Two- and Three-particle States in a Nonrelativistic Four-fermion Model in the Fine-tuning Renormalization Scheme. Goldstone mode "against" extension theory

In a nonrelativistic contact four-fermion model we show that simple regularisation prescriptions together with a definite fine-tuning of the cut-off-parameter dependence of ``bare'' quantities give the exact solutions for the two-particle sector and Goldstone modes. Their correspondence with the self-adjoint extension into Pontryagin space is established leading to self-adjoint semi-bounded Hamiltonians in three-particle sectors as well. Renormalized Faddeev equations for the bound states with Fredholm properties are obtained and analysed.Comment: 23 pages, LaTeX, changed content, added references and two figures, to appear in the Few Body System

Topological phase in two flavor neutrino oscillations

We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between non-orthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.Comment: 11 pages, 3 figures, accepted in Phys. Rev.

Vortex-to-Polarization Phase Transformation Path in Pb(ZrTi)O3_3 Nanoparticles

Phase transformation in finite-size ferroelectrics is of fundamental relevance for understanding collective behaviors and balance of competing interactions in low-dimensional systems. We report a first-principles effective Hamiltonian study of vortex-to-polarization transformation in Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ nanoparticles, caused by homogeneous electric fields normal to the vortex plane. The transformation is shown to (1) follow an unusual {\it macroscopic} path that is symmetry non-conforming and characterized by the occurrence of a previously unknown structure as the bridging phase; (2) lead to the discovery of a striking collective phenomenon, revealing how ferroelectric vortex is annihilated {\it microscopically}. Interactions underlying these behaviors are discussed