Simulation of the hydrogen ground state in Stochastic Electrodynamics

Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar \omega$ in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham -- Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency components, next the dynamics is solved numerically using OpenCL. The approach improves on work by Cole and Zou 2003 by treating the full $3d$ problem and reaching longer simulation times. The results are compared with a conjecture for the ground state phase space density. Though short time results suggest a trend towards confirmation, in all attempted modelings the atom ionises at longer times.Comment: 20 pages, 9 figures. Published version, minor change

Electronic Instabilities of the AA-Honeycomb Bilayer

We use a functional renormalization group approach to study the instabilities due to electron-electron interactions in a bilayer honeycomb lattice model with AA stacking, as it might be relevant for layered graphene with this structure. Starting with a tight- binding description for the four $\pi$-bands, we integrate out the modes of the dispersion by successively lowering an infrared cutoff and determine the leading tendencies in the effective interactions. The antiferromagnetic spin-density wave is an expected instability for dominant local repulsion among the electrons, but for nonlocal interaction terms also other instabilities occur. We discuss the phase diagrams depending on the model parameters. We compare our results to single-layer graphene and the more common AB-stacked bilayer, both qualitatively and quantitatively.Comment: 9 pages, 3 figures, Annalen der Physik, online available (2014

Optimal Control Realizations of Lagrangian Systems with Symmetry

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in \cite{Bl98}, \cite{Bl00}. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications

The LIL for UU-statistics in Hilbert spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of arbitrary order, which are of independent interest

Uniaxial strain-induced Kohn anomaly and electron-phonon coupling in acoustic phonons of graphene

Recent advances in strain engineering at the nanoscale have shown the feasibility to modulate the properties of graphene. Although the electron-phonon (e-ph) coupling and Kohn anomalies in graphene define the phonon branches contributing to the resonance Raman scattering, and is relevant to the electronic and thermal transport as a scattering source, the evolution of the e-ph coupling as a function of strain has been less studied. In this work, the Kohn anomalies and the e-ph coupling in uniaxially strained graphene along armchair (AC) and zigzag (ZZ) directions were studied by means of density functional perturbation theory calculations. In addition to the phonon anomaly at the transversal optical (TO) phonon branch in the K point for pristine graphene, we found that uniaxial strain induces a discontinuity in the frequency derivative of the longitudinal acoustic (LA) phonon branch. This behavior corresponds to the emergence of a Kohn anomaly, as a consequence of a strain-enhanced e-ph coupling. Thus, the present results for uniaxially strained graphene contrast with the commonly assumed view that the e-ph coupling around the K point is only present in the TO phonon branch.Comment: Accepted for publication in Physical Review B (12 July 2016