On weakly tight families

Using ideas from Shelah's recent proof that a completely separable maximal almost disjoint family exists when $\c < {\aleph}_{\omega}$, we construct a weakly tight family under the hypothesis \s \leq \b < {\aleph}_{\omega}. The case when \s < \b is handled in \ZFC and does not require \b < {\aleph}_{\omega}, while an additional PCF type hypothesis, which holds when \b < {\aleph}_{\omega} is used to treat the case \s = \b. The notion of a weakly tight family is a natural weakening of the well studied notion of a Cohen indestructible maximal almost disjoint family. It was introduced by Hru{\v{s}}{\'a}k and Garc{\'{\i}}a Ferreira \cite{Hr1}, who applied it to the Kat\'etov order on almost disjoint families

Generalized reduction formula for Discrete Wigner functions of multiqubit systems

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computingComment: 7 Pages and zero figure

Studying Electroweak Baryogenesis using Evenisation and the Wigner Formalism

We derive the kinetic equation for fermions and antifermions interacting with a planar Higgs bubble wall during the electroweak phase transition using the `evenisation' procedure and the Wigner formalism for a Lagrangian with the phase of the complex fermion mass rotated away. We obtain the energy, velocity and force for the particles in the presence of the Higgs bubble wall. Our results using both methods are in agreement. This indicates the robustness of evenisation as a method to study quantum corrections to the velocity and force for particles in the Higgs wall during the electroweak phase transition. We also derive the transport equations from the zeroth and first moment of the kinetic equation.Comment: no figures (Error in indentification of antiparticle states corrected.