8,738 research outputs found
Integrable systems and holomorphic curves
In this paper we attempt a self-contained approach to infinite dimensional
Hamiltonian systems appearing from holomorphic curve counting in Gromov-Witten
theory. It consists of two parts. The first one is basically a survey of
Dubrovin's approach to bihamiltonian tau-symmetric systems and their relation
with Frobenius manifolds. We will mainly focus on the dispersionless case, with
just some hints on Dubrovin's reconstruction of the dispersive tail. The second
part deals with the relation of such systems to rational Gromov-Witten and
Symplectic Field Theory. We will use Symplectic Field theory of
as a language for the Gromov-Witten theory of a closed symplectic manifold .
Such language is more natural from the integrable systems viewpoint. We will
show how the integrable system arising from Symplectic Field Theory of
coincides with the one associated to the Frobenius structure of
the quantum cohomology of .Comment: Partly material from a working group on integrable systems organized
by O. Fabert, D. Zvonkine and the author at the MSRI - Berkeley in the Fall
semester 2009. Corrected some mistake
Integrability, quantization and moduli spaces of curves
This paper has the purpose of presenting in an organic way a new approach to
integrable (1+1)-dimensional field systems and their systematic quantization
emerging from intersection theory of the moduli space of stable algebraic
curves and, in particular, cohomological field theories, Hodge classes and
double ramification cycles. This methods are alternative to the traditional
Witten-Kontsevich framework and its generalizations by Dubrovin and Zhang and,
among other advantages, have the merit of encompassing quantum integrable
systems. Most of this material originates from an ongoing collaboration with A.
Buryak, B. Dubrovin and J. Gu\'er\'e
Measuring Large Scale Space Perception in Literary Texts
The center and radius of perception associated with a written text are
defined, and algorithms for their computation are presented. Indicators for
anisotropy in large scale space perception are introduced. The relevance of
these notions for the analysis of literary and historical records is briefly
discussed and illustrated with an example taken from medieval historiography.Comment: 8 pages, 1 figur
Nijenhuis operator in contact homology and descendant recursion in symplectic field theory
In this paper we investigate the algebraic structure related to a new type of
correlator associated to the moduli spaces of -parametrized curves in
contact homology and rational symplectic field theory. Such correlators are the
natural generalization of the non-equivariant linearized contact homology
differential (after Bourgeois-Oancea) and give rise to an invariant Nijenhuis
(or hereditary) operator (\`a la Magri-Fuchssteiner) in contact homology which
recovers the descendant theory from the primaries. We also sketch how such
structure generalizes to the full SFT Poisson homology algebra to a (graded
symmetric) bivector. The descendant hamiltonians satisfy to recursion
relations, analogous to bihamiltonian recursion, with respect to the pair
formed by the natural Poisson structure in SFT and such bivector. In case the
target manifold is the product stable Hamiltonian structure , with
a symplectic manifold, the recursion coincides with genus topological
recursion relations in the Gromov-Witten theory of .Comment: 30 pages, 3 figure
Invariant expectation values in the sampling of discrete frequency distributions
The general relationship between an arbitrary frequency distribution and the
expectation value of the frequency distributions of its samples is discussed. A
wide set of measurable quantities ("invariant moments") whose expectation value
does not in general depend on the size of the sample is constructed and
illustrated by applying the results to Ewens sampling formula. Invariant
moments are especially useful in the sampling of systems characterized by the
absence of an intrinsic scale. Distribution functions that may parametrize the
samples of scale-free distributions are considered and their invariant
expectation values are computed. The conditions under which the scaling limit
of such distributions may exist are described.Comment: arXiv admin note: substantial text overlap with arXiv:1210.141
On the effective Lagrangian of CP^(N-1) models in the large N limit
The effective low energy Lagrangian of models in
dimensions can be constructed in the large limit by solving the saddle
point equations in the presence of a constant field strength. The two
dimensional case is explicitly worked out and possible applications are briefly
discussed
On the time dependence of the -index
The time dependence of the -index is analyzed by considering the average
behaviour of as a function of the academic age for about 1400 Italian
physicists, with career lengths spanning from 3 to 46 years. The individual
-index is strongly correlated with the square root of the total citations
: . For academic ages ranging from 12 to 24
years, the distribution of the time scaled index is
approximately time-independent and it is well described by the Gompertz
function. The time scaled index has an average approximately
equal to 3.8 and a standard deviation approximately equal to 1.6. Finally, the
time scaled index appears to be strongly correlated with the
contemporary -index
Generalized Crossover in multiparameter Hamiltonians
Many systems near criticality can be described by Hamiltonians involving
several relevant couplings and possessing many nontrivial fixed points. A
simple and physically appealing characterization of the crossover lines and
surfaces connecting different nontrivial fixed points is presented. Generalized
crossover is related to the vanishing of the RG function . An
explicit example is discussed in detail based on the tetragonal GLW
Hamiltonian.Comment: 4 pages, 1figur
Double Ramification Cycles and Quantum Integrable Systems
In this paper we define a quantization of the Double Ramification Hierarchies
of [Bur15b] and [BR14], using intersection numbers of the double ramification
cycle, the full Chern class of the Hodge bundle and psi-classes with a given
cohomological field theory. We provide effective recursion formulae which
determine the full quantum hierarchy starting from just one Hamiltonian, the
one associated with the first descendant of the unit of the cohomological field
theory only. We study various examples which provide, in very explicit form,
new -dimensional integrable quantum field theories whose classical
limits are well-known integrable hierarchies such as KdV, Intermediate Long
Wave, Extended Toda, etc. Finally we prove polynomiality in the ramification
multiplicities of the integral of any tautological class over the double
ramification cycle.Comment: Revised version, to be published in Letters in Mathematical Physics,
21 page
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