3,253 research outputs found
Finite size scaling of current fluctuations in the totally asymmetric exclusion process
We study the fluctuations of the current J(t) of the totally asymmetric
exclusion process with open boundaries. Using a density matrix renormalization
group approach, we calculate the cumulant generating function of the current.
This function can be interpreted as a free energy for an ensemble in which
histories are weighted by exp(-sJ(t)). We show that in this ensemble the model
has a first order space-time phase transition at s=0. We numerically determine
the finite size scaling of the cumulant generating function near this phase
transition, both in the non-equilibrium steady state and for large times.Comment: 18 pages, 11 figure
Deformations of modules of differential forms
We study non-trivial deformations of the natural action of the Lie algebra
on the space of differential forms on . We calculate abstractions for integrability of infinitesimal
multi-parameter deformations and determine the commutative associative algebra
corresponding to the miniversal deformation in the sense of \cite{ff}.Comment: Published by JNMP at http://www.sm.luth.se/math/JNM
Conformally equivariant quantization: Existence and uniqueness
We prove the existence and the uniqueness of a conformally equivariant symbol
calculus and quantization on any conformally flat pseudo-Riemannian manifold
(M,\rg). In other words, we establish a canonical isomorphism between the
spaces of polynomials on and of differential operators on tensor
densities over , both viewed as modules over the Lie algebra \so(p+1,q+1)
where . This quantization exists for generic values of the weights
of the tensor densities and compute the critical values of the weights yielding
obstructions to the existence of such an isomorphism. In the particular case of
half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio
Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
Let be an odd-dimensional Euclidean space endowed with a contact 1-form
. We investigate the space of symmetric contravariant tensor fields on
as a module over the Lie algebra of contact vector fields, i.e. over the
Lie subalgebra made up by those vector fields that preserve the contact
structure. If we consider symmetric tensor fields with coefficients in tensor
densities, the vertical cotangent lift of contact form is a contact
invariant operator. We also extend the classical contact Hamiltonian to the
space of symmetric density valued tensor fields. This generalized Hamiltonian
operator on the symbol space is invariant with respect to the action of the
projective contact algebra . The preceding invariant operators lead
to a decomposition of the symbol space (expect for some critical density
weights), which generalizes a splitting proposed by V. Ovsienko
Differential operators on supercircle: conformally equivariant quantization and symbol calculus
We consider the supercircle equipped with the standard contact
structure. The conformal Lie superalgebra K(1) acts on as the Lie
superalgebra of contact vector fields; it contains the M\"obius superalgebra
. We study the space of linear differential operators on weighted
densities as a module over . We introduce the canonical isomorphism
between this space and the corresponding space of symbols and find interesting
resonant cases where such an isomorphism does not exist
Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold
Let be a manifold and be the cotangent bundle. We introduce a
1-cocycle on the group of diffeomorphisms of with values in the space of
linear differential operators acting on When is the
-dimensional sphere, , we use this 1-cocycle to compute the
first-cohomology group of the group of diffeomorphisms of , with
coefficients in the space of linear differential operators acting on
contravariant tensor fields.Comment: arxiv version is already officia
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