On the equivalence between stochastic baker's maps and two-dimensional spin systems

We show that there is a class of stochastic baker's transformations that is equivalent to the class of equilibrium solutions of two-dimensional spin systems with finite interaction. The construction is such that the equilibrium distribution of the spin lattice is identical to the invariant measure in the corresponding baker's transformation. We also find that the entropy of the spin system is up to a constant equal to the rate of entropy production in the corresponding stochastic baker's transformation. We illustrate the equivalence by deriving two stochastic baker's maps representing the Ising model at a temperature above and below the critical temperature, respectively. We calculate the invariant measure of the stochastic baker's transformation numerically. The equivalence is demonstrated by finding that the free energy in the baker system is in agreement with analytic results of the two-dimensional Ising model.Comment: 4 pages, 4 figure

Quantum Mechanics of Damped Systems II. Damping and Parabolic Potential Barrier

We investigate the resonant states for the parabolic potential barrier known also as inverted or reversed oscillator. They correspond to the poles of meromorphic continuation of the resolvent operator to the complex energy plane. As a byproduct we establish an interesting relation between parabolic cylinder functions (representing energy eigenfunctions of our system) and a class of Gel'fand distributions used in our recent paper.Comment: 14 page

Gluon-gluon contributions to the production of continuum diphoton pairs at hadron colliders

We compute the contributions to continuum photon pair production at hadron colliders from processes initiated by gluon-gluon and gluon-quark scattering into two photons through a four-leg virtual quark loop. Complete two-loop cross sections in perturbative quantum chromodynamics are combined with contributions from soft parton radiation resummed to all orders in the strong coupling strength. The structure of the resummed cross section is examined in detail, including a new type of unintegrated parton distribution function affecting azimuthal angle distributions of photons in the pair's rest frame. As a result of this analysis, we predict diphoton transverse momentum distributions in gluon-gluon scattering in wide ranges of kinematic parameters at the Fermilab Tevatron collider and the CERN Large Hadron Collider.Comment: 28 pages, 11 figures; published versio

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Simulating noisy quantum protocols with quantum trajectories

The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability of a quantum algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the baker's map. Our results demonstrate that, using the quantum trajectories approach, we are able to simulate quantum protocols in the presence of noise and with large system sizes of more than 20 qubits.Comment: 11 pages, 7 fig

Technical Note: Shrinkage Properties of Partially Cad-Deficient Loblolly Pine Lumber

Partially cinnamyl alcohol dehydrogenase-deficient and wild-type loblolly pine (Pinus taeda) were studied for shrinkage properties. The study established no significant difference between these two genotypes. Results also showed that shrinkage of juvenile wood is significantly different from the corresponding shrinkage of mature wood only in the radial direction. Tangential shrinkage difference between juvenile and mature wood was significant when the uncorrected values were used but not when the true shrinkage values were used, thus highlighting the need to account for the effect of growth ring curvature on tangential shrinkage measurement of small-diameter trees