29,295 research outputs found
Ladder operators and endomorphisms in combinatorial Physics
Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of Combinatorics. These may be expressed in terms of infinite, but row-finite, matrices, which may also be considered as endomorphisms of C[x]. This leads us to consider endomorphisms in more general spaces, and these in turn may be expressed in terms of generalizations of the ladder-operators familiar in physics
On a conjecture by Pierre Cartier about a group of associators
In \cite{cartier2}, Pierre Cartier conjectured that for any non commutative
formal power series on with coefficients in a
\Q-extension, , subjected to some suitable conditions, there exists an
unique algebra homomorphism from the \Q-algebra generated by the
convergent polyz\^etas to such that is computed from
Drinfel'd associator by applying to each coefficient. We prove
exists and it is a free Lie exponential over . Moreover, we give a
complete description of the kernel of polyz\^eta and draw some consequences
about a structure of the algebra of convergent polyz\^etas and about the
arithmetical nature of the Euler constant
Localization for Schrodinger operators with random vector potentials
We prove Anderson localization at the internal band-edges for periodic
magnetic Schr{\"o}dinger operators perturbed by random vector potentials of
Anderson-type. This is achieved by combining new results on the Lifshitz tails
behavior of the integrated density of states for random magnetic
Schr{\"o}dinger operators, thereby providing the initial length-scale estimate,
and a Wegner estimate, for such models
3D-2D analysis of a thin film with periodic microstructure
The purpose of this article is to study the behavior of a heterogeneous thin
film whose microstructure oscillates on a scale that is comparable to that of
the thickness of the domain. The argument is based on a 3D-2D dimensional
reduction through a -convergence analysis, techniques of two-scale
convergence and a decoupling procedure between the oscillating variable and the
in-plane variable.Comment: 19 page
Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators
In this paper, we consider one dimensional adiabatic quasi-periodic
Schr\"{o}dinger operators in the regime of strong resonant tunneling. We show
the emergence of a level repulsion phenomenon which is seen to be very
naturally related to the local spectral type of the operator: the more singular
the spectrum, the weaker the repulsion
Magnetization reversal behavior in complex shaped Co nanowires: a nanomagnet morphology optimization
A systematic micromagnetic study of the morphological characteristic effects
over the magnetic static properties of Co-based complex shaped nanowires is
presented. The relevance of each characteristic size (i.e. length L, diameter
d, and size of the nanowires head T) and their critical values are discussed in
the coercive field optimization goal. Our results strongly confirms that once
the aspect ratio (L/d) of the nanowire is bigger than around 10, the length is
no more the pertinent parameter and instead the internal diameter and the shape
of the nanowires play a key role. We attribute this behavior to the non uniform
distribution of the demagnetizing field which is localized in the nanowires
head and acts as a nucleation point for the incoherent magnetization reversal.
Finally, angular dependence of the magnetization are simulated and compared to
the case of a prolate spheroid for all considered morphologies.Comment: 7 pages, 6 figure
Lifting vector bundles to Witt vector bundles
Let be a prime, and let be a scheme of characteristic . Let be an integer. Denote by the scheme of Witt vectors
of length , built out of . The main objective of this paper concerns the
question of extending (=lifting) vector bundles on to vector bundles on
. After introducing the formalism of Witt-Frobenius Modules
and Witt vector bundles, we study two significant particular cases, for which
the answer is positive: that of line bundles, and that of the tautological
vector bundle of a projective space. We give several applications of our point
of view to classical questions in deformation theory---see the Introduction for
details. In particular, we show that the tautological vector bundle of the
Grassmannian does not extend to
, if . In the
Appendix, we give algebraic details on our (new) approach to Witt vectors,
using polynomial laws and divided powers. It is, we believe, very convenient to
tackle lifting questions.Comment: Enriched version, with an appendi
M\"obius inversion formula for monoids with zero
The M\"obius inversion formula, introduced during the 19th century in number
theory, was generalized to a wide class of monoids called locally finite such
as the free partially commutative, plactic and hypoplactic monoids for
instance. In this contribution are developed and used some topological and
algebraic notions for monoids with zero, similar to ordinary objects such as
the (total) algebra of a monoid, the augmentation ideal or the star operation
on proper series. The main concern is to extend the study of the M\"obius
function to some monoids with zero, i.e., with an absorbing element, in
particular the so-called Rees quotients of locally finite monoids. Some
relations between the M\"obius functions of a monoid and its Rees quotient are
also provided.Comment: 12 pages, r\'esum\'e \'etendu soumis \`a FPSAC 201
Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program
Computer programs may go wrong due to exceptional behaviors, out-of-bound
array accesses, or simply coding errors. Thus, they cannot be blindly trusted.
Scientific computing programs make no exception in that respect, and even bring
specific accuracy issues due to their massive use of floating-point
computations. Yet, it is uncommon to guarantee their correctness. Indeed, we
had to extend existing methods and tools for proving the correct behavior of
programs to verify an existing numerical analysis program. This C program
implements the second-order centered finite difference explicit scheme for
solving the 1D wave equation. In fact, we have gone much further as we have
mechanically verified the convergence of the numerical scheme in order to get a
complete formal proof covering all aspects from partial differential equations
to actual numerical results. To the best of our knowledge, this is the first
time such a comprehensive proof is achieved.Comment: N° RR-8197 (2012). arXiv admin note: text overlap with
arXiv:1112.179
A 2D nanosphere array for atomic spectroscopy
We are interested in the spectroscopic behaviour of a gas confined in a
micrometric or even nanometric volume. Such a situation could be encountered by
the filling-up of a porous medium, such as a photonic crystal, with an atomic
gas. Here, we discuss the first step of this program, with the generation and
characterization of a self-organized 2D film of nanospheres of silica. We show
that an optical characterization by laser light diffraction permits to extract
some information on the array structure and represents an interesting
complement to electron microscopy.Comment: accept\'e pour publication \`a Annales de Physique- proceedings of
COLOQ1
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