Matrix Models, Argyres-Douglas singularities and double scaling limits

We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level superpotential whose matrix model spectral curve develops an A_{n+1} Argyres-Douglas singularity. We evaluate the coupling constants of the low-energy U(1)^n theory and show that the large N expansion is singular at the Argyres-Douglas points. Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield four dimensional non-critical string theories as proposed by Ferrari. In the Argyres-Douglas limit the n-cut spectral curve degenerates into a solution with n/2 cuts for even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been corrected and the calculation of the coupling constants of the low-energy theory has been adde

Multi-Valley Superconductivity In Ion-Gated MoS2 Layers

Layers of transition metal dichalcogenides (TMDs) combine the enhanced effects of correlations associated with the two-dimensional limit with electrostatic control over their phase transitions by means of an electric field. Several semiconducting TMDs, such as MoS$_2$, develop superconductivity (SC) at their surface when doped with an electrostatic field, but the mechanism is still debated. It is often assumed that Cooper pairs reside only in the two electron pockets at the K/K' points of the Brillouin Zone. However, experimental and theoretical results suggest that a multi-valley Fermi surface (FS) is associated with the SC state, involving 6 electron pockets at the Q/Q' points. Here, we perform low-temperature transport measurements in ion-gated MoS$_2$ flakes. We show that a fully multi-valley FS is associated with the SC onset. The Q/Q' valleys fill for doping$\gtrsim2\cdot10^{13}$cm$^{-2}$, and the SC transition does not appear until the Fermi level crosses both spin-orbit split sub-bands Q$_1$ and Q$_2$. The SC state is associated with the FS connectivity and promoted by a Lifshitz transition due to the simultaneous population of multiple electron pockets. This FS topology will serve as a guideline in the quest for new superconductors.Comment: 12 pages, 7 figure

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure

Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at rates $p$ and $1-p$ (here $p>1/2$) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers' equation; the latter has shock solutions with a discontinuous jump from left density $\rho_-$ to right density $\rho_+$, $\rho_-<\rho_+$, which travel with velocity $(2p-1)(1-\rho_+-\rho_-)$. In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice site $n$, measured from this particle, approaches $\rho_{\pm}$ at an exponential rate as $n\to\pm\infty$, with a characteristic length which becomes independent of $p$ when $p/(1-p)>\sqrt{\rho_+(1-\rho_-)/\rho_-(1-\rho_+)}$. For a special value of the asymmetry, given by $p/(1-p)=\rho_+(1-\rho_-)/\rho_-(1-\rho_+)$, the measure is Bernoulli, with density $\rho_-$ on the left and $\rho_+$ on the right. In the weakly asymmetric limit, $2p-1\to0$, the microscopic width of the shock diverges as $(2p-1)^{-1}$. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle.Comment: 34 pages, LaTeX, 2 figures are included in the LaTeX file. Email: [email protected], [email protected], [email protected]

Singularities of N=1 Supersymmetric Gauge Theory and Matrix Models

In N=1 supersymmetric U(N) gauge theory with adjoint matter $\Phi$ and polynomial tree-level superpotential $W(\Phi)$, the massless fluctuations about each quantum vacuum are generically described by $U(1)^n$ gauge theory for some n. However, by tuning the parameters of $W(\Phi)$ to non-generic values, we can reach singular vacua where additional fields become massless. Using both the matrix model prescription and the strong-coupling approach, we study in detail three examples of such singularities: the singularities of the n=1 branch, intersections of n=1 and n=2 branches, and a class of N=1 Argyres-Douglas points. In all three examples, we find that the matrix model description of the low-energy physics breaks down in some way at the singularity.Comment: 29 pages, 1 figure. Revised section 1, fixed misprints in section 3.1, added clarifications and reference

The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories

We classify the physical observables in spontaneously broken nonlinearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical nonlinearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.Comment: 20 pages, 1 figur

A Nonconvex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries

Abstract. Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping; see, for example, Karatzas and Shreve [SIAM J. Control Optim., 22 (1984), pp. 856–877]. The aim of this paper is to inves-tigate how far connections of this type generalize to a nonconvex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a nonconvex infinite time horizon SSC problem whose state consists of an un-controlled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory. We analyze the geometry of the action and inaction regions by characterizing their (optimal) boundaries. Unlike the case of convex SSC problems we find that the optimal boundaries may be both reflecting and repelling and it is natural to interpret the problem as one of SSC with discretionary stopping

Air change rates and infection risk in school environments: Monitoring naturally ventilated classrooms in a northern Italian urban context

The importance of building ventilation in avoiding long-distance airborne transmission has been highlighted with the advent of the COVID-19 pandemics. Among others, school environments, in particular classrooms, present criticalities in the implementation of ventilation strategies and their impact on indoor air quality and risk of contagion. In this work, three naturally ventilated school buildings located in northern Italy have undergone monitoring at the end of the heating season. Environmental parameters, such as CO2 concentration and indoor/outdoor air temperature, have been recorded together with the window opening configurations to develop a two-fold analysis: i) the estimation of real air change rates through the transient mass balance equation method, and ii) the individual infection risk via the Wells-Riley equation. A strong statistical correlation has been found between the air change rates and the windows opening configuration by means of a window-to-volume ratio between the total opening area and the volume of the classroom, which has been used to estimate the individual infection risk. Results show that the European Standard recommendation for air renewal could be achieved by a window opening area of at least 1.5 m2, in the most prevailing Italian classrooms. Furthermore, scenarios in which the infector agent is a teacher show higher individual infection risk than those in which the infector is a student. In addition, the outcomes serve school staff as a reference to ensure adequate ventilation in classrooms and keep the risk of infection under control based on the number of the students and the volume of the classroom

Angiotensin-converting enzyme insertion/deletion polymorphism does not influence the restenosis rate after coronary stent implantation

Background. Experimental studies have shown an activation of the angiotensin-converting enzyme (ACE) system as a response to endothelial injury. Recent publications have elucidated the hypothesis that the ACE gene polymorphism may influence the level of late luminal loss after coronary stent implantation. It is still unclear whether the polymorphism of the angiotensin gene is a major predictor of the extent of neointimal hyperplasia. In this multicenter study, we therefore tested the relationship between the ACE gene polymorphism and the restenosis rate after coronary stent implantation. Methods: As a substudy of the optimization with intracoronary, ultrasound (ICUS) to reduce stent restenosis (OPTICUS) study, we analyzed ACE serum levels and the ACE gene polymorphism in 154 patients at 9 different centers. All patients underwent elective coronary stent implantation in a stenosis of a major coronary vessel. Balloon inflations were repeated until a satisfactory result was achieved in on-line quantitative coronary angiography or ICUS fulfilling the OPTICUS study criteria. After follow-up of 6 months, all patients underwent reangiography tinder identical projections as the baseline procedure. A blinded quantitative analysis of the initial procedure as well as the follow-up examinations were performed by an independent core laboratory. ACE gene polymorphism and ACE serum activity were measured at the 6-month follow-up in a double-blinded setting. Results: With respect to the ACE gene polymorphism, there were three subgroups: DID genotype (48 patients), ID (83 patients) and 11 (23 patients). The subgroups did not differ in regard to age, gender, extent of coronary artery disease, stenosis length, initial degree of stenosis or degree of stenosis after stent implantation. In all, 39 patients (25.3%) had significant restenosis: 12 DD patients (25.0%), 18 ID patients (21.7%) and 9 II patients (39.1%) (odds ratio 2.164, 95% confidence interval 0.853-5.493). We obtained the following results for ACE serum levels: 0.53 mumol/l/s in the DD subgroup, 0.29 mumol/l/s in the ID