5,765 research outputs found
Algebraic methods in the theory of generalized Harish-Chandra modules
This paper is a review of results on generalized Harish-Chandra modules in
the framework of cohomological induction. The main results, obtained during the
last 10 years, concern the structure of the fundamental series of
modules, where is a semisimple Lie
algebra and is an arbitrary algebraic reductive in
subalgebra. These results lead to a classification of simple
modules of finite type with generic minimal
types, which we state. We establish a new result about the
Fernando-Kac subalgebra of a fundamental series module. In addition, we pay
special attention to the case when is an eligible subalgebra
(see the definition in section 4) in which we prove stronger versions of our
main results. If is eligible, the fundamental series of
modules yields a natural algebraic generalization
of Harish-Chandra's discrete series modules.Comment: Keywords : generalized Harish-Chandra module, (g,k)-module of finite
type, minimal k-type, Fernando-Kac subalgebra, eligible subalgebra; Pages no.
: 13; Bibliography : 21 item
Coupled opto-electronic simulation of organic bulk-heterojunction solar cells: parameter extraction and sensitivity analysis
A general problem arising in computer simulations is the number of material
and device parameters, which have to be determined by dedicated experiments and
simulation-based parameter extraction. In this study we analyze measurements of
the short-circuit current dependence on the active layer thickness and
current-voltage curves in poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid
methyl ester (P3HT:PCBM) based solar cells. We have identified a set of
parameter values including dissociation parameters that describe the
experimental data. The overall agreement of our model with experiment is good,
however a discrepancy in the thickness dependence of the current-voltage curve
questions the influence of the electric field in the dissociation process. In
addition transient simulations are analyzed which show that a measurement of
the turn-off photocurrent can be useful for estimating charge carrier
mobilities.Comment: 10 pages, 12 figures, 2 tables, Accepted for publication in Journal
of Applied Physic
Topological Exchange Statistics in One Dimension
The standard topological approach to indistinguishable particles formulates
exchange statistics by using the fundamental group to analyze the connectedness
of the configuration space. Although successful in two and more dimensions,
this approach gives only trivial or near trivial exchange statistics in one
dimension because two-body coincidences are excluded from configuration space.
Instead, we include these path-ambiguous singular points and consider
configuration space as an orbifold. This orbifold topological approach allows
unified analysis of exchange statistics in any dimension and predicts novel
possibilities for anyons in one-dimensional systems, including non-abelian
anyons obeying alternate strand groups. These results clarify the
non-topological origin of fractional statistics in one-dimensional anyon
models.Comment: v3: major revision and expansion from last edition; 16 pgs., 5 figs.,
109 ref
On the scattering theory of the classical hyperbolic C(n) Sutherland model
In this paper we study the scattering theory of the classical hyperbolic
Sutherland model associated with the C(n) root system. We prove that for any
values of the coupling constants the scattering map has a factorized form. As a
byproduct of our analysis, we propose a Lax matrix for the rational C(n)
Ruijsenaars-Schneider-van Diejen model with two independent coupling constants,
thereby setting the stage to establish the duality between the hyperbolic C(n)
Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.Comment: 15 page
Differential Calculi on Some Quantum Prehomogeneous Vector Spaces
This paper is devoted to study of differential calculi over quadratic
algebras, which arise in the theory of quantum bounded symmetric domains. We
prove that in the quantum case dimensions of the homogeneous components of the
graded vector spaces of k-forms are the same as in the classical case. This
result is well-known for quantum matrices.
The quadratic algebras, which we consider in the present paper, are
q-analogues of the polynomial algebras on prehomogeneous vector spaces of
commutative parabolic type. This enables us to prove that the de Rham complex
is isomorphic to the dual of a quantum analogue of the generalized
Bernstein-Gelfand-Gelfand resolution.Comment: LaTeX2e, 51 pages; changed conten
Use of Linear Free Energy Relationships (LFERs) to Elucidate the Mechanisms of Reaction of a Îł-Methyl-ÎČ-alkynyl and an ortho-Substituted Aryl Chloroformate Ester
The specific rates of solvolysis of 2-butyn-1-yl-chloroformate (1) and 2-methoxyphenyl chloroformate (2) are studied at 25.0 °C in a series of binary aqueousorganic mixtures. The rates of reaction obtained are then analyzed using the extended Grunwald-Winstein (G-W) equation and the results are compared to previously published G-W analyses for phenyl chloroformate (3), propargyl chloroformate (4), p-methoxyphenyl choroformate (5), and p-nitrophenyl chloroformate (6). For 1, the results indicate that dual side-by-side addition-elimination and ionization pathways are occurring in some highly ionizing solvents due to the presence of the electron-donating γ-methyl group. For 2, the analyses indicate that the dominant mechanism is a bimolecular one where the formation of a tetrahedral intermediate is rate-determining
Beyond braid anyons: A lattice model for one-dimensional anyons with a Galilean invariant continuum limit
Anyonic exchange statistics can emerge when the configuration space of
quantum particles is not simply-connected. Most famously, anyon statistics
arises for particles with hard-core two-body constraints in two dimensions.
Here, the exchange paths described by the braid group are associated to
non-trivial geometric phases, giving rise to abelian braid anyons. Hard-core
three-body constraints in one dimension (1D) also make the configuration space
of particles non-simply connected, and it was recently shown that this allows
for a different form of anyons with statistics given by the traid group instead
of the braid group. In this article we propose a first concrete model for such
traid anyons. We first construct a bosonic lattice model with number-dependent
Peierls phases which implement the desired geometric phases associated with
abelian representations of the traid group and then define anyonic operators so
that the Hamiltonian becomes local and quadratic with respect to them. The
ground-state of this traid-anyon-Hubbard model shows various indications of
emergent approximate Haldane exclusion statistics. The continuum limit results
in a Galilean invariant Hamiltonian with eigenstates that correspond to
previously constructed continuum traid-anyonic wave functions. This provides
not only an a-posteriori justification of our model, but also shows that our
construction serves as an intuitive approach to traid anyons. Moreover, it
contrasts with the non-Galilean invariant continuum limit of the anyon-Hubbard
model [Keilmann et al., Nat.\ Comm.~\textbf{2}, 361 (2011)] describing braid
anyons on a discrete 1D configuration space. We attribute this difference to
the fact that (unlike braid anyons) traid anyons are well defined also in the
continuum in 1D.Comment: 24 pages, 15 figure
Refining Nodes and Edges of State Machines
State machines are hierarchical automata that are widely used to structure complex behavioural specifications. We develop two notions of refinement of state machines, node refinement and edge refinement. We compare the two notions by means of examples and argue that, by adopting simple conventions, they can be combined into one method of refinement. In the combined method, node refinement can be used to develop architectural aspects of a model and edge refinement to develop algorithmic aspects. The two notions of refinement are grounded in previous work. Event-B is used as the foundation for our refinement theory and UML-B state machine refinement influences the style of node refinement. Hence we propose a method with direct proof of state machine refinement avoiding the detour via Event-B that is needed by UML-B
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