9,418 research outputs found
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
Noncommutative Blowups of Elliptic Algebras
We develop a ring-theoretic approach for blowing up many noncommutative
projective surfaces. Let T be an elliptic algebra (meaning that, for some
central element g of degree 1, T/gT is a twisted homogeneous coordinate ring of
an elliptic curve E at an infinite order automorphism). Given an effective
divisor d on E whose degree is not too big, we construct a blowup T(d) of T at
d and show that it is also an elliptic algebra. Consequently it has many good
properties: for example, it is strongly noetherian, Auslander-Gorenstein, and
has a balanced dualizing complex. We also show that the ideal structure of T(d)
is quite rigid. Our results generalise those of the first author. In the
companion paper "Classifying Orders in the Sklyanin Algebra", we apply our
results to classify orders in (a Veronese subalgebra of) a generic cubic or
quadratic Sklyanin algebra.Comment: 39 pages. Minor changes from previous version. The final publication
is available from Springer via http://dx.doi.org/10.1007/s10468-014-9506-
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
Noncommutative curves and noncommutative surfaces
In this survey article we describe some geometric results in the theory of
noncommutative rings and, more generally, in the theory of abelian categories.
Roughly speaking and by analogy with the commutative situation, the category
of graded modules modulo torsion over a noncommutative graded ring of
quadratic, respectively cubic growth should be thought of as the noncommutative
analogue of a projective curve, respectively surface. This intuition has lead
to a remarkable number of nontrivial insights and results in noncommutative
algebra. Indeed, the problem of classifying noncommutative curves (and
noncommutative graded rings of quadratic growth) can be regarded as settled.
Despite the fact that no classification of noncommutative surfaces is in sight,
a rich body of nontrivial examples and techniques, including blowing up and
down, has been developed.Comment: Suggestions by many people (in particular Haynes Miller and Dennis
Keeler) have been incorporated. The formulation of some results has been
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