Process chain approach to high-order perturbation calculus for quantum lattice models

A method based on Rayleigh-Schroedinger perturbation theory is developed that allows to obtain high-order series expansions for ground-state properties of quantum lattice models. The approach is capable of treating both lattice geometries of large spatial dimensionalities d and on-site degrees of freedom with large state space dimensionalities. It has recently been used to accurately compute the zero-temperature phase diagram of the Bose-Hubbard model on a hypercubic lattice, up to arbitrary large filling and for d=2, 3 and greater [Teichmann et al., Phys. Rev. B 79, 100503(R) (2009)].Comment: 11 pages, 6 figure

An Algorithmic Approach to Quantum Field Theory

The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper we review the theoretical foundations and the most basic algorithms required to implement a typical lattice computation, including the Metropolis, the Gibbs sampling, the Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis is on gauge theories with fermions such as QCD. We also provide examples of typical results from lattice QCD computations for quantities of phenomenological interest.Comment: 44 pages, to be published in IJMP

Quantifying Timing Leaks and Cost Optimisation

We develop a new notion of security against timing attacks where the attacker is able to simultaneously observe the execution time of a program and the probability of the values of low variables. We then show how to measure the security of a program with respect to this notion via a computable estimate of the timing leakage and use this estimate for cost optimisation.Comment: 16 pages, 2 figures, 4 tables. A shorter version is included in the proceedings of ICICS'08 - 10th International Conference on Information and Communications Security, 20-22 October, 2008 Birmingham, U

Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties

New Phases of SU(3) and SU(4) at Finite Temperature

The addition of an adjoint Polyakov loop term to the action of a pure gauge theory at finite temperature leads to new phases of SU(N) gauge theories. For SU(3), a new phase is found which breaks Z(3) symmetry in a novel way; for SU(4), the new phase exhibits spontaneous symmetry breaking of Z(4) to Z(2), representing a partially confined phase in which quarks are confined, but diquarks are not. The overall phase structure and thermodynamics is consistent with a theoretical model of the effective potential for the Polyakov loop based on perturbation theory.Comment: 18 pages, 17 figures, RevTeX

Hadronic Decays of Excited Heavy Mesons

We studied the hadronic decays of excited states of heavy mesons (D, D_s, B and B_s) to lighter states by emission of pi, eta or K. Wavefunctions and energy levels of these excited states are determined using a Dirac equation for the light quark in the potential generated by the heavy quark (including first order corrections in the heavy quark expansion). Transition amplitudes are computed in the context of the Heavy Chiral Quark Model.Comment: 4 pages (incl. figures), proceedings of the IV International Conference on "Hyperons, Charm and Beauty Hadrons", Valencia (Spain

Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N

We study two-dimensional N=(2,2) SU(N) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte-Carlo simulation for N=2,3,4,5 and then extrapolate the result to N = infinity. With the periodic boundary conditions for the fermions along both circles, we establish the existence of a bound state in which scalar fields clump around the origin, in spite of the existence of a classical flat direction. In this phase the global (Z_N)^2 symmetry turns out to be broken. We provide a simple explanation for this fact and discuss its physical implications.Comment: 24 pages, 13 figure

On dynamical probabilities, or: how to learn to shoot straight

© IFIP International Federation for Information Processing 2016.In order to support, for example, a quantitative analysis of various algorithms, protocols etc. probabilistic features have been introduced into a number of programming languages and calculi. It is by now quite standard to define the formal semantics of (various) probabilistic languages, for example, in terms of Discrete Time Markov Chains (DTMCs). In most cases however the probabilities involved are represented by constants, i.e. one deals with static probabilities. In this paper we investigate a semantical framework which allows for changing, i.e. dynamic probabilities which is still based on time-homogenous DTMCs, i.e. the transition matrix representing the semantics of a program does not change over time

The second moment of the pion's distribution amplitude

We present preliminary results for the second moment of the pion's distribution amplitude. The lattice formulation and the phenomenological implications are briefly reviewed, with special emphasis on some subtleties that arise when the Lorentz group is replaced by the hypercubic group. Having analysed more than half of the available configurations, the result obtained is \xi^2_L = 0.06 \pm 0.02.Comment: Lattice 99 (matrix elements), 3 page