The three flavour chiral phase transition with an improved quark and gluon action in lattice QCD

The finite-temperature chiral phase transition is investigated for three flavours of staggered quarks on a lattice of temporal extent N_t=4. In the simulation we use an improved fermion action which reduces rotational symmetry breaking of the quark propagator (p4-action), include fat-links to improve the flavour symmetry and use the tree level improved (1,2) gluon action. We study the nature of the phase transition for quark masses of ma=0.025, ma=0.05 and ma=0.1 on lattices with spatial sizes of 8^3 and 16^3.Comment: LATTICE98(hightemp), 3 pages, 7 figures, LaTeX2e-File, espcrc2.st

Quark Mass and Flavour Dependence of the QCD Phase Transition

We analyze the quark mass and flavour dependence of the QCD phase transition temperature. When the lightest pseudo-scalar meson mass (m_PS) is larger than 2 GeV the critical temperature is controlled by the gluonic sector of QCD alone. For smaller values of the lightest meson mass the pseudo-critical temperature decreases slowly with m_PS. For a large regime of meson masses the pseudo-critical temperature of 2-flavour QCD is about 10% larger than in the 3-flavour case. On lattices with temporal extent N_t=4 an extrapolation to the chiral limit yields T_c = 173(8) MeV and 154(8) MeV for 2 and 3-flavour QCD, respectively. We also analyze dynamical quark mass effects on the screening of the heavy quark potential. A detailed analysis of the heavy quark free energy in 3-flavour QCD shows that close to T_c screening effects are approximately quark mass independent already for pseudo-scalar meson masses m_PS = 800 MeV and screening sets in at distances r = 0.3 fm.Comment: 25 pages, LaTeX2e File, 11 EPS-file

QCD Thermodynamics with 2 and 3 Quark Flavors

We discuss the flavor dependence of the pressure and critical temperature calculated in QCD with 2, 2+1 and 3 flavors using improved gauge and staggered fermion actions on lattices with temporal extent Nt=4. For T > 2 Tc we find that bulk thermodynamics of QCD with 2 light and a heavier strange quark is well described by 3-flavor QCD while the transition temperature is closer to that of 2-flavor QCD. Furthermore, we present evidence that the chiral critical point of 3-flavor QCD, i.e. the second order endpoint of the line of first order chiral phase transitions, belongs to the universality class of the 3d Ising model.Comment: 6 pages, LaTeX2e File, 7 EPS-figures, presented at SEWM 2000, Marseille, June 13-17th, 200

Higher moments of charge fluctuations in QCD at high temperature

We present lattice results for baryon number, strangeness and electric charge fluctuations as well as their correlations at finite temperature and vanishing chemical potentials, i.e. under conditions relevant for RHIC and LHC. We find that the fluctuations change rapidly at the transition temperature $T_c$ and approach the ideal quark gas limit already at approximately $1.5T_c$. This indicates that quarks are the relevant degrees of freedom that carry the quantum numbers of conserved charges at $T\geq 1.5T_c$. At low temperature, qualitative features of the lattice results are well described by a hadron resonance gas model.Comment: 4 pages, 3 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

Co- and postseismic deformation patterns and Coulomb stress changes on thrust and normal faults: Insights from finite-element models including pore fluid pressure changes and postseismic viscoelastic relaxation

Earthquakes on intra-continental faults do not only cause immediate displacements and damage on the surface, but also induce sudden changes in pore fluid pressure as well as postseismic viscoelastic flow in the lower crust and lithospheric mantle. Such transient processes affect the velocity and stress field of the crust in the surrounding of the source fault for decades and cause significant Coulomb stress changes, which may trigger or delay next earthquakes on adjacent faults (receiver faults). The calculation of these stress changes has become an important tool for seismic hazard evaluation, but the combined influence of coseismic slip, interseismic stress accumulation and transient postseismic processes including poroelastic effects and viscoelastic relaxation on the velocity and stress field in the crust has not been systematically studied so far. 2D and 3D finite-element models with a generalized model setup are used to investigate the relative importance of the different earthquake-induced processes during the co- and postseismic phase of an intra-continental dip-slip earthquake. The models include gravity, isostatic effects, a regional stress field, elastic and viscoelastic layers and pore fluid pressure. In different experiments, important model parameters, including permeability, viscosity, friction coefficient, the size of the coseismic slip and the extension/shortening rate are varied to evaluate their influence on the model results. In the 2D models, a variation of the permeability of the crust and the viscosity of the lower crust and lithospheric mantle shows, that postseismic velocity fields contain signals from overlapping poroelastic and viscoelastic effects. Both processes may influence the velocity field already in the early postseismic phase, up to several decades, depending on the combination of upper-crustal permeability and lower-crustal viscosity. In the 3D models, the permeability of the crust and the viscosity of the lower crust and lithospheric mantle, as well as the friction coefficient, coseismic slip and deformation rate are varied, to evaluate their effect on the Coulomb stress changes on the receiver faults in the model fault array. While the latter three parameters have only an effect on the stress change magnitude, poroelastic effects and viscoelastic relaxation have a strong impact on the magnitudes and patterns of Coulomb stress changes. Poroelastic effects alter the coseismic Coulomb stress changes immediately in the first month after the earthquake, causing stress changes one order of magnitude stronger than those caused by viscoelastic relaxation. If the permeability and viscosity are low enough, the signals from both processes overlap already in the early postseismic phase for decades after the earthquake

