Metastability, Mode Coupling and the Glass Transition

Mode coupling theory (MCT) has been successful in explaining the observed sequence of time relaxations in dense fluids. Previous expositions of this theory showing this sequence have required the existence of an ideal glass transition temperature $T_0$. Recent experiments show no evidence of $T_0$. We show here how the theory can be reformulated, in a fundamental way, such that one retains this sequence of relaxation behaviors but with a smooth temperature dependence and without any indication of $T_0$. The key ingredient in the reformulation is the inclusion of the metastable nature of the glass transition problem through a coupling of the mass density to the defect density. A main result of our theory is that the exponents governing the sequence of time relaxations are weak functions of the temperature in contrast to the results from conventional MCT.Comment: 14 pages (2 figures upon request), REVTEX

Exact Gap Computation for Code Coverage Metrics in ISO-C

Test generation and test data selection are difficult tasks for model based testing. Tests for a program can be meld to a test suite. A lot of research is done to quantify the quality and improve a test suite. Code coverage metrics estimate the quality of a test suite. This quality is fine, if the code coverage value is high or 100%. Unfortunately it might be impossible to achieve 100% code coverage because of dead code for example. There is a gap between the feasible and theoretical maximal possible code coverage value. Our review of the research indicates, none of current research is concerned with exact gap computation. This paper presents a framework to compute such gaps exactly in an ISO-C compatible semantic and similar languages. We describe an efficient approximation of the gap in all the other cases. Thus, a tester can decide if more tests might be able or necessary to achieve better coverage.Comment: In Proceedings MBT 2012, arXiv:1202.582

Nonequilibrium mesoscopic transport: a genealogy

Models of nonequilibrium quantum transport underpin all modern electronic devices, from the largest scales to the smallest. Past simplifications such as coarse graining and bulk self-averaging served well to understand electronic materials. Such particular notions become inapplicable at mesoscopic dimensions, edging towards the truly quantum regime. Nevertheless a unifying thread continues to run through transport physics, animating the design of small-scale electronic technology: microscopic conservation and nonequilibrium dissipation. These fundamentals are inherent in quantum transport and gain even greater and more explicit experimental meaning in the passage to atomic-sized devices. We review their genesis, their theoretical context, and their governing role in the electronic response of meso- and nanoscopic systems.Comment: 21p

Magnetic phases of the mixed-spin J1−J2J_1-J_2 Heisenberg model on a square lattice

We study the zero-temperature phase diagram and the low-energy excitations of a mixed-spin ($S_1>S_2$) $J_1-J_2$ Heisenberg model defined on a square lattice by using a spin-wave analysis, the coupled cluster method, and the Lanczos exact-diagonalization technique. As a function of the frustration parameter $J_2/J_1$ ($>0$), the phase diagram exhibits a quantized ferrimagnetic phase, a canted spin phase, and a mixed-spin collinear phase. The presented results point towards a strong disordering effect of the frustration and quantum spin fluctuations in the vicinity of the classical spin-flop transition. In the extreme quantum system $(S_1,S_2)=(1,{1/2})$, we find indications of a new quantum spin state in the region $0.46< J_2/J_1<0.5$Comment: 5 PRB pages, 7 figure

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Exact solution of the nuclear pairing problem

In many applications to finite Fermi-systems, the pairing problem has to be treated exactly. We suggest a numerical method of exact solution based on SU(2) quasispin algebras and demonstrate its simplicity and practicality. We show that the treatment of binding energies with the use of the exact pairing and uncorrelated monopole contribution of other residual interactions can serve as an effective alternative to the full shell-model diagonalization in spherical nuclei. A self-consistent combination of the exactly treated pairing and Hartree-Fock method is discussed. Results for Sn isotopes indicate a good agreement with experimental data.Comment: 10 pages, 2 figure

Three heavy jet events at hadron colliders as a sensitive probe of the Higgs sector

Assuming that a non-standard neutral Higgs with an enhanced Yukawa coupling to a bottom quark is observed at future hadron experiments, we propose a method for a better understanding of the Higgs sector. Our procedure is based on "counting" the number of events with heavy jets (where "heavy" stands for a c or b jet) versus b jets, in the final state of processes in which the Higgs is produced in association with a single high p_T c or b jet. We show that an observed signal of the type proposed, at either the Tevatron or the LHC, will rule out the popular two Higgs doublet model of type II as well as its supersymmetric version - the Minimal Supersymmetric Standard Model (MSSM), and may provide new evidence in favor of some more exotic multi Higgs scenarios. As an example, we show that in a version of a two Higgs doublet model which naturally accounts for the large mass of the top quark, our signal can be easily detected at the LHC within that framework. We also find that such a signal may be observable at the upgraded Tevatron RunIII, if the neutral Higgs in this model has a mass around 100 GeV and \tan\beta > 50 and if the efficiency for distinguishing a c jet from a light jet will reach the level of 50%.Comment: Revtex, 11 pages, 4 figures embedded in the text. Main changes with respect to Version 1: Numerical results re-calculated using the CTEQ5L pdf, improved discussion on the experimental consequences, new references added. Conclusions remain unchanged. As will appear in Phys. Rev.

Quantum Transport in Nonuniform Magnetic Fields: Aharonov-Bohm Ring as a Spin Switch

We study the spin-dependent magneto conductance in mesoscopic rings subject to an inhomogeneous in-plane magnetic field. We show that the polarization direction of transmitted spin-polarized electrons can be controlled via an additional magnetic flux such that spin flips are induced at half a flux quantum. This quantum interference effect is independent of the strength of the nonuniform field applied. We give an analytical explanation for one-dimensional rings and numerical results for corresponding ballistic microstructures.Comment: 5 pages, 3 figures. To be published in Physical Review Letter

Metastable Dynamics of the Hard-Sphere System

The reformulation of the mode-coupling theory (MCT) of the liquid-glass transition which incorporates the element of metastability is applied to the hard-sphere system. It is shown that the glass transition in this system is not a sharp one at the special value of the density or the packing fraction, which is in contrast to the prediction by the conventional MCT. Instead we find that the slowing down of the dynamics occurs over a range of values of the packing fraction. Consequently, the exponents governing the sequence of time relaxations in the intermediate time regime are given as functions of packing fraction with one additional parameter which describes the overall scale of the metastable potential energy for defects in the hard-sphere system. Implications of the present model on the recent experiments on colloidal systems are also discussed.Comment: 21 pages, 5 figures (available upon request), RevTEX3.0, JFI Preprint

Metastable Dynamics above the Glass Transition

The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable $n$ into the set of slow variables with the mass density $\rho$ and the momentum density ${\bf g}$. As a first approximation, we consider the case where motions associated with $n$ are much slower than those associated with $\rho$. Self-consistently, assuming one is near a critical surface in the MCT sense, we find that the observed slowing down of the dynamics corresponds to a certain limit of a very shallow metastable well and a weak coupling between $\rho$ and $n$. The metastability parameters as well as the exponents describing the observed sequence of time relaxations are given as smooth functions of the temperature without any evidence for a special temperature. We then investigate the case where the defect dynamics is included. We find that the slowing down of the dynamics corresponds to the system arranging itself such that the kinetic coefficient $\gamma_v$ governing the diffusion of the defects approaches from above a small temperature-dependent value $\gamma^c_v$.Comment: 38 pages, 14 figures (6 figs. are included as a uuencoded tar- compressed file. The rest is available upon request.), RevTEX3.0+eps