Variational Monte Carlo for spin-orbit interacting systems

Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a general variational Monte Carlo approach is here introduced that treats in an efficient and very accurate way the spin degrees of freedom in atoms when spin orbit effects are included in the Hamiltonian describing the electronic structure. We illustrate the algorithm on the evaluation of the spin-orbit splittings of isolated carbon and lead atoms. In the case of the carbon atom, we investigate the differences between the inclusion of spin-orbit in its realistic and effective spherically symmetrized forms. The method exhibits a very good accuracy in describing the small energy splittings, opening the way for a systematic quantum Monte Carlo studies of spin-orbit effects in atomic systems.Comment: 7 pages, 0 figure

Small coupling limit and multiple solutions to the Dirichlet Problem for Yang Mills connections in 4 dimensions - Part I

In this paper (Part I) and its sequels (Part II and Part III), we analyze the structure of the space of solutions to the epsilon-Dirichlet problem for the Yang-Mills equations on the 4-dimensional disk, for small values of the coupling constant epsilon. These are in one-to-one correspondence with solutions to the Dirichlet problem for the Yang Mills equations, for small boundary data. We prove the existence of multiple solutions, and, in particular, non minimal ones, and establish a Morse Theory for this non-compact variational problem. In part I, we describe the problem, state the main theorems and do the first part of the proof. This consists in transforming the problem into a finite dimensional problem, by seeking solutions that are approximated by the connected sum of a minimal solution with an instanton, plus a correction term due to the boundary. An auxiliary equation is introduced that allows us to solve the problem orthogonally to the tangent space to the space of approximate solutions. In Part II, the finite dimensional problem is solved via the Ljusternik-Schirelman theory, and the existence proofs are completed. In Part III, we prove that the space of gauge equivalence classes of Sobolev connections with prescribed boundary value is a smooth manifold, as well as some technical lemmas used in Part I. The methods employed still work when the 4-dimensional disk is replaced by a more general compact manifold with boundary, and SU(2) is replaced by any compact Lie group

Percolation-to-hopping crossover in conductor-insulator composites

Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few characteristics of the composite. Specifically, we find that the relevant parameters that give rise to one regime or the other are $D/\xi$ (where $D$ is the size of the conducting particles and $\xi$ is the tunneling length) and the specific composite microstructure. For large values of $D/\xi$, percolation arises when the composite microstructure can be modeled as a regular lattice that is fractionally occupied by conducting particle, while the tunneling regime is always obtained for equilibrium distributions of conducting particles in a continuum insulating matrix. As $D/\xi$ decreases the percolating behavior of the conductivity of lattice-like composites gradually crosses over to the tunneling-like regime characterizing particle dispersions in the continuum. For $D/\xi$ values lower than $D/\xi\simeq 5$ the conductivity has tunneling-like behavior independent of the specific microstructure of the composite.Comment: 8 pages, 5 figure

Solution of the tunneling-percolation problem in the nanocomposite regime

We noted that the tunneling-percolation framework is quite well understood at the extreme cases of percolation-like and hopping-like behaviors but that the intermediate regime has not been previously discussed, in spite of its relevance to the intensively studied electrical properties of nanocomposites. Following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter-particle electron tunneling process. We show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any \textit{a priori} imposed cut-off in the inter-particle conductances, as usually done in the percolation-like interpretation of these systems. Furthermore, we demonstrate that our numerical results are fully reproduced by the critical path method, which is generalized here in order to include the particle filler shapes. By exploiting this method, we provide simple analytical formulas for the composite conductivity valid for many regimes of interest. The validity of our formulation is assessed by reinterpreting existing experimental results on nanotube, nanofiber, nanosheet and nanosphere composites and by extracting the characteristic tunneling decay length, which is found to be within the expected range of its values. These results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites.Comment: 13 pages with 8 figures + 10 pages with 9 figures of supplementary material (Appendix B

Población Obrera Sociedad Explotadora de Tierra del Fuego: expresión espacial de paternalismo industrial en Punta Arenas

