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

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

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

Relaxation and Localization in Interacting Quantum Maps

We quantise and study several versions of finite multibaker maps. Classically these are exactly solvable K-systems with known exponential decay to global equilibrium. This is an attempt to construct simple models of relaxation in quantum systems. The effect of symmetries and localization on quantum transport is discussed.Comment: 32 pages. LaTex file. 9 figures, not included. For figures send mail to first author at '[email protected]

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

Coin Tossing as a Billiard Problem

We demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this new class of billiards. This provides a demonstration that coin tossing, the prototypical example of an independent random process, is a completely chaotic (Bernoulli) problem. The related question of which billiard geometries can be represented as rigid body systems is examined.Comment: 16 pages, LaTe

Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.Comment: 14 pages, AmS-LaTeX, no figur