arXiv
(422.153 recursos)
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Mostrando recursos 1 - 20 de 13.279
1.
Quantisation of Lie-Poisson manifolds - Racaniere, Sebastien
In quantum physics, the operators associated with the position and the
momentum of a particle are unbounded operators and $C^*$-algebraic quantisation
does therefore not deal with such operators. In the present article, I propose
a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid
which deals with a big enough class of functions to include the above mentioned
example. As an application, I show with an example how the quantisation of the
dual of the Lie algebroid associated to a Poisson manifold can lead to a
quantisation of the Poisson manifold itself. The example I consider is the
torus with constant Poisson structure, in which...
2.
Singular cotangent bundle reduction and spin Calogero-Moser systems - Hochgerner, Simon
We develop a bundle picture for the case that the configuration manifold has
only a single isotropy type, and give a formula for the reduced symplectic form
in this setting. Furthermore, as an application of this bundle picture we
consider Calogero-Moser systems with spin associated to polar representations
of compact Lie groups.
3.
KMS states and the chemical potential for disordered systems - Fidaleo, Francesco
We extend the theory of the chemical potential associated to a compact
separable gauge group to the case of disordered quantum systems. This is done
in the natural framework of operator algebras. Among the other results, we show
that the chemical potential does not depend on the disorder. The situation of
the $n$--torus is treated in some detail. Indeed, provided that the zero--point
is fixed independently on the disorder, the chemical potential is intrinsically
defined in terms of the direct integral decomposition of the
Connes--Radon--Nikodym cocycle associated to the KMS state $\omega$ and its
trasforms $\omega\circ\rho$ by the localized automorphisms $\rho$ of the
observable algebra, carrying the abelian charges...
4.
Hyper-K\"ahler quotients of solvable Lie groups - Barberis, M. L.; Dotti, I.; Fino, A.
In this paper we apply the hyper-K\"ahler quotient construction to Lie groups
with a left invariant hyper-K\"ahler structure under the action of a closed
abelian subgroup by left multiplication. This is motivated by the fact that
some known hyper-K\"ahler metrics can be recovered in this way by considering
different Lie group structures on $\H^p \times \H^q$ ($\H$: the quaternions).
We obtain new complete hyper-K\"ahler metrics on Euclidean spaces and give
their local expressions.
5.
Overtwisted energy-minimizing curl eigenfields - Ghrist, R.; Komendarczyk, R.
We consider energy-minimizing divergence-free eigenfields of the curl
operator in dimension three from the perspective of contact topology. We give a
negative answer to a question of Etnyre and the first author by constructing
curl eigenfields which minimize $L^2$ energy on their co-adjoint orbit, yet are
orthogonal to an overtwisted contact structure. We conjecture that $K$-contact
structures on $S^1$-bundles always define tight minimizers, and prove a partial
result in this direction.
6.
Classical Field theory on Lie algebroids: multisymplectic formalism - Martinez, Eduardo
The jet formalism for Classical Field theories is extended to the setting of
Lie algebroids. We define the analog of the concept of jet of a section of a
bundle and we study some of the geometric structures of the jet manifold. When
a Lagrangian function is given, we find the equations of motion in terms of a
Cartan form canonically associated to the Lagrangian. The Hamiltonian formalism
is also extended to this setting and we find the relation between the solutions
of both formalism. When the first Lie algebroid is a tangent bundle we give a
variational description of the equations of motion. In addition to...
7.
Quantum Hele-Shaw flow - Hedenmalm, Haakan; Makarov, Nikolai
In this note, we discuss the quantum Hele-Shaw flow, a random measure process
in the complex plane introduced by the physicists P.Wiegmann, A. Zabrodin, et
al. This process arises in the theory of electronic droplets confined to a
plane under a strong magnetic field, as well as in the theory of random normal
matrices. We extend a result of Elbau and Felder to general external field
potentials, and also show that if the potential is $C^2$-smooth, then the
quantum Hele-Shaw flow converges, under appropriate scaling, to the classical
(weighted) Hele-Shaw flow, which can be modeled in terms of an obstacle
problem.
8.
On the Mehlig-Wilkinson representation of metaplectic operators - de Gosson, Maurice A.
We study the Weyl representation of metaplectic operators studied by Mehlig
and Wilkinson. We give precise calculations ofthe associated Maslov indices;
these intervene in a crucial way in Gutzwiller's trace formula of semiclassical
mechanics.
10.
Fluctuation of planar Brownian loop capturing large area - Hammond, Alan; Peres, Yuval
We consider a planar Brownian loop $B$ that is run for a time $T$ and
conditioned on the event that its range encloses the unusually high area of
$\pi T^2$, with $T$ being large. We study the deviation of the range of the
conditioned process $X$ from a circle of radius $T$, as a model for the
fluctuation of a phase boundary. This deviation is measured by means of the
inradius and outradius of the region enclosed by the range of $X$. We prove
that in a typical realization of the conditioned measure, each of these
quantities differs from $T$ by at most $T^{2/3 + \epsilon}$.
