13,682 research outputs found
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, 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 flakes. We show that a fully multi-valley FS is associated with the SC
onset. The Q/Q' valleys fill for dopingcm, and the
SC transition does not appear until the Fermi level crosses both spin-orbit
split sub-bands Q and Q. 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 and (here ) 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 to right density , , which
travel with velocity . 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 , measured from this particle,
approaches at an exponential rate as , with a
characteristic length which becomes independent of when
. For a special value of the
asymmetry, given by , the measure is
Bernoulli, with density on the left and on the right. In the
weakly asymmetric limit, , the microscopic width of the shock
diverges as . 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 and
polynomial tree-level superpotential , the massless fluctuations about
each quantum vacuum are generically described by gauge theory for some
n. However, by tuning the parameters of 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
Orchestrating Tuple-based Languages
The World Wide Web can be thought of as a global computing architecture supporting the deployment of distributed networked applications. Currently, such applications can be programmed by resorting mainly to two distinct paradigms: one devised for orchestrating distributed services, and the other designed for coordinating distributed (possibly mobile) agents. In this paper, the issue of designing a pro-
gramming language aiming at reconciling orchestration and coordination is investigated. Taking as starting point the orchestration calculus Orc and the tuple-based coordination language Klaim, a new formalism is introduced combining concepts and primitives of the original calculi.
To demonstrate feasibility and effectiveness of the proposed approach, a prototype implementation of the new formalism is described and it is then used to tackle a case study dealing with a simplified but realistic electronic marketplace, where a number of on-line stores allow client
applications to access information about their goods and to place orders
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