events in disordered conductors
We determine the statistical properties of wave functions in disordered
quantum systems by exact diagonalization of one-, two- and quasi-one
dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we
find that the tails of the distribution of wave-function amplitudes are
described by the non-linear sigma-model. In two dimensions, the tails of the
distribution function are consistent with a recent prediction based on a direct
optimal fluctuation method.Comment: 13 pages, 5 figure
GHz Spin Noise Spectroscopy in n-Doped Bulk GaAs
We advance spin noise spectroscopy to an ultrafast tool to resolve high
frequency spin dynamics in semiconductors. The optical non-demolition
experiment reveals the genuine origin of the inhomogeneous spin dephasing in
n-doped GaAs wafers at densities at the metal-to-insulator transition. The
measurements prove in conjunction with depth resolved spin noise measurements
that the broadening of the spin dephasing rate does not result from thermal
fluctuations or spin-phonon interaction, as previously suggested, but from
surface electron depletion
Localized collective excitations in doped graphene in strong magnetic fields
We consider collective excitations in graphene with filled Landau levels (LL’s) in the presence of an external potential due to a single charged donor D+ or acceptor A− impurity. We show that localized collective modes split off the magnetoplasmon continuum and, in addition, quasibound states are formed within the continuum. A study of the evolution of the strengths and energies of magneto-optical transitions is performed for integer filling factors ν=1,2,3,4 of the lowest LL. We predict impurity absorption peaks above as well as below the cyclotron resonance. We find that the single-particle electron-hole symmetry of graphene leads to a duality between the spectra of collective modes for the D+ and A−. The duality shows up as a set of the D+ and A− magnetoabsorption peaks having the same energies but active in different circular polarizations
Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions
We present an investigation of the sinh-cosh (SC) interaction model with
twisted boundary conditions. We argue that, when unlike particles repel, the SC
model may be usefully viewed as a Heisenberg-Ising fluid with moving
Heisenberg-Ising spins. We derive the Luttinger liquid relation for the
stiffness and the susceptibility, both from conformal arguments, and directly
from the integral equations. Finally, we investigate the opening and closing of
the ground state gaps for both SC and Heisenberg-Ising models, as the
interaction strength is varied.Comment: 10 REVTeX pages + 4 uuencoded figures, UoU-002029
Interacting particles at a metal-insulator transition
We study the influence of many-particle interaction in a system which, in the
single particle case, exhibits a metal-insulator transition induced by a finite
amount of onsite pontential fluctuations. Thereby, we consider the problem of
interacting particles in the one-dimensional quasiperiodic Aubry-Andre chain.
We employ the density-matrix renormalization scheme to investigate the finite
particle density situation. In the case of incommensurate densities, the
expected transition from the single-particle analysis is reproduced. Generally
speaking, interaction does not alter the incommensurate transition. For
commensurate densities, we map out the entire phase diagram and find that the
transition into a metallic state occurs for attractive interactions and
infinite small fluctuations -- in contrast to the case of incommensurate
densities. Our results for commensurate densities also show agreement with a
recent analytic renormalization group approach.Comment: 8 pages, 8 figures The original paper was splitted and rewritten.
This is the published version of the DMRG part of the original pape
Inferring Displacement Fields from Sparse Measurements Using the Statistical Finite Element Method
A well-established approach for inferring full displacement and stress fields
from possibly sparse data is to calibrate the parameter of a given constitutive
model using a Bayesian update. After calibration, a (stochastic) forward
simulation is conducted with the identified model parameters to resolve
physical fields in regions that were not accessible to the measurement device.
A shortcoming of model calibration is that the model is deemed to best
represent reality, which is only sometimes the case, especially in the context
of the aging of structures and materials. While this issue is often addressed
with repeated model calibration, a different approach is followed in the
recently proposed statistical Finite Element Method (statFEM). Instead of using
Bayes' theorem to update model parameters, the displacement is chosen as the
stochastic prior and updated to fit the measurement data more closely. For this
purpose, the statFEM framework introduces a so-called model-reality mismatch,
parametrized by only three hyperparameters. This makes the inference of
full-field data computationally efficient in an online stage: If the stochastic
prior can be computed offline, solving the underlying partial differential
equation (PDE) online is unnecessary. Compared to solving a PDE, identifying
only three hyperparameters and conditioning the state on the sensor data
requires much fewer computational resources.
This paper presents two contributions to the existing statFEM approach:
First, we use a non-intrusive polynomial chaos method to compute the prior,
enabling the use of complex mechanical models in deterministic formulations.
Second, we examine the influence of prior material models (linear elastic and
St.Venant Kirchhoff material with uncertain Young's modulus) on the updated
solution. We present statFEM results for 1D and 2D examples, while an extension
to 3D is straightforward.Comment: 29 pages, 15 figures, Preprint submitted to Elsevie
- …