11.
The initial drift of a 2D droplet at zero temperature - Cerf, Raphael; Louhichi, Sana
We consider the 2D stochastic Ising model evolving according to the Glauber
dynamics at zero temperature. We compute the initial drift for droplets which
are suitable approximations of smooth domains. A specific spatial average of
the derivative at time~0 of the volume variation of a droplet close to a
boundary point is equal to its curvature multiplied by a direction dependent
coefficient. We compute the explicit value of this coefficient.
12.
Moduli spaces of d-connections and difference Painleve equations - Arinkin, D.; Borodin, A.
We show that difference Painleve equations can be interpreted as isomorphisms
of moduli spaces of d-connections on the projective line with given singularity
structure. We also derive a new difference equation. It is the most general
difference Painleve equation known so far, and it degenerates to both
difference Painleve V and classical (differential) Painleve VI equations.
13.
A shadowing lemma for abelian Higgs vortices - Macri', Marta; Nolasco, Margherita; Ricciardi, Tonia
We use a shadowing-type lemma in order to analyze the singular, semilinear
elliptic equation describing static self-dual abelian Higgs vortices. Such an
approach allows us to construct new solutions having an \textit{infinite}
number of arbitrarily prescribed vortex points. Furthermore, we obtain the
precise asymptotic profile of the solutions in the form of an approximate
superposition rule, up to an error which is exponentially small.
14.
A Transform Method for Evolution PDEs on a Finite Interval - Fokas, A. S.; Pelloni, B.
We study initial boundary value problems for linear scalar partial
differential equations with constant coefficients, with spatial derivatives of
{\em arbitrary order}, posed on the domain $\{t>0, 0
15.
Boundary Value Problems for Linear PDEs with Variable Coefficients - Fokas, A. S.
A new method is introduced for studying boundary value problems for a class
of linear PDEs with {\it variable} coefficients. This method is based on ideas
recently introduced by the author for the study of boundary value problems for
PDEs with {\it constant} coefficients. As illustrative examples the following
boundary value problems are solved: (a) A Dirichlet and a Neumann problem on
the half line for the time-dependent Schr\"odinger equation with a space
dependent potential. (b) A Poincar\'e problem on the quarter plane for a
variable coefficient eneralisation of the Laplace equation.
16.
The Basic Elliptic Equations in an Equilateral Triangle - Dassios, G.; Fokas, A. S.
In his deep and prolific investigations of heat diffusion, Lam\'e was led to
the investigation of the eigenvalues and eigenfunctions of the Laplace operator
in an equilateral triangle. In particular he derived explicit results for the
Dirichlet and Neumann cases using an ingenious change of variables. The
relevant eigenfunctions are complicated infinite series in terms of his
variables. Here we first show that boundary value problems with simple boundary
conditions, such as the Dirichlet and the Neumann problems, can be solved in an
elementary manner. In particular for these problems, the unknown Neumann and
Dirichlet boundary values respectively, can be expressed in terms of a Fourier
series. Our analysis...
17.
Generalized complex structures and Lie brackets - Crainic, Marius
We look at generalized complex structures from the point of view of Poisson
and Dirac geometry and we remark that the puzzling equations underlying the
notion of generalized complex structure have miraculously simple meaning when
passing to Lie algebroids/groupoids.
18.
Computational methods and experiments in analytic number theory - Rubinstein, Michael O.
We cover some useful techniques in computational aspects of analytic number
theory, with specific emphasis on ideas relevant to the evaluation of
L-functions. These techniques overlap considerably with basic methods from
analytic number theory. On the elementary side, summation by parts, Euler
Maclaurin summation, and Mobius inversion play a prominent role. In the
slightly less elementary sphere, we find tools from analysis, such as Poisson
summation, generating function methods, Cauchy's residue theorem, asymptotic
methods, and the fast Fourier transform. We then describe conjectures and
experiments that connect number theory and random matrix theory.
19.
BV-generators and Lie algebroids - Michea, Sebastien; Novitchkov, Gleb
Let $A=A^0+A^1+A^2+...$ be a Gerstenhaber algebra generated by $A^0$ and
$A^1$. Given a degree -1 operator $D$ on $A^0 + A^1$, we find the condition on
$D$ that makes $A$ a BV-algebra. Subsequently, we apply it to the Gerstenhaber
or BV algebra associated to a Lie algebroid and obtain a global proof of the
correspondence between BV-generators and flat connections.
20.
Reidemeister torsion of a symplcetic complex - Sozen, Yasar
We consider a claim mentioned in \cite{Witten} pp 187 about the relation
between a symplectic chain complex with $\omega-$compatible bases and
Reidemeister Torsion of it. This is an explanation of it.
1.
