Dispersionless Hirota equations and the genus 3 hyperelliptic divisor

Equations of dispersionless Hirota type have been thoroughly investigated in the mathematical physics and differential geometry literature. It is known that the parameter space of integrable Hirota type equations in 3D is 21-dimensional and the action of the natural equivalence group Sp(6, R) on the parameter space has an open orbit. However the structure of the `master-equation' corresponding to this orbit remained elusive. Here we prove that the master-equation is specified by the vanishing of any genus 3 theta constant with even characteristic. The rich geometry of integrable Hirota type equations sheds new light on local differential geometry of the genus 3 hyperelliptic divisor, in particular, the integrability conditions can be viewed as local differential-geometric constraints that characterise the hyperelliptic divisor uniquely modulo Sp(6, C)-equivalence.Comment: amended version, to appear in Comm. Math. Phys., 15 page

Existence of mesons after deconfinement

We investigate the possibility for a quark-antiquark pair to form a bound state at temperatures higher than the critical one ($T>T_c$), thus after deconfinement. Our main goal is to find analytical criteria constraining the existence of such mesons. Our formalism relies on a Schr\"{o}dinger equation for which we study the physical consequences of both using the free energy and the internal energy as potential term, assuming a widely accepted temperature-dependent Yukawa form for the free energy and a recently proposed nonperturbative form for the screening mass. We show that using the free energy only allows for the 1S bottomonium to be bound above $T_c$, with a dissociation temperature around $1.5\times T_c$. The situation is very different with the internal energy, where we show that no bound states at all can exist in the deconfined phase. But, in this last case, quasi-bound states could be present at higher temperatures because of a positive barrier appearing in the potential.Comment: 14 pages, 3 figures; only the case T>T_c is discussed in v

Strains Induced by Point Defects in Graphene on a Metal

Strains strongly affect the properties of low-dimensional materials, such as graphene. By combining in situ, in operando, reflection high energy electron diffraction experiments with first-principles calculations, we show that large strains, above 2%, are present in graphene during its growth by chemical vapor deposition on Ir(111) and when it is subjected to oxygen etching and ion bombardment. Our results unravel the microscopic relationship between point defects and strains in epitaxial graphene and suggest new avenues for graphene nanostructuring and engineering its properties through introduction of defects and intercalation of atoms and molecules between graphene and its metal substrate

Modified Newton's law, braneworlds, and the gravitational quantum well

Most of the theories involving extra dimensions assume that only the gravitational interaction can propagate in them. In such approaches, called brane world models, the effective, 4-dimensional, Newton's law is modified at short as well as at large distances. Usually, the deformation of Newton's law at large distances is parametrized by a Yukawa potential, which arises mainly from theories with compactified extra dimensions. In many other models however, the extra dimensions are infinite. These approaches lead to a large distance power-law deformation of the gravitational newtonian potential $V_N(r)$, namely $V(r)=(1+k_b/r^b)V_N(r)$, which is less studied in the literature. We investigate here the dynamics of a particle in a gravitational quantum well with such a power-law deformation. The effects of the deformation on the energy spectrum are discussed. We also compare our modified spectrum to the results obtained with the GRANIT experiment, where the effects of the Earth's gravitational field on quantum states of ultra cold neutrons moving above a mirror are studied. This comparison leads to upper bounds on $b$ and $k_b$.Comment: 11 pages, 1 figur

Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy

We present a generalization of the classical Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] to quantum systems. The algorithm proceeds by stochastically evaluating the coefficients of a high temperature series expansion or a finite temperature perturbation expansion to arbitrary order. Similar to their classical counterpart, the algorithms are efficient at thermal and quantum phase transitions, greatly reducing the tunneling problem at first order phase transitions, and allow the direct calculation of the free energy and entropy.Comment: Added a plot showing the efficiency at first order phase transition

Interacting classical dimers on the square lattice

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett.{\bf 61}, 2376 (1988)]. By means of Monte Carlo and Transfer Matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.Comment: 4 pages, 4 figures; v2 : Added results on doped models; published versio

The Message Complexity of Distributed Graph Optimization

The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization problems. We focus on four classical graph optimization problems: Maximum Matching (MaxM), Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). In the sequential setting, these problems are representative of a wide spectrum of hardness of approximation. While there has been some progress in understanding the round complexity of distributed algorithms (for both exact and approximate versions) for these problems, much less is known about their message complexity and its relation with the quality of approximation. We almost fully quantify the message complexity of distributed graph optimization by showing the following results...[see paper for full abstract

Chiral molecule formation in interstellar ice analogs: alpha-aminoethanol NH 2 CH(CH 3 )OH

International audienceAims. Aminoalcohol molecules such as alpha-aminoethanol NH 2 CH(CH 3)OH may be aminoacid precursors. We attempt to charac-terize and detect this kind of molecules which is important to establish a possible link between interstellar molecules and life as we know it on Earth. Methods. We use Fourier transform infrared (FTIR) spectroscopy and mass spectrometry to study the formation of alpha-aminoethanol NH 2 CH(CH 3)OH in H 2 O:NH 3 : CH 3 CHO ice mixtures. Isotopic substitution with 15 NH 3 and ab-initio calculation are used to confirm the identification of alpha-aminoethanol. Results. After investigating the thermal reaction of solid NH 3 and acetaldehyde CH 3 CHO at low temperature, we find that this reac-tion leads to the formation of a chiral molecule, the alpha aminoethanol NH 2 CH(CH 3)OH. For the first time, we report the infrared and mass spectra of this molecule. We also report on its photochemical behavior under VUV irradiation. We find that the main photo-product is acetamide (NH 2 COCH 3). Data provided in this work indicates that alpha-aminoethanol is formed in one hour at 120 K and suggests that its formation in warm interstellar environments such as protostellar envelopes or cometary environments is likely

Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space

In this paper we provide a new proof that the Grosse-Wulkenhaar non-commutative scalar Phi^4_4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).Comment: 32 pages, v2: correction of lemmas 3.1 and 3.2 with no consequence on the main resul

Stability of the thermohaline circulation examined with a one-dimensional fluid loop

The Stommel box model elegantly demonstrates that the oceanic response to mixed boundary conditions, combining a temperature relaxation with a fixed salt flux forcing, is nonlinear owing to the so-called salt advection feedback. This nonlinearity produces a parameter range of bi-stability associated with hysteresis effects characterised by a fast thermally-driven mode and a slow salinity-driven mode. Here we investigate whether a similar dynamical behaviour can be found in the thermohaline loop model, a one-dimensional analogue of the box model. A semi-analytical method to compute possible steady states of the loop model is presented, followed by a linear stability analysis carried out for a large range of loop configurations. While the salt advection feedback is found as in the box model, a major difference is obtained for the fast mode: an oscillatory instability is observed near the turning point of the fast mode branch, such that the range of bi-stability is systematically reduced, or even removed, in some cases. The oscillatory instability originates from a salinity anomaly that grows exponentially as it turns around the loop, a situation that may occur only when the salinity torque is directed against the loop flow. Factors such as mixing intensity, the relative strength of thermal and haline forcings, the nonlinearity of the equation of state or the loop geometry can strongly affect the stability properties of the loop