5,233 research outputs found
The Auslander-Gorenstein property for Z-algebras
We provide a framework for part of the homological theory of Z-algebras and
their generalizations, directed towards analogues of the Auslander-Gorenstein
condition and the associated double Ext spectral sequence that are useful for
enveloping algebras of Lie algebras and related rings. As an application, we
prove the equidimensionality of the characteristic variety of an irreducible
representation of the Z-algebra, and for related representations over quantum
symplectic resolutions. In the special case of Cherednik algebras of type A,
this answers a question raised by the authors.Comment: 31 page
Comment on "Density Functional Simulation of a Breaking Nanowire"
In a recent Letter, Nakamura et al. [Phys. Rev. Lett. 82, 1538 (1999)]
described first principles calculations for a breaking Na nanocontact. Their
system consists of a periodic one-dimensional array of supercells, each of
which contains 39 Na atoms, originally forming a straight, crystalline wire
with a length of 6 atoms. The system is elongated by increasing the length of
the unit cell. At each step, the atomic configuration is relaxed to a new local
equilibrium, and the tensile force is evaluated from the change of the total
energy with elongation. Aside from a discontinuity of the force occuring at the
transition from a crytalline to an amorphous configuration during the early
stages of elongation, they were unable to identify any simple correlations
between the force and the number of electronic modes transmitted through the
contact. An important question is whether their model is realistic, i.e.,
whether it can be compared to experimental results obtained for a single
nanocontact between two macroscopic pieces of metal. In this Comment, we
demonstrate that with such a small unit cell, the interference effects between
neighboring contacts are of the same size as the force oscillations in a single
nanocontact.Comment: 1 pag
Many-body theory of electronic transport in single-molecule heterojunctions
A many-body theory of molecular junction transport based on nonequilibrium
Green's functions is developed, which treats coherent quantum effects and
Coulomb interactions on an equal footing. The central quantity of the many-body
theory is the Coulomb self-energy matrix of the junction.
is evaluated exactly in the sequential tunneling limit, and
the correction due to finite tunneling width is evaluated self-consistently
using a conserving approximation based on diagrammatic perturbation theory on
the Keldysh contour. Our approach reproduces the key features of both the
Coulomb blockade and coherent transport regimes simultaneously in a single
unified transport theory. As a first application of our theory, we have
calculated the thermoelectric power and differential conductance spectrum of a
benzenedithiol-gold junction using a semi-empirical -electron Hamiltonian
that accurately describes the full spectrum of electronic excitations of the
molecule up to 8--10eV.Comment: 13 pages, 7 figure
Correlated charge polarization in a chain of coupled quantum dots
Coherent charge transfer in a linear array of tunnel-coupled quantum dots,
electrostatically coupled to external gates, is investigated using the Bethe
ansatz for a symmetrically biased Hubbard chain. Charge polarization in this
correlated system is shown to proceed via two distinct processes: formation of
bound states in the metallic phase, and charge transfer processes corresponding
to a superposition of antibound states at opposite ends of the chain in the
Mott-insulating phase. The polarizability in the insulating phase of the chain
exhibits a universal scaling behavior, while the polarization charge in the
metallic phase of the model is shown to be quantized in units of .Comment: 9 pages, 3 figures, 1 tabl
An Outbreak of Salmonella typhimurium at a teaching hospital
An outbreak of Salmonella typhimurium infection in December 1996 affected 52 patients, relatives, and staff of a large teaching hospital in southeast Queensland. Assorted sandwiches were identified as the vehicle of transmission. This article describes the outbreak investigation and demonstrates the importance of food hygiene and timely public health interventions
Transport Properties of One-Dimensional Hubbard Models
We present results for the zero and finite temperature Drude weight D(T) and
for the Meissner fraction of the attractive and the repulsive Hubbard model, as
well as for the model with next nearest neighbor repulsion. They are based on
Quantum Monte Carlo studies and on the Bethe ansatz. We show that the Drude
weight is well defined as an extrapolation on the imaginary frequency axis,
even for finite temperature. The temperature, filling, and system size
dependence of D is obtained. We find counterexamples to a conjectured
connection of dissipationless transport and integrability of lattice models.Comment: 10 pages, 14 figures. Published versio
An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization
In this paper we develop an axiomatic setup for algorithmic homological
algebra of Abelian categories. This is done by exhibiting all existential
quantifiers entering the definition of an Abelian category, which for the sake
of computability need to be turned into constructive ones. We do this
explicitly for the often-studied example Abelian category of finitely presented
modules over a so-called computable ring , i.e., a ring with an explicit
algorithm to solve one-sided (in)homogeneous linear systems over . For a
finitely generated maximal ideal in a commutative ring we
show how solving (in)homogeneous linear systems over can be
reduced to solving associated systems over . Hence, the computability of
implies that of . As a corollary we obtain the computability
of the category of finitely presented -modules as an Abelian
category, without the need of a Mora-like algorithm. The reduction also yields,
as a by-product, a complexity estimation for the ideal membership problem over
local polynomial rings. Finally, in the case of localized polynomial rings we
demonstrate the computational advantage of our homologically motivated
alternative approach in comparison to an existing implementation of Mora's
algorithm.Comment: Fixed a typo in the proof of Lemma 4.3 spotted by Sebastian Posu
Stability and Symmetry Breaking in Metal Nanowires
A general linear stability analysis of simple metal nanowires is presented
using a continuum approach which correctly accounts for material-specific
surface properties and electronic quantum-size effects. The competition between
surface tension and electron-shell effects leads to a complex landscape of
stable structures as a function of diameter, cross section, and temperature. By
considering arbitrary symmetry-breaking deformations, it is shown that the
cylinder is the only generically stable structure. Nevertheless, a plethora of
structures with broken axial symmetry is found at low conductance values,
including wires with quadrupolar, hexapolar and octupolar cross sections. These
non-integrable shapes are compared to previous results on elliptical cross
sections, and their material-dependent relative stability is discussed.Comment: 12 pages, 4 figure
Rabi Oscillations at Exceptional Points in Microwave Billiards
We experimentally investigated the decay behavior with time t of resonances
near and at exceptional points, where two complex eigenvalues and also the
associated eigenfunctions coalesce. The measurements were performed with a
dissipative microwave billiard, whose shape depends on two parameters. The
t^2-dependence predicted at the exceptional point on the basis of a two-state
matrix model could be verified. Outside the exceptional point the predicted
Rabi oscillations, also called quantum echoes in this context, were detected.
To our knowledge this is the first time that quantum echoes related to
exceptional points were observed experimentally.Comment: 10 pages, 3 figure
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