Towards the deformation quantization of linearized gravity

We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell Lagrangian which allows the construction of a Hamiltonian in the standard way. The deformation quantization procedure for free fields is applied to this Hamiltonian. As a result we obtain the complete set of quantum states and its discrete spectrum.Comment: 13 pages, no figures **preliminary entry **

Analysis of Probabilistic Basic Parallel Processes

Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates other processes according to a probability distribution. We study the decidability and complexity of fundamental qualitative problems over probabilistic BPPs -- in particular reachability with probability 1 of different classes of target sets (e.g. upward-closed sets). Our results concern both the Markov-chain model, where processes are scheduled randomly, and the MDP model, where processes are picked by a scheduler.Comment: This is the technical report for a FoSSaCS'14 pape

Twist Deformations of the Supersymmetric Quantum Mechanics

The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.Comment: 18 pages; two references adde

Comparison Of Structure And Properties Of Femtosecond And Nanosecond Laser-Structured Silicon

We compare the optical properties,chemical composition, and crystallinity of siliconmicrostructures formed in the presence of SF6 by femtosecond laserirradiation and by nanosecond laser irradiation. In spite of very different morphology and crystallinity, the optical properties and chemical composition of the two types of microstructures are very similar. The structures formed with femtosecond (fs) pulses are covered with a disordered nanocrystalline surface layer less than 1 μm thick, while those formed with nanosecond (ns) pulses have very little disorder. Both ns-laser-formed and fs-laser-formed structures absorb near-infrared (1.1–2.5 μm) radiation strongly and have roughly 0.5% sulfur impurities

Weak Bisimulation Approximants

Bisimilarity ∼ and weak bisimilarity ≈ are canonical notions of equivalence between processes, which are defined co-inductively, but may be approached – and even reached – by their (transfinite) inductively-defined approximants ∼α and ≈α. For arbitrary processes this approximation may need to climb arbitrarily high through the infinite ordinals before stabilising. In this paper we consider a simple yet well-studied process algebra, the Basic Parallel Processes (BPP), and investigate for this class of processes the minimal ordinal α such that ≈ = ≈α. The main tool in our investigation is a novel proof of Dickson’s Lemma. Unlike classical proofs, the proof we provide gives rise to a tight ordinal bound, of ω n, on the order type of non-increasing sequences of n-tuples of natural numbers. With this we are able to reduce a long-standing bound on the approximation hierarchy for weak bisimilarity ≈ over BPP, and show that ≈ = ≈ω ω

Crystal Structures and Electronic Properties of Haloform-Intercalated C60

Using density functional methods we calculated structural and electronic properties of bulk chloroform and bromoform intercalated C60, C60 2CHX3 (X=Cl,Br). Both compounds are narrow band insulator materials with a gap between valence and conduction bands larger than 1 eV. The calculated widths of the valence and conduction bands are 0.4-0.6 eV and 0.3-0.4 eV, respectively. The orbitals of the haloform molecules overlap with the $\pi$ orbitals of the fullerene molecules and the p-type orbitals of halogen atoms significantly contribute to the valence and conduction bands of C60 2CHX3. Charging with electrons and holes turns the systems to metals. Contrary to expectation, 10 to 20 % of the charge is on the haloform molecules and is thus not completely localized on the fullerene molecules. Calculations on different crystal structures of C60 2CHCl3 and C60 2CHBr3 revealed that the density of states at the Fermi energy are sensitive to the orientation of the haloform and C60 molecules. At a charging of three holes, which corresponds to the superconducting phase of pure C60 and C60 2CHX3, the calculated density of states (DOS) at the Fermi energy increases in the sequence DOS(C60) < DOS(C60 2CHCl3) < DOS(C60 2CHBr3).Comment: 11 pages, 7 figures, 4 table

Discharge of repulsive grains from a silo: experiments and simulations

In granular matter, sliding friction and collisions among grains are fundamental mechanisms of energy dissipation that determine the particles dynamics. Here we consider an unconventional granular system composed of magnetic repelling grains confined in a two dimensional cell that interact only through their magnetic field. The repulsive interaction prevents contact among grains and therefore produces a different dynamics compared to the dynamics of classical granular systems. In particular, we present experiments and simulations on the discharge of this repulsive granular medium from a silo. The results reveal an inverted density profile and a plug-flow through the aperture that contrast with the dynamics displayed by contacting grains. Moreover, the simulations allow to estimate the friction coefficient generated by the lateral confinement

Quantum gravitational corrections to black hole geometries

We calculate perturbative quantum gravity corrections to eternal two-dimensional black holes. We estimate the leading corrections to the AdS_2 black hole entropy and determine the quantum modification of N-dimensional Schwarzschild spacetime.Comment: 15 pages, 6 figures. Revised version: Introduction and conclusion expanded, section II reshaped, references added. Accepted for publication in Phys. Rev.