3,182 research outputs found
Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension
The magnetic translation algebra plays an important role in the quantum Hall
effect. Murthy and Shankar, arXiv:1207.2133, have shown how to realize this
algebra using fermionic bilinears defined on a two-dimensional square lattice.
We show that, in any dimension , it is always possible to close the magnetic
translation algebra using fermionic bilinears, whether in the continuum or on
the lattice. We also show that these generators are complete in even, but not
odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions
that conserves particle number can be represented in terms of the generators of
this algebra, whether or not time-reversal symmetry is broken. As an example,
we reproduce the -sum rule of interacting electrons at vanishing magnetic
field using this representation. We also show that interactions can
significantly change the bare bandwidth of lattice Hamiltonians when
represented in terms of the generators of the magnetic translation algebra.Comment: 14 page
Fourier Transform Multiple Quantum Nuclear Magnetic Resonance
The excitation and detection of multiple quantum transitions in systems of coupled spins offers, among other advantages, an increase in resolution over single quantum n.m.r. since the number of lines decreases as the order of the transition increases. This paper reviews the motivation for detecting multiple quantum transitions by a Fourier transform experiment and describes an experimental approach to high resolution multiple quantum spectra in dipolar systems along with results on some protonated liquid crystal systems. A simple operator formalism for the essential features of the time development is presented and some applications in progress are discussed
Bragg spectroscopy of a strongly interacting Fermi gas
We present a comprehensive study of the Bose-Einstein condensate to
Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic Li using Bragg
spectroscopy. A smooth transition from molecular to atomic spectra is observed
with a clear signature of pairing at and above unitarity. These spectra probe
the dynamic and static structure factors of the gas and provide a direct link
to two-body correlations. We have characterised these correlations and measured
their density dependence across the broad Feshbach resonance at 834 G.Comment: Replaced with published versio
Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas
The discrete Fourier transform is approximated by summing over part of the
terms with corresponding weights. The approximation reduces significantly the
requirement for computer memory storage and enhances the numerical computation
efficiency with several orders without loosing accuracy. As an example, we
apply the algorithm to study the three-dimensional interacting electron gas
under the renormalized-ring-diagram approximation where the Green's function
needs to be self-consistently solved. We present the results for the chemical
potential, compressibility, free energy, entropy, and specific heat of the
system. The ground-state energy obtained by the present calculation is compared
with the existing results of Monte Carlo simulation and random-phase
approximation.Comment: 11 pages, 13 figure
Nonlinear and adaptive estimation techniques in reentry
The development and testing of nonlinear and adaptive estimators for reentry (e.g. space shuttle) navigation and model parameter estimation or identification are reported. Of particular interest is the identifcation of vehicle lift and drag characteristics in real time. Several nonlinear filters were developed and simulated. Adaptive filters for the real time identification of vehicle lift and drag characteristics, and unmodelable acceleration, were also developed and tested by simulation. The simulations feature an uncertain system environment with rather arbitrary model errors, thus providing a definitive test of estimator performance. It was found that nonlinear effects are indeed significant in reentry trajectory estimation and a nonlinear filter is demonstrated which successfully tracks through nonlinearities without degrading the information content of the data. Under the same conditions the usual extended Kalman filter diverges and is useless. The J-adaptive filter is shown to successfully track errors in the modeled vehicle lift and drag characteristics. The same filter concept is also shown to track successfully through rather arbitrary model errors, including lift and drag errors, vehicle mass errors, atmospheric density errors, and wind gust errors
Comment on "Diffusion Monte Carlo study of jellium surfaces: Electronic densities and pair correlation functions"
In a fixed-node diffusion Monte Carlo calculation of the total energy of
jellium slabs, Acioli and Ceperley [Phys. Rev. B {\bf 54}, 17199 (1996)]
reported jellium surface energies that at low electron densities were
significantly higher than those predicted in the local-density approximation
(LDA) of density-functional theory. Assuming that the fixed-node error in the
slab and the bulk calculations cancel out, we show that their data yield
surface energies that are considerably closer to the LDA and in reasonable
agreement with those obtained in the random-phase approximation.Comment: 3 pages, 2 figures, to appear in Phys. Rev.
Umklapp collisions and center of mass oscillation of a trapped Fermi gas
Starting from the the Boltzmann equation, we study the center of mass
oscillation of a harmonically trapped normal Fermi gas in the presence of a
one-dimensional periodic potential. We show that for values of the the Fermi
energy above the first Bloch band the center of mass motion is strongly damped
in the collisional regime due to umklapp processes. This should be contrasted
with the behaviour of a superfluid where one instead expects the occurrence of
persistent Josephson-like oscillations.Comment: 11 pages, 3 figures, corrected typo
Generic strong coupling behavior of Cooper pairs in the surface of superfluid nuclei
With realistic HFB calculations, using the D1S Gogny force, we reveal a
generic behavior of concentration of small sized Cooper pairs (2-3 fm) in the
surface of superfluid nuclei. This study confirms and extends previous results
given in the literature that use more schematic approaches.Comment: 5 pages, 5 figure
Mesoscopic Transport: The Electron-Gas Sum Rules in a Driven Quantum Point Contact
The nature of the electron gas is characterized, above all, by its
multi-particle correlations. The conserving sum rules for the electron gas have
been thoroughly studied for many years, and their centrality to the physics of
metallic conduction is widely understood (at least in the many-body community).
We review the role of the conserving sum rules in mesoscopic transport, as
normative criteria for assessing the conserving status of mesoscopic models. In
themselves, the sum rules are specific enough to rule out any such theory if it
fails to respect the conservation laws. Of greater interest is the capacity of
the compressibility sum rule, in particular, to reveal unexpected fluctuation
effects in nonuniform mesoscopic structures.Comment: TeX, 11pp, no fi
Theory of the Optical Conductivity in the Cuprate Superconductors
We present a study of the normal state optical conductivity in the cuprate
superconductors using the nearly antiferromagnetic Fermi liquid (NAFL)
description of the magnetic interaction between their planar quasiparticles. We
find that the highly anisotropic scattering rate in different regions of the
Brillouin zone, both as a function of frequency and temperature, a benchmark of
NAFL theory, leads to an average relaxation rate of the Marginal Fermi Liquid
form for overdoped and optimally doped systems, as well as for underdoped
systems at high temperatures. We carry out numerical calculations of the
optical conductivity for several compounds for which the input spin fluctuation
parameters are known. Our results, which are in agreement with experiment on
both overdoped and optimally doped systems, show that NAFL theory explains the
anomalous optical behavior found in these cuprate superconductors.Comment: REVTEX file, 8 PostScript figure
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