Uncertanties in Air-showers from Small-x pQCD Mini-Jets

To investigate uncertainties in air shower simulations caused by the small-x regime, a model including leading-twist hard pQCD plus soft processes was built, which are separated by an energy dependent transverse momentum cut-off. We provide a fit of the cut-off to the total pp cross section for different PDFs using the eikonal formalism and show that for modern PDF sets there is only a small uncertainty in the mini-jet cross section, and hence in the final-state multiplicity and the number of produced muons.Comment: 4 pages, 2 figures, contribution to QM2005 proceedings, revised version after referee comment

The role of local and global strangeness neutrality at the inhomogeneous freeze-out in relativistic heavy ion collisions

The decoupling surface in relativistic heavy-ion collisions may not be homogeneous. Rather, inhomogeneities should form when a rapid transition from high to low entropy density occurs. We analyze the hadron "chemistry" from high-energy heavy-ion reactions for the presence of such density inhomogeneities. We show that due to the non-linear dependence of the particle densities on the temperature and baryon-chemical potential such inhomogeneities should be visible even in the integrated, inclusive abundances. We analyze experimental data from Pb+Pb collisions at CERN-SPS and Au+Au collisions at BNL-RHIC to determine the amplitude of inhomogeneities and the role of local and global strangeness neutrality.Comment: 8 pages, 6 figures, To appear in proceedings of the workshop on 'Particle Correlations and Femtoscopy' September 9-11, 2006, Sao Paulo, Brazi

Group-theoretic Approach for Symbolic Tensor Manipulation: II. Dummy Indices

Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of names of dummy indices. The problem of finding canonical forms for indexed objects with dummy indices reduces to finding double coset canonical representatives. Well known computational group algorithms are applied to index manipulation, which allow to address the simplification of expressions with hundreds of indices going further to what is needed in practical applications.Comment: 14 pages, 1 figure, LaTe

Thermodynamics of N-dimensional quantum walks

The entanglement between the position and coin state of a $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated to the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc. We study in detail the case of a $2$-dimensional quantum walk, in the case of two different initial conditions: a non-separable coin-position initial state, and a separable one. The resulting entanglement temperature is presented as function of the parameters of the system and those of the initial conditions.Comment: 10 pages, 4 fig

Spatial search in a honeycomb network

The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. In this paper, a quantum algorithm for the spatial search problem on a honeycomb lattice with $N$ sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on a hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh is used to show that the time complexity of this quantum search algorithm is $O(\sqrt{N \log N})$.Comment: 10 pages, 2 figures; Minor typos corrected, one Reference added. accepted in Math. Structures in Computer Science, special volume on Quantum Computin