Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Carrier Concentration Control of GaSb/GaInAsSb System

International audienc

Structural, Optical and Electrical Characterizations of Midwave Infrared Ga-Free Type-II InAs/InAsSb Superlattice Barrier Photodetector

In this paper, a full set of structural, optical and electrical characterizations performed on midwave infrared barrier detectors based on a Ga-free InAs/InAsSb type-II superlattice, grown by molecular beam epitaxy (MBE) on a GaSb substrate, are reported and analyzed. a Minority carrier lifetime value equal to 1 µs at 80 K, carried out on dedicated structure showing photoluminescence peak position at 4.9 µm, is extracted from a time resolved photoluminescence measurement. Dark current density as low as 3.2 × 10−5 A/cm2 at 150 K is reported on the corresponding device exhibiting a 50% cut-off wavelength around 5 µm. A performance analysis through normalized spectral response and dark current density-voltage characteristics was performed to determine both the operating bias and the different dark current regimes

Magneto-spectroscopy investigation of InAs/InAsSb superlattices for midwave infrared detection

International audienc

Una nuova dedica a Ercole da un manoscritto di Bonifacius Amerbach

The manuscript C VI a 77, once belonged to the XVIth century humanist Bonifacius Amerbach and now preserved in the Universitätsbibliothek Basel, is not a high quality epigraphic manuscript, but includes at least a couple of Roman inscriptions elsewhere unknown. One of them, already published in the previous years, is a dedication to Iuppiter Optimus Maximus set by an eques singularis; the other one is a dedication to Hercules Invictus – here published for the first time - set, when he was an urban praetor, by L. Turranius Venustus Gratianus, member of a well known senatorial family of the III/IV century AD

The ubiquitous Prouhet-Thue-Morse sequence

We discuss a well-known binary sequence called the ThueMorse sequence, or the Prouhet-Thue-Morse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences