Pseudo-Automorphisms of positive entropy on the blowups of products of projective spaces

We use a concise method to construct pseudo-automorphisms f_n of the first dynamical degree d_1(f_n) > 1 on the blowups of the projective n-space for all n > 1 and more generally on the blowups of products of projective spaces. These f_n, for n = 3 have positive entropy, and for n > 3 seem to be the first examples of pseudo-automorphisms with d_1(f_n) > 1 (and of non-product type) on rational varieties of higher dimensions.Comment: Mathematische Annalen (to appear

Spin polarization of electrons with Rashba double-refraction

We demonstrate how the Rashba spin-orbit coupling in semiconductor heterostructures can produce and control a spin-polarized current without ferromagnetic leads. Key idea is to use spin-double refraction of an electronic beam with a nonzero incidence angle. A region where the spin-orbit coupling is present separates the source and the drain without spin-orbit coupling. We show how the transmission and the beam spin-polarization critically depend on the incidence angle. The transmission halves when the incidence angle is greater than a limit angle and a significant spin-polarization appears. Increasing the spin-orbit coupling one can obtain the modulation of the intensity and of the spin-polarization of the output electronic current when the input current is unpolarized. Our analysis shows the possibility to realize a spin-field-effect transistor based on the propagation of only one mode with the region with spin-orbit coupling. Where the original Datta and Das device [Appl.Phys.Lett. {\bf 56}, 665 (1990)] use the spin-precession that originates from the interference between two modes with orthogonal spin.Comment: 12 pages with 7 figure

Modelling of strain effects in manganite films

Thickness dependence and strain effects in films of $La_{1-x}A_xMnO_3$ perovskites are analyzed in the colossal magnetoresistance regime. The calculations are based on a generalization of a variational approach previously proposed for the study of manganite bulk. It is found that a reduction in the thickness of the film causes a decrease of critical temperature and magnetization, and an increase of resistivity at low temperatures. The strain is introduced through the modifications of in-plane and out-of-plane electron hopping amplitudes due to substrate-induced distortions of the film unit cell. The strain effects on the transition temperature and transport properties are in good agreement with experimental data only if the dependence of the hopping matrix elements on the $Mn-O-Mn$ bond angle is properly taken into account. Finally variations of the electron-phonon coupling linked to the presence of strain turn out important in influencing the balance of coexisting phases in the filmComment: 7 figures. To be published on Physical Review

On the Crepant Resolution Conjecture in the Local Case

In this paper we analyze four examples of birational transformations between local Calabi-Yau 3-folds: two crepant resolutions, a crepant partial resolution, and a flop. We study the effect of these transformations on genus-zero Gromov-Witten invariants, proving the Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture in each case. Our results suggest that this form of the Crepant Resolution Conjecture may also hold for more general crepant birational transformations. They also suggest that Ruan's original Crepant Resolution Conjecture should be modified, by including appropriate "quantum corrections", and that there is no straightforward generalization of either Ruan's original Conjecture or the Cohomological Crepant Resolution Conjecture to the case of crepant partial resolutions. Our methods are based on mirror symmetry for toric orbifolds.Comment: 27 pages. This is a substantially revised and shortened version of my preprint "Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples"; all results contained here are also proved there. To appear in Communications in Mathematical Physic

On the validity of the Franck-Condon principle in the optical spectroscopy: optical conductivity of the Fr\"{o}hlich polaron

The optical absorption of the Fr\"{o}hlich polaron model is obtained by an approximation-free Diagrammatic Monte Carlo method and compared with two new approximate approaches that treat lattice relaxation effects in different ways. We show that: i) a strong coupling expansion, based on the the Franck-Condon principle, well describes the optical conductivity for large coupling strengths ($\alpha >10$); ii) a Memory Function Formalism with phonon broadened levels reproduces the optical response for weak coupling strengths ($\alpha <6$) taking the dynamic lattice relaxation into account. In the coupling regime $6<\alpha<10$ the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.Comment: accepted for publication in PR

Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM

Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence

The theoretical motivations to perform experimental tests of the stationary state fluctuation relation are reviewed. The difficulties involved in such tests, evidenced by numerical simulations, are also discussed.Comment: 36 pages, 4 figures. Extended version of a presentation to the discussion "Is it possible to experimentally verify the fluctuation theorem?", IHP, Paris, December 1, 2006. Comments are very welcom

On the effects of the magnetic field and the isotopic substitution upon the infrared absorption of manganites

Employing a variational approach that takes into account electron-phonon and magnetic interactions in $La_{1-x}A_xMnO_3$ perovskites with $0<x<0.5$, the effects of the magnetic field and the oxygen isotope substitution on the phase diagram, the electron-phonon correlation function and the infrared absorption at $x=0.3$ are studied. The lattice displacements show a strong correlation with the conductivity and the magnetic properties of the system. Then the conductivity spectra are characterized by a marked sensitivity to the external parameters near the phase boundary.Comment: 10 figure

Polaron formation for a non-local electron-phonon coupling: A variational wave-function study

We introduce a variational wave-function to study the polaron formation when the electronic transfer integral depends on the relative displacement between nearest-neighbor sites giving rise to a non-local electron-phonon coupling with optical phonon modes. We analyze the ground state properties such as the energy, the electron-lattice correlation function, the phonon number and the spectral weight. Variational results are found in good agreement with analytic weak-coupling perturbative calculations and exact numerical diagonalization of small clusters. We determine the polaronic phase diagram and we find that the tendency towards strong localization is hindered from the pathological sign change of the effective next-nearest-neighbor hopping.Comment: 11 page

An integrated clinical program and crowdsourcing strategy for genomic sequencing and Mendelian disease gene discovery.

Despite major progress in defining the genetic basis of Mendelian disorders, the molecular etiology of many cases remains unknown. Patients with these undiagnosed disorders often have complex presentations and require treatment by multiple health care specialists. Here, we describe an integrated clinical diagnostic and research program using whole-exome and whole-genome sequencing (WES/WGS) for Mendelian disease gene discovery. This program employs specific case ascertainment parameters, a WES/WGS computational analysis pipeline that is optimized for Mendelian disease gene discovery with variant callers tuned to specific inheritance modes, an interdisciplinary crowdsourcing strategy for genomic sequence analysis, matchmaking for additional cases, and integration of the findings regarding gene causality with the clinical management plan. The interdisciplinary gene discovery team includes clinical, computational, and experimental biomedical specialists who interact to identify the genetic etiology of the disease, and when so warranted, to devise improved or novel treatments for affected patients. This program effectively integrates the clinical and research missions of an academic medical center and affords both diagnostic and therapeutic options for patients suffering from genetic disease. It may therefore be germane to other academic medical institutions engaged in implementing genomic medicine programs