Vector de crecimiento económico en la Patagonia chilena, la gran industria ganadera desarrolló, a través de sus estancias, un modo particular de subdivisión del espacio rural y una estructura de apropiación singular. En contraste, y pese a la gran cantidad de mano de obra que empleó, la ganadería fue incapaz de ofrecer en las ciudades de Puerto Natales o Punta Arenas conjuntos de viviendas a gran escala para la fuerza de trabajo asociada a la diversidad de tareas del campo o de los frigoríficos. Así, la Población Obrera que aquí se analiza desde una perspectiva histórica, urbana y arquitectónica constituye una excepción que emerge tardíamente, cuando la Sociedad Explotadora de Tierra del Fuego decidió construir en la periferia de Punta Arenas un conjunto residencial en arriendo destinado a sus obreros y sus familias. Hábitat colectivo y expresión espacial de un paternalismo industrial, el conjunto de viviendas construido permitió estructurar un área de la ciudad y presentó en su arquitectura significativas innovaciones espaciales, funcionales y técnicas en el territorio de Magallanes

Usher syndrome: An effective sequencing approach to establish a genetic and clinical diagnosis

12noUsher syndrome is an autosomal recessive disorder characterized by retinitis pigmentosa, sensorineural hearing loss and, in some cases, vestibular dysfunction. The disorder is clinically and genetically heterogeneous and, to date, mutations in 11 genes have been described. This finding makes difficult to get a precise molecular diagnosis and offer patients accurate genetic counselling. To overcome this problem and to increase our knowledge of the molecular basis of Usher syndrome, we designed a targeted resequencing custom panel. In a first validation step a series of 16 Italian patients with known molecular diagnosis were analysed and 31 out of 32 alleles were detected (97% of accuracy). After this step, 31 patients without a molecular diagnosis were enrolled in the study. Three out of them with an uncertain Usher diagnosis were excluded. One causative allele was detected in 24 out 28 patients (86%) while the presence of both causative alleles characterized 19 patients out 28 (68%). Sixteen novel and 27 known alleles were found in the following genes: USH2A (50%), MYO7A (7%), CDH23 (11%), PCDH15 (7%) and USH1G (2%). Overall, on the 44 patients the protocol was able to characterize 74 alleles out of 88 (84%). These results suggest that our panel is an effective approach for the genetic diagnosis of Usher syndrome leading to: 1) an accurate molecular diagnosis, 2) better genetic counselling, 3) more precise molecular epidemiology data fundamental for future interventional plans.partially_openembargoed_20160106Lenarduzzi, S.; Vozzi, D; Morgan, A.; Rubinato, E.; D'Eustacchio, A.; Osland, T.M.; Rossi, C.; Graziano, C.; Castorina, P.; Ambrosetti, U.; Morgutti, M.; Girotto, G.Lenarduzzi, Stefania; Vozzi, Diego; Morgan, Anna; Rubinato, Elisa; D'Eustacchio, A.; Osland, TERESA MARIA; Rossi, C.; Graziano, C.; Castorina, P.; Ambrosetti, U.; Morgutti, Marcello; Girotto, Giorgi

Action minimizing orbits in the n-body problem with simple choreography constraint

In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in \RR^d under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, where $\tau = 2\pi / n$. In this setting, we first prove that for every d,n \in \NN and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrodinger equations with attractive self-interaction. However, when self-interaction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrodinger equations with repulsive self-interaction but strongly attractive interspecies interaction. For such coupled nonlinear Schrodinger equations in two and three dimensional domains, we prove the existence of least energy solutions and study the location and configuration of symbiotic bright solitons. We use Nehari's manifold to construct least energy solutions and derive their asymptotic behaviors by some techniques of singular perturbation problems.Comment: to appear in Nonlinearit

Regularization of point vortices for the Euler equation in dimension two

In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic problem [ -\ep^2 \Delta u=(u-q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep})_+^p, \quad & x\in\Omega, u=0, \quad & x\in\partial\Omega, ] where $p>1$, $\Omega\subset\mathbb{R}^2$ is a bounded domain, $q$ is a harmonic function. We showed that if $\Omega$ is simply-connected smooth domain, then for any given non-degenerate critical point of Kirchhoff-Routh function $\mathcal{W}(x_1,...,x_m)$ with the same strength $\kappa>0$, there is a stationary classical solution approximating stationary $m$ points vortex solution of incompressible Euler equations with vorticity $m\kappa$. Existence and asymptotic behavior of single point non-vanishing vortex solutions were studied by D. Smets and J. Van Schaftingen (2010).Comment: 32page