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

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

Physical Adsorption at the Nanoscale: Towards Controllable Scaling of the Substrate-Adsorbate van der Waals Interaction

The Lifshitz-Zaremba-Kohn (LZK) theory is commonly considered as the correct large-distance limit for the van der Waals (vdW) interaction of adsorbates (atoms, molecules, or nanoparticles) with solid substrates. In the standard approximate form, implicitly based on "local" dielectric functions, the LZK approach predicts universal power laws for vdW interactions depending only on the dimensionality of the interacting objects. However, recent experimental findings are challenging the universality of this theoretical approach at finite distances of relevance for nanoscale assembly. Here, we present a combined analytical and numerical many-body study demonstrating that physical adsorption can be significantly enhanced at the nanoscale. Regardless of the band gap or the nature of the adsorbate specie, we find deviations from conventional LZK power laws that extend to separation distances of up to 10--20 nanometers. Comparison with recent experimental observation of ultra long-ranged vdW interactions in the delamination of graphene from a silicon substrate reveals qualitative agreement with the present theory. The sensitivity of vdW interactions to the substrate response and to the adsorbate characteristic excitation frequency also suggests that adsorption strength can be effectively tuned in experiments, paving the way to an improved control of physical adsorption at the nanoscale

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

Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence

We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation $$-\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq \mathbb{R}^{N},\ N\geq 3,$$ where $\Omega$ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\partial \Omega$ if $\Omega \neq \mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty$ if $\Omega$ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq 0$ is also considered.Comment: 29 pages, 8 figure

Stationary solutions of the nonlinear Schr\"odinger equation with fast-decay potentials concentrating around local maxima

We study positive bound states for the equation $$- \epsilon^2 \Delta u + Vu = u^p, \qquad \text{in $\mathbf{R}^N$},$$ where $\epsilon > 0$ is a real parameter, $\frac{N}{N-2} < p < \frac{N+2}{N-2}$ and $V$ is a nonnegative potential. Using purely variational techniques, we find solutions which concentrate at local maxima of the potential $V$ without any restriction on the potential.Comment: 25 pages, reformatted the abstract for MathJa

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

Performance Analysis of a Novel Air-based Cavity Receiver

AbstractIn this paper a new design of a novel CSP cavity receiver for parabolic trough collector is analyzed by means of an analytical Matlab model. The receiver, designed by the Swiss company Airlight Energy Manufacturing SA, is 212 m long consisting essentially of a feed pipe, a run-back pipe and 4608 helically coiled heat exchangers designed to capture the incident solar energy concentrated by a parabolic trough. The heat transfer fluid is air heated to temperatures above 600°C.The analytical Matlab model based on a pneumatic - electric circuit analogy was developed to assess the receiver performance in terms of mass flow rate distribution, pressure drop, air outlet temperature and thermal efficiency. A solution was proposed to approximately ensure the same mass flow rate for each cavity.Different skew angles for the incoming solar radiation were considered and the receiver geometry was optimized minimizing the pressure drop and the thermal losses through the runback pipe. The main requirement was to achieve, at the outlet section of the receiver, an air temperature of 650°C; therefore, the total inlet mass flow rate was tuned accordingly.The helically coiled heat exchanger and the receiver insulation sub-models were validated against accurate computational fluid dynamics simulations