148 research outputs found

### A construction of Frobenius manifolds with logarithmic poles and applications

A construction theorem for Frobenius manifolds with logarithmic poles is
established. This is a generalization of a theorem of Hertling and Manin. As an
application we prove a generalization of the reconstruction theorem of
Kontsevich and Manin for projective smooth varieties with convergent
Gromov-Witten potential. A second application is a construction of Frobenius
manifolds out of a variation of polarized Hodge structures which degenerates
along a normal crossing divisor when certain generation conditions are
fulfilled.Comment: 46 page

### A canonical Frobenius structure

We show that it makes sense to speak of THE Frobenius manifold attached to a
convenient and nondegenerate Laurent polynomialComment: 24 page

### tt*-geometry on the big phase space

The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a Hermitian geometry on the big phase space.
Using the approach of Dijkgraaf and Witten, we lift various geometric structures of the small phase space to the big phase space. The main results of our paper state that various notions from tt*-geometry are preserved under such liftings

### Interval total colorings of graphs

A total coloring of a graph $G$ is a coloring of its vertices and edges such
that no adjacent vertices, edges, and no incident vertices and edges obtain the
same color. An \emph{interval total $t$-coloring} of a graph $G$ is a total
coloring of $G$ with colors $1,2,\...,t$ such that at least one vertex or edge
of $G$ is colored by $i$, $i=1,2,\...,t$, and the edges incident to each vertex
$v$ together with $v$ are colored by $d_{G}(v)+1$ consecutive colors, where
$d_{G}(v)$ is the degree of the vertex $v$ in $G$. In this paper we investigate
some properties of interval total colorings. We also determine exact values of
the least and the greatest possible number of colors in such colorings for some
classes of graphs.Comment: 23 pages, 1 figur

### RCS043938-2904.9: A New Rich Cluster of Galaxies at z=0.951

We present deep I, J_s, K_s imaging and optical spectroscopy of the newly
discovered Red-Sequence Cluster Survey cluster RCS043938-2904.9. This cluster,
drawn from an extensive preliminary list, was selected for detailed study on
the basis of its apparent optical richness. Spectroscopy of 11 members places
the cluster at z=0.951 +- 0.006, and confirms the photometric redshift estimate
from the (R-z) color-magnitude diagram. Analysis of the infrared imaging data
demonstrates that the cluster is extremely rich, with excess counts in the
Ks-band exceeding the expected background counts by 9 sigma. The properties of
the galaxies in RCS043938-2904.9 are consistent with those seen in other
clusters at similar redshifts. Specifically, the red-sequence color, slope and
scatter, and the size-magnitude relation of these galaxies are all consistent
with that seen in the few other high redshift clusters known, and indeed are
consistent with appropriately evolved properties of local cluster galaxies. The
apparent consistency of these systems implies that the rich, high-redshift RCS
clusters are directly comparable to the few other systems known at z ~ 1, most
of which have been selected on the basis of X-ray emission.Comment: 12 pages, 1 color figure. Accepted for publication on The ApJ Letter

### Macroscopic conductivity of free fermions in disordered media

We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint starting with [1-3]. We show, in particular, the existence and finiteness of the conductivity measure Å’ÂºÅ’Â£ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, Å’ÂºÅ’Â£ converges in the weak*-topology to the trivial measure in the case of perfect insulators (strong disorder, complete localization), whereas in the limit of perfect conductors (absence of disorder) it converges to an atomic measure concentrated at frequency Å’Î© = 0. However, the AC-conductivity Å’ÂºÅ’Â£| â€šÃ‘Ã¹\{0} does not vanish in general: We show that Å’ÂºÅ’Â£(â€šÃ‘Ã¹\{0}) > 0, at least for large temperatures and a certain regime of small disorder

### AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media

We extend (Bru et al. in J Math Phys 56:051901-1-51, 2015) in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric field that is time- and space-dependent. We obtain the notion of a macroscopic AC-conductivity measure which only results from the second principle of thermodynamics. The latter corresponds here to the positivity of the heat production for cyclic processes on equilibrium states. Its Fourier transform is a continuous bounded function which is naturally called (macroscopic) conductivity. We additionally derive Greenâ€“Kubo relations involving time-correlations of bosonic fields coming from current fluctuations in the system. This is reminiscent of non-commutative central limit theorems

### Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles

We consider free lattice fermions subjected to a static bounded potential and
a time- and space-dependent electric field. For any bounded convex region
$\mathcal{R}\subset \mathbb{R}^{d}$ ($d\geq 1$) of space, electric fields
$\mathcal{E}$ within $\mathcal{R}$ drive currents. At leading order, uniformly
with respect to the volume $\left| \mathcal{R}\right|$ of $\mathcal{R}$ and
the particular choice of the static potential, the dependency on $\mathcal{E}$
of the current is linear and described by a conductivity distribution. Because
of the positivity of the heat production, the real part of its Fourier
transform is a positive measure, named here (microscopic) conductivity measure
of $\mathcal{R}$, in accordance with Ohm's law in Fourier space. This finite
measure is the Fourier transform of a time-correlation function of current
fluctuations, i.e., the conductivity distribution satisfies Green-Kubo
relations. We additionally show that this measure can also be seen as the
boundary value of the Laplace-Fourier transform of a so-called quantum current
viscosity. The real and imaginary parts of conductivity distributions satisfy
Kramers-Kronig relations. At leading order, uniformly with respect to
parameters, the heat production is the classical work performed by electric
fields on the system in presence of currents. The conductivity measure is
uniformly bounded with respect to parameters of the system and it is never the
trivial measure $0\,\mathrm{d}\nu$. Therefore, electric fields generally
produce heat in such systems. In fact, the conductivity measure defines a
quadratic form in the space of Schwartz functions, the Legendre-Fenchel
transform of which describes the resistivity of the system. This leads to
Joule's law, i.e., the heat produced by currents is proportional to the
resistivity and the square of currents

### Quantum deformations of associative algebras and integrable systems

Quantum deformations of the structure constants for a class of associative
noncommutative algebras are studied. It is shown that these deformations are
governed by the quantum central systems which has a geometrical meaning of
vanishing Riemann curvature tensor for Christoffel symbols identified with the
structure constants. A subclass of isoassociative quantum deformations is
described by the oriented associativity equation and, in particular, by the
WDVV equation. It is demonstrated that a wider class of weakly (non)associative
quantum deformations is connected with the integrable soliton equations too. In
particular, such deformations for the three-dimensional and
infinite-dimensional algebras are described by the Boussinesq equation and KP
hierarchy, respectively.Comment: Numeration of the formulas is correcte

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