An Analytic Approach to the Wave Packet Formalism in Oscillation Phenomena

We introduce an approximation scheme to perform an analytic study of the oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian wave packets, we show that the oscillation is bounded by a time-dependent vanishing function which characterizes the slippage between the mass-eigenstate wave packets. We also demonstrate that the wave packet spreading represents a secondary effect which plays a significant role only in the non-relativistic limit. In our analysis, we note the presence of a new time-dependent phase and calculate how this additional term modifies the oscillating character of the flavor conversion formula. Finally, by considering Box and Sine wave packets we study how the choice of different functions to describe the particle localization changes the oscillation probability.Comment: 16 pages, 7 figures, AMS-Te

The octonionic eigenvalue problem

By using a real matrix translation, we propose a coupled eigenvalue problem for octonionic operators. In view of possible applications in quantum mechanics, we also discuss the hermiticity of such operators. Previous difficulties in formulating a consistent octonionic Hilbert space are solved by using the new coupled eigenvalue problem and introducing an appropriate scalar product for the probability amplitudes.Comment: 21 page

Wave and Particle Limit for Multiple Barrier Tunneling

The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the plane wave results. In particular, the existence of resonance/transparency for twin tunnelling in the wave limit is immediately obvious. The known resonances for three and four barriers are also derived. The transition from the wave limit to the particle limit is exhibit numerically.Comment: 15 pages, 3 figure

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te

Quaternionic potentials in non-relativistic quantum mechanics

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to investigate an underlying quaternionic quantum dynamics in particle physics. Experimental tests and proposals to observe quaternionic quantum effects by neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te

Quaternionic Electroweak Theory and CKM Matrix

We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this quaternionic puzzle.Comment: 8, Revtex, Int. J. Theor. Phys. (to be published

Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te

Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem

We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long--lasting quasi--stationary states (QSS) are found, whose pdfs appear to converge to $q$--Gaussians associated with nonextensive statistical mechanics. More generally, however, as $N$ increases, the pdfs describe a sequence of QSS that pass from a $q$--Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in the International Journal of Bifurcation and Chaos, on Jun 21, 201

Chromosomal anchoring of linkage groups and identification of wing size QTL using markers and FISH probes derived from microdissected chromosomes in Nasonia(Pteromalidae : Hymenoptera)

Nasonia vitripennis is a small parasitic hymenopteran with a 50-year history of genetic work including linkage mapping with mutant and molecular markers. For the first time we are now able to anchor linkage groups to specific chromosomes. Two linkage maps based on a hybrid cross (N. vitripennis x N. longicornis) were constructed using STS, RAPID and microsatellite markers, where 17 of the linked STS markers were developed from single microdissected banded chromosomes. Based on these microdissections we anchored all linkage groups to the five chromosomes of N. vitripennis. We also verified the chromosomal specificity of the microdissection through in situ hybridization and linkage analyses. This information and technique will allow us in the future to locate genes or QTL detected in different mapping populations efficiently and fast on homologous chromosomes or even chromosomal regions. To test this approach we asked whether QTL responsible for the wing size in two different hybrid crosses (N. vitripennis x N. longicornis and N. vitripennis x N. giraulti) map to the same location. One QTL with a major effect was found to map to the centromere region of chromosome 3 in both crosses. This could indicate that indeed the same gene/s is involved in the reduction of wing in N. vitripennis and N. longicornis. Copyright (C) 2003 S. Karger AG, Basel

Dirac Equation Studies in the Tunnelling Energy Zone

We investigate the tunnelling zone V0 < E < V0+m for a one-dimensional potential within the Dirac equation. We find the appearance of superluminal transit times akin to the Hartman effect.Comment: 12 pages, 4 figure