A Criterion for the Critical Number of Fermions and Chiral Symmetry Breaking in Anisotropic QED(2+1)

By analyzing the strength of a photon-fermion coupling using basic scattering processes we calculate the effect of a velocity anisotropy on the critical number of fermions at which mass is dynamically generated in planar QED. This gives a quantitative criterion which can be used to locate a quantum critical point at which fermions are gapped and confined out of the physical spectrum in a phase diagram of various condensed matter systems. We also discuss the mechanism of relativity restoration within the symmetric, quantum-critical phase of the theory.Comment: To appear in Physical Review

Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study

We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions around single lattice sites. Overall, the peak widths and anisotropy signs for different lattice directions agree, however, it is found that Fundamental Measure theory gives slightly narrower peaks with more anisotropy than seen in the simulations. Among the three types of Fundamental Measure functionals studied, only the White Bear II functional (Hansen-Goos and Roth, J. Phys.: Condens. Matter 18, 8413 (2006)) exhibits sensible results for the equilibrium vacancy concentration and a physical behavior of the chemical potential in crystals constrained by a fixed vacancy concentration.Comment: 17 pages, submitted to Phys. Rev.

Extension of PRISM by Synthesis of Optimal Timeouts in Fixed-Delay CTMC

We present a practically appealing extension of the probabilistic model checker PRISM rendering it to handle fixed-delay continuous-time Markov chains (fdCTMCs) with rewards, the equivalent formalism to the deterministic and stochastic Petri nets (DSPNs). fdCTMCs allow transitions with fixed-delays (or timeouts) on top of the traditional transitions with exponential rates. Our extension supports an evaluation of expected reward until reaching a given set of target states. The main contribution is that, considering the fixed-delays as parameters, we implemented a synthesis algorithm that computes the epsilon-optimal values of the fixed-delays minimizing the expected reward. We provide a performance evaluation of the synthesis on practical examples

Potts-Percolation-Gauss Model of a Solid

We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookian springs. If the energy is larger than a threshold the "spring" is more likely to fail, while if the energy is lower than the threshold the spring is more likely to be alive. The phase diagram and thermodynamic quantities, such as free energy, numbers of bonds and clusters, and their fluctuations, are determined using renormalization-group and Monte-Carlo techniques.Comment: 10 pages, 12 figure

Analysis of the temperature-dependent quantum point contact conductance in view of the metal-insulator transition in two dimensions

The temperature dependence of the conductance of a quantum point contact has been measured. The conductance as a function of the Fermi energy shows temperature-independent fixed points, located at roughly multiple integers of $e^{2}/h$. Around the first fixed point at e$^{2}$/h, the experimental data for different temperatures can been scaled onto a single curve. For pure thermal smearing of the conductance steps, a scaling parameter of one is expected. The measured scaling parameter, however, is significantly larger than 1. The deviations are interpreted as a signature of the potential landscape of the quantum point contact, and of the source-drain bias voltage. We relate our results phenomenologically to the metal-insulator transition in two dimensions.Comment: 5 pages, 3 figure

Plasticization and antiplasticization of polymer melts diluted by low molar mass species

An analysis of glass formation for polymer melts that are diluted by structured molecular additives is derived by using the generalized entropy theory, which involves a combination of the Adam-Gibbs model and the direct computation of the configurational entropy based on a lattice model of polymer melts that includes monomer structural effects. Antiplasticization is accompanied by a "toughening" of the glass mixture relative to the pure polymer, and this effect is found to occur when the diluents are small species with strongly attractive interactions with the polymer matrix. Plasticization leads to a decreased glass transition temperature T_g and a "softening" of the fragile host polymer in the glass state. Plasticization is prompted by small additives with weakly attractive interactions with the polymer matrix. The shifts in T_g of polystyrene diluted by fully flexible short oligomers are evaluated from the computations, along with the relative changes in the isothermal compressibility at T_g to characterize the extent to which the additives act as antiplasticizers or plasticizers. The theory predicts that a decreased fragility can accompany both antiplasticization and plasticization of the glass by molecular additives. The general reduction in the T_g and fragility of polymers by these molecular additives is rationalized by analyzing the influence of the diluent's properties (cohesive energy, chain length, and stiffness) on glass formation in diluted polymer melts. The description of glass formation at fixed temperature that is induced upon change the fluid composition directly implies the Angell equation for the structural relaxation time as function of the polymer concentration, and the computed "zero mobility concentration" scales linearly with the inverse polymerization index N.Comment: 12 pages, 15 figure

Optimizing Performance of Continuous-Time Stochastic Systems using Timeout Synthesis

We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters

Spin Effects in a Quantum Ring

Recent experiments are reviewed that explore the spin states of a ring-shaped many-electron quantum dot. Coulomb-blockade spectroscopy is used to access the spin degree of freedom. The Zeeman effect observed for states with successive electron number allows to select possible sequences of spin ground states of the ring. Spin-paired orbital levels can be identified by probing their response to magnetic fields normal to the plane of the ring and electric fields caused by suitable gate voltages. This narrows down the choice of ground-state spin sequences. A gate-controlled singlet--triplet transition is identified and the size of the exchange interaction matrix element is determined.Comment: 13 pages, 3 figures, Proceedings of the QD2004 conference in Banf

Freezing transition of the vortex liquid in anisotropic superconductors

We study the solid-liquid transition of a model of pancake vortices in laminar superconductors using a density functional theory of freezing. The physical properties of the system along the melting line are discussed in detail. We show that there is a very good agreement with experimental data in the shape and position of the first order transition in the phase diagram and in the magnitude and temperature dependence of the magnetic induction jump at the transition. We analyze the validity of the Lindemann melting criterion and the Hansen-Verlet freezing criterion. Both criteria are shown to be good to predict the phase diagram in the region where a first order phase transition is experimentally observed.Comment: 9 pages, 10 figure