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 μΣ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, μΣ 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 ν = 0. However, the AC-conductivity μΣ| ℝ\{0} does not vanish in general: We show that μΣ(ℝ\{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 Green–Kubo relations involving time-correlations of bosonic fields coming from current fluctuations in the system. This is reminiscent of non-commutative central limit theorems

Quasars Clustering at z approx 3 on Scales less sim 10 h^{-1} Mpc

We test the hypothesis whether high redshift QSOs would preferentially appear in small groups or pairs, and if they are associated with massive, young clusters. We carried out a photometric search for \Ly emitters on scales $\lesssim 10 h^{-1}$ Mpc, in the fields of a sample of 47 $z\approx3$ known QSOs. Wide and narrow band filter color-magnitude diagrams were generated for each of the $6'.6\times6'.6$ fields. A total of 13 non resolved objects with a significant color excess were detected as QSO candidates at a redshift similar to that of the target. All the candidates are significantly fainter than the reference QSOs, with only 2 of them within 2 magnitudes of the central object. Follow-up spectroscopic observations have shown that 5, i.e., about 40% of the candidates, are QSOs at the same redshift of the target; 4 are QSOs at different z (two of them probably being a lensed pair at z = 1.47); 2 candidates are unresolved HII galaxies at z$\sim$0.3; one unclassified and one candidate turned out to be a CCD flaw. These data indicate that at least 10% of the QSOs at z$\sim$3 do have companions. We have also detected a number of resolved, rather bright \Ly Emitter Candidates. Most probably a large fraction of them might be bright galaxies with [OII] emission, at z$\approx$ 0.3. The fainter population of our candidates corresponds to the current expectations. Thus, there are no strong indication for the existence of an overdensity of \Ly galaxies brighter than m $\approx$ 25 around QSOs at $z\approx$ 3.Comment: 29 pages, 8 figures, tar gzip LaTex file, accepted to appear in Ap

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

Computation with Advice

Computation with advice is suggested as generalization of both computation with discrete advice and Type-2 Nondeterminism. Several embodiments of the generic concept are discussed, and the close connection to Weihrauch reducibility is pointed out. As a novel concept, computability with random advice is studied; which corresponds to correct solutions being guessable with positive probability. In the framework of computation with advice, it is possible to define computational complexity for certain concepts of hypercomputation. Finally, some examples are given which illuminate the interplay of uniform and non-uniform techniques in order to investigate both computability with advice and the Weihrauch lattice

ACS Observations of a Strongly Lensed Arc in a Field Elliptical

We report the discovery of a strongly lensed arc system around a field elliptical galaxy in Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) images of a parallel field observed during NICMOS observations of the HST Ultra-Deep Field. The ACS parallel data comprise deep imaging in the F435W, F606W, F775W, and F850LP bandpasses. The main arc is at a radius of 1.6 arcsec from the galaxy center and subtends about 120 deg. Spectroscopic follow-up at Magellan Observatory yields a redshift z=0.6174 for the lensing galaxy, and we photometrically estimate z_phot = 2.4\pm0.3 for the arc. We also identify a likely counter-arc at a radius of 0.6 arcsec, which shows structure similar to that seen in the main arc. We model this system and find a good fit to an elliptical isothermal potential of velocity dispersion $\sigma \approx 300$ \kms, the value expected from the fundamental plane, and some external shear. Several other galaxies in the field have colors similar to the lensing galaxy and likely make up a small group.Comment: Accepted for publication in ApJ Letters. 10 pages, 3 figures. Figures have been degraded to meet size limit; a higher resolution version and addtional pictures available at http://acs.pha.jhu.edu/~jpb/UDFparc

Results of the ontology alignment evaluation initiative 2019

The Ontology Alignment Evaluation Initiative (OAEI) aims at comparing ontology matching systems on precisely defined test cases. These test cases can be based on ontologies of different levels of complexity (from simple thesauri to expressive OWL ontologies) and use different evaluation modalities (e.g., blind evaluation, open evaluation, or consensus). The OAEI 2019 campaign offered 11 tracks with 29 test cases, and was attended by 20 participants. This paper is an overall presentation of that campaign

Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte