A study of Wigner functions for discrete-time quantum walks

We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative volume in phase space, as a function of time, for different initial states. This negativity can be used to quantify the degree of departure of the system from a classical state. We also relate this quantity to the entanglement between the coin and walker subspaces.Comment: 16 pages, 8 figure

Contractions, Hopf algebra extensions and cov. differential calculus

We re-examine all the contractions related with the ${\cal U}_q(su(2))$ deformed algebra and study the consequences that the contraction process has for their structure. We also show using ${\cal U}_q(su(2))\times{\cal U}(u(1))$ as an example that, as in the undeformed case, the contraction may generate Hopf algebra cohomology. We shall show that most of the different Hopf algebra deformations obtained have a bicrossproduct or a cocycle bicrossproduct structure, for which we shall also give their dual `group' versions. The bicovariant differential calculi on the deformed spaces associated with the contracted algebras and the requirements for their existence are examined as well.Comment: TeX file, 25 pages. Macros are include

Correlations in nuclear energy recurrence relations

The excitation energies of states belonging to the ground state bands of heavy even-even nuclei are analysed using recurrence relations. Excellent agreement with experimental data at the 10 keV level is obtained by taking into account strong correlations which emerge in the analysis. This implies that the excitation energies can be written as a polynomial of maximum degree four in the angular momentum.Comment: 4 pages, 1 figure, 1 table, 9 reference