On the Angular Dependence of the Radiative Gluon Spectrum

The induced momentum spectrum of soft gluons radiated from a high energy quark produced in and propagating through a QCD medium is reexamined in the BDMPS formalism. A mistake in our published work (Physical Review C60 (1999) 064902) is corrected. The correct dependence of the fractional induced loss $R(\theta_{{\rm cone}})$ as a universal function of the variable $\theta^2_{{\rm cone}} L^3 \hat q$ where $L$ is the size of the medium and $\hat q$ the transport coefficient is presented. We add the proof that the radiated gluon momentum spectrum derived in our formalism is equivalent with the one derived in the Zakharov-Wiedemann approach.Comment: LaTex, 5 pages, 1 figur

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc

Efficient computation of matched solutions of the Kapchinskij-Vladimirskij envelope equations for periodic focusing lattices

A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parameterizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to all physically achievable system parameters -- including where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.Comment: 20 pages, 5 figures, Mathematica source code provide

The Coulomb Interaction between Pion-Wavepackets: The piplus-piminus Puzzle

The time dependent Schr\"odinger equation for $\pi^+$--$\pi^-$ pairs, which are emitted from the interaction zone in relativistic nuclear collisions, is solved using wavepacket states. It is shown that the Coulomb enhancement in the momentum correlation function of such pairs is smaller than obtained in earlier calculations based on Coulomb distorted plane waves. These results suggest that the experimentally observed positive correlation signal cannot be caused by the Coulomb interaction between pions emitted from the interaction zone. But other processes which involve long-lived resonances and the related extended source dimensions could provide a possible explanation for the observed signal.Comment: 12 pages, LaTeX, 1 figur

Flow effects on the freeze-out phase-space density in heavy ion collisions

The strong longitudinal expansion of the reaction zone formed in relativistic heavy-ion collisions is found to significantly reduce the spatially averaged pion phase-space density, compared to naive estimates based on thermal distributions. This has important implications for data interpretation and leads to larger values for the extracted pion chemical potential at kinetic freeze-out.Comment: 5 pages, 3 figures included via epsfig, added discussion of different transverse density profiles, 1 new figur

Emission times and opacities from interferometry in non-central Relativistic Nuclear Collisions

The nuclear overlap zone in non-central relativistic heavy ion collisions is azimuthally very asymmetric. By varying the angle between the axes of deformation and the transverse direction of the pair momenta, the transverse HBT radii oscillate in a characteristic way. It is shown that these oscillations allow determination of source sizes, deformations as well as the opacity and duration of emission of the source created in any non-central high energy nuclear collisions. The behavior of the physical quantities with centrality of the collisions is discussed --- in particular changes caused by a possible phase transition to a quark-gluon plasma.Comment: Revised version, to appear in Phys. Rev. Letter

Classical and Quantum-like approaches to Charged-Particle Fluids in a Quadrupole

A classical description of the dynamics of a dissipative charged-particle fluid in a quadrupole-like device is developed. It is shown that the set of the classical fluid equations contains the same information as a complex function satisfying a Schrodinger-like equation in which Planck's constant is replaced by the time-varying emittance, which is related to the time-varying temperature of the fluid. The squared modulus and the gradient of the phase of this complex function are proportional to the fluid density and to the current velocity, respectively. Within this framework, the dynamics of an electron bunch in a storage ring in the presence of radiation damping and quantum-excitation is recovered. Furthermore, both standard and generalized (including dissipation) coherent states that may be associated with the classical particle fluids are fully described in terms of the above formalism.Comment: LaTex, to appear in Physica Script

Morphology of High-Multiplicity Events in Heavy Ion Collisions

We discuss opportunities that may arise from subjecting high-multiplicity events in relativistic heavy ion collisions to an analysis similar to the one used in cosmology for the study of fluctuations of the Cosmic Microwave Background (CMB). To this end, we discuss examples of how pertinent features of heavy ion collisions including global characteristics, signatures of collective flow and event-wise fluctuations are visually represented in a Mollweide projection commonly used in CMB analysis, and how they are statistically analyzed in an expansion over spherical harmonic functions. If applied to the characterization of purely azimuthal dependent phenomena such as collective flow, the expansion coefficients of spherical harmonics are seen to contain redundancies compared to the set of harmonic flow coefficients commonly used in heavy ion collisions. Our exploratory study indicates, however, that these redundancies may offer novel opportunities for a detailed characterization of those event-wise fluctuations that remain after subtraction of the dominant collective flow signatures. By construction, the proposed approach allows also for the characterization of more complex collective phenomena like higher-order flow and other sources of fluctuations, and it may be extended to the characterization of phenomena of non-collective origin such as jets.Comment: Matches version accepted for publication in Physical Review C. 13 pages, 9 figure

New Formulation of Causal Dissipative Hydrodynamics: Shock wave propagation

The first 3D calculation of shock wave propagation in a homogeneous QGP has been performed within the new formulation of relativistic dissipative hydrodynamics which preserves the causality. We found that the relaxation time plays an important role and also affects the angle of Mach cone.Comment: 4 pages, 1 figure, Proceedings of Quark Matter 200