Diophantine approximation on Veech surfaces

We show that Y. Cheung's general $Z$-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates. The saddle connection continued fractions then allow one to recognize certain transcendental directions by their developments

The entanglement spectrum of chiral fermions on the torus

We determine the reduced density matrix of chiral fermions on the torus, for an arbitrary set of disjoint intervals and generic torus modulus. We find the resolvent, which yields the modular Hamiltonian in each spin sector. Together with a local term, it involves an infinite series of bi-local couplings, even for a single interval. These accumulate near the endpoints, where they become increasingly redshifted. Remarkably, in the presence of a zero mode, this set of points 'condenses' within the interval at low temperatures, yielding continuous non-locality.Comment: Several minor changes done in order to improve readability. Accepted for publication in PR

Asymptotic and bootstrap specification tests of nonlinear in variable econometric models

We address the issue of consistent specification testing in general econometric models definedı by multiple moment conditions. We develop two c1asses of moment conditions based tests. The first class of tests depends upon nonparametric functions that are estimated by kernel smoothers. The second class of tests depends upon a marked empirical process. Asymptotic and bootstrap versions of these tests are formally justified, and their finite sample performances are investigated by means of Monte-CarIo experiments

Consistent tests of conditional moment restrictions

We propose two classes of consistent tests in parametric econometric models defined through multiple conditional moment restrictions. The first type of tests relies on nonparametric estimation, while the second relies on a functional of a marked empirical process. For both tests, a simulation procedure for obtaining critical values is shown to be asymptotically valid. Finite sample performances of the tests are investigated by means of several Monte-Carlo experiments.Publicad

Quantum mechanics based force field for carbon (QMFF-Cx) validated to reproduce the mechanical and thermodynamics properties of graphite

As assemblies of graphene sheets, carbon nanotubes, and fullerenes become components of new nanotechnologies, it is important to be able to predict the structures and properties of these systems. A problem has been that the level of quantum mechanics practical for such systems (density functional theory at the PBE level) cannot describe the London dispersion forces responsible for interaction of the graphene planes (thus graphite falls apart into graphene sheets). To provide a basis for describing these London interactions, we derive the quantum mechanics based force field for carbon (QMFF-Cx) by fitting to results from density functional theory calculations at the M06-2X level, which demonstrates accuracies for a broad class of molecules at short and medium range intermolecular distances. We carried out calculations on the dehydrogenated coronene (C24) dimer, emphasizing two geometries: parallel-displaced X (close to the observed structure in graphite crystal) and PD-Y (the lowest energy transition state for sliding graphene sheets with respect to each other). A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads to accurate predictions of available experimental mechanical and thermodynamics data of graphite (lattice vibrations, elastic constants, Poisson ratios, lattice modes, phonon dispersion curves, specific heat, and thermal expansion). This validates the use of M06-2X as a practical method for development of new first principles based generations of QMFF force fields

Discrete symmetries from hidden sectors

We study the presence of abelian discrete symmetries in globally consistent orientifold compactifications based on rational conformal field theory. We extend previous work [1] by allowing the discrete symmetries to be a linear combination of U(1) gauge factors of the visible as well as the hidden sector. This more general ansatz significantly increases the probability of finding a discrete symmetry in the low energy effective action. Applied to globally consistent MSSM-like Gepner constructions we find multiple models that allow for matter parity or Baryon triality.Comment: 20 page