On Eigenvalue spacings for the 1-D Anderson model with singular site distribution

We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main additional new input are regular properties of the Furstenberg measures and the density of states obtained in some of the author's earlier work.Comment: 13 page

The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Large deviations for clocks of self-similar processes

The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a L\'evy process drifting to $\infty$ and its inverse, the clock of the corresponding positive self-similar process. We describe here asymptotical properties of these clocks in large time, extending the results of Yor and Zani

Noncommutative fields in three dimensions and mass generation

We apply the noncommutative fields method for gauge theory in three dimensions where the Chern-Simons term is generated in the three-dimensional electrodynamics. Under the same procedure, the Chern-Simons term is shown to be cancelled in the Maxwell-Chern-Simons theory for the appropriate value of the noncommutativity parameter. Hence the mutual interchange between Maxwell-Chern-Simons theory and pure Maxwell theory turns out to be generated within this method.Comment: Comments 5 pages, epl, version accepted for publication in Europhysics Letter

Singular diffusion and criticality in a confined sandpile

We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to derive a continuum nonlinear diffusion equation that displays singularities in both the diffusion and drift terms. The stationary-state solutions of this equation, which maximizes the Fermi-Dirac entropy, are in perfect agreement with the spatial profiles of time-averaged occupancy obtained from model numerical simulations in one as well as in two dimensions. Surprisingly, our results also show that, regardless of dimensionality, the presence of a confining potential can lead to the emergence of typical attributes of critical behavior in the two-state sandpile model, namely, a power-law tail in the distribution of avalanche sizes.Comment: 5 pages, 5 figure

What does it mean to be a “citizen of the world”: A prototype approach

The superordinate social category “citizen of the world” is used by laypeople and scholars to embody several constructs (e.g., cosmopolitanism; global identity and citizenship), and prior research suggests that the concept is better represented as a prototype rather than having a clear-cut definition. This research aims to systematically examine the prototypical meaning of this social category, and how it is cognitively processed. Relying on a prototype approach, six studies (n = 448) showed that certain attributes of this category were communicated more frequently and were regarded as more central (e.g., multiculturalism), and that central (vs. peripheral) attributes were more quickly identified, more often remembered, and more appropriate to identify a group member, as well as the self, as a “citizen of the world.” These results systematically demonstrated that this category has a prototypical structure and there is a differentiated cognitive automatic processing for central and peripheral attributes. We propose that the specific content activated by the attributes regarded as central to the prototype of “citizens of the world” (e.g., intercultural contact; diversity), and the fact that these are more accessible in memory to form a mental representation, are important aspects to understand identity processes and their impact on intergroup outcomes.info:eu-repo/semantics/publishedVersio

Grain growth in newly discovered young eruptive stars

FU Orionis-type stars are young stellar objects showing large outbursts due to highly enhanced accretion from the circumstellar disk onto the protostar. FUor-type outbursts happen in a wide variety of sources from the very embedded ones to those with almost no sign of extended emission beyond the disk. The subsequent eruptions might gradually clear up the obscuring envelope material and drive the protostar on its way to become a disk-only T Tauri star. We used VLT/VISIR to obtain the first spectra that cover the 8-13 $\mu$m mid-infrared wavelength range in low-resolution of five recently discovered FUors. Four objects from our sample show the 10 $\mu$m silicate feature in emission. We study the shape and strength of the silicate feature in these objects and find that they mostly contain large amorphous grains, suggesting that large grains are typically not settled to the midplane in FUor disks. This is a general characteristic of FUors, as opposed to regular T Tauri-type stars whose disks display anything from pristine small grains to significant grain growth. We classify our targets by determining whether the silicate feature is in emission or in absorption, and confront them with the evolutionary scenarios on the dispersal of the envelopes around young stars. In our sample, all Class II objects exhibit silicate emission, while for Class I objects, the appearance of the feature in emission or absorption depends on the viewing angle with respect to the outflow cavity. This highlights the importance of geometric effects when interpreting the silicate feature.Comment: 7 pages, 1 table, 3 figures, accepted for publication in the Astrophysical Journal Letter

Activation of H-H, HO-H, C(sp2)-H, C(sp3)-H, and RO-H bonds by transition-metal frustrated lewis pairs based onon M/N (M = Rh, Ir) couples

Reaction of the dimers (Cp*MCl)2(µ-Cl)2] (Cp* = 5-C5Me5) with Ph2PCH2CH2NC(NH(p-Tolyl))2 (H2L) in the presence of NaSbF6 affords the chlorido complexes Cp*MCl(¿2N, P-H2L)]SbF6] (M = Rh, 1; Ir, 2). Upon treatment with aqueous NaOH, solutions of 1 and 2 yield the corresponding complexes Cp*M(¿3N, N', P-HL)]SbF6] (M = Rh, 3; Ir, 4) in which the ligand HL presents a fac ¿3N, N', P coordination mode. Treatment of THF solutions of complexes 3 and 4 with hydrogen gas, at room temperature, results in the formation of the metal hydrido-complexes Cp*MH(¿2N, P-H2L)]SbF6] (M = Rh, 5; Ir, 6) in which the N(p-Tolyl) group has been protonated. Complexes 3 and 4 react with deuterated water in a reversible fashion resulting in the gradual deuteration of the Cp* group. Heating at 383 K THF/H2O solutions of the complexes 3 and 4 affords the orthometalated complexes Cp*M(¿3C, N, P-H2L-H)]SbF6] M = Rh, 7; Ir, 8, H2L-H = Ph2PCH2CH2NC(NH(p-Tolyl))(NH(4-C6H3Me))], respectively. At 333 K, complexes 3 and 4 react in THF with methanol, primary alcohols, or 2-propanol giving the metal-hydrido complexes 5 and 6, respectively. The reaction involves the acceptorless dehydrogenation of the alcohols at a relatively low temperature, without the assistance of an external base. The new complexes have been characterized by the usual analytical and spectroscopic methods including the X-ray diffraction determination of the crystal structures of complexes 1-5, 7, and 8. Notably, the chlorido complexes 1 and 2 crystallize both as enantiopure conglomerates and as racemates. Reaction mechanisms are proposed based on stoichiometric reactions, nuclear magnetic resonance studies, and X-ray crystallography as well as density functional theory calculations. © 2022 The Authors. Published by American Chemical Society