Cryptographic error correction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 67-71).It has been said that "cryptography is about concealing information, and coding theory is about revealing it." Despite these apparently conflicting goals, the two fields have common origins and many interesting relationships. In this thesis, we establish new connections between cryptography and coding theory in two ways: first, by applying cryptographic tools to solve classical problems from the theory of error correction; and second, by studying special kinds of codes that are motivated by cryptographic applications. In the first part of this thesis, we consider a model of error correction in which the source of errors is adversarial, but limited to feasible computation. In this model, we construct appealingly simple, general, and efficient cryptographic coding schemes which can recover from much larger error rates than schemes for classical models of adversarial noise. In the second part, we study collusion-secure fingerprinting codes, which are of fundamental importance in cryptographic applications like data watermarking and traitor tracing. We demonstrate tight lower bounds on the lengths of such codes by devising and analyzing a general collusive attack that works for any code.by Christopher Jason Peikert.Ph.D

String Tension and Thermodynamics with Tree Level and Tadpole Improved Actions

We calculate the string tension, deconfinement transition temperature and bulk thermodynamic quantities of the SU(3) gauge theory using tree level and tadpole improved actions. Finite temperature calculations have been performed on lattices with temporal extent N_tau = 3 and 4. Compared to calculations with the standard Wilson action on this size lattices we observe a drastic reduction of the cut-off dependence of bulk thermodynamic observables at high temperatures. In order to test the influence of improvement on long-distance observables at T_c we determine the ratio T_c/sqrt(sigma). For all actions, including the standard Wilson action, we find results which differ only little from each other. We do, however, observe an improved asymptotic scaling behaviour for the tadpole improved action compared to the Wilson and tree level improved actions.Comment: 20 pages, LaTeX2e File, 8 coloured Postscript figures, new analysis added, recent Wilson action string tension results included, figures replace

Hardness of the (Approximate) Shortest Vector Problem: A Simple Proof via Reed-Solomon Codes

$\newcommand{\NP}{\mathsf{NP}}\newcommand{\GapSVP}{\textrm{GapSVP}}$We give a simple proof that the (approximate, decisional) Shortest Vector Problem is \NP-hard under a randomized reduction. Specifically, we show that for any $p \geq 1$ and any constant $\gamma < 2^{1/p}$, the $\gamma$-approximate problem in the $\ell_p$ norm ($\gamma$-\GapSVP_p) is not in $\mathsf{RP}$ unless \NP \subseteq \mathsf{RP}. Our proof follows an approach pioneered by Ajtai (STOC 1998), and strengthened by Micciancio (FOCS 1998 and SICOMP 2000), for showing hardness of $\gamma$-\GapSVP_p using locally dense lattices. We construct such lattices simply by applying "Construction A" to Reed-Solomon codes with suitable parameters, and prove their local density via an elementary argument originally used in the context of Craig lattices. As in all known \NP-hardness results for \GapSVP_p with $p < \infty$, our reduction uses randomness. Indeed, it is a notorious open problem to prove \NP-hardness via a deterministic reduction. To this end, we additionally discuss potential directions and associated challenges for derandomizing our reduction. In particular, we show that a close deterministic analogue of our local density construction would improve on the state-of-the-art explicit Reed-Solomon list-decoding lower bounds of Guruswami and Rudra (STOC 2005 and IEEE Trans. Inf. Theory 2006). As a related contribution of independent interest, we also give a polynomial-time algorithm for decoding $n$-dimensional "Construction A Reed-Solomon lattices" (with different parameters than those used in our hardness proof) to a distance within an $O(\sqrt{\log n})$ factor of Minkowski's bound. This asymptotically matches the best known distance for decoding near Minkowski's bound, due to Mook and Peikert (IEEE Trans. Inf. Theory 2022), whose work we build on with a somewhat simpler construction and analysis