11,080 research outputs found
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
Surprises in the phase diagram of an Anderson impurity model for a single C molecule
We find by Wilson numerical renormalization group and conformal field theory
that a three-orbital Anderson impurity model for a C molecule has a
very rich phase diagram which includes non-Fermi-liquid stable and unstable
fixed points with interesting properties, most notably high sensitivity to
doping . We discuss the implications of our results to the conductance
behavior of C-based single-molecule transistor devices.Comment: 4 pages, 3 figures, 2 tables. Accepted versio
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
Solitons in a double pendulums chain model, and DNA roto-torsional dynamics
It was first suggested by Englander et al to model the nonlinear dynamics of
DNA relevant to the transcription process in terms of a chain of coupled
pendulums. In a related paper [q-bio.BM/0604014] we argued for the advantages
of an extension of this approach based on considering a chain of double
pendulums with certain characteristics. Here we study a simplified model of
this kind, focusing on its general features and nonlinear travelling wave
excitations; in particular, we show that some of the degrees of freedom are
actually slaved to others, allowing for an effective reduction of the relevant
equations
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 eigenvalue problem
We discuss the (right) eigenvalue equation for , and
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
Quaternionic Electroweak Theory
We explicitly develop a quaternionic version of the electroweak theory, based
on the local gauge group . The need of a complex
projection for our Lagrangian and the physical significance of the anomalous
scalar solutions are also discussed.Comment: 12 pages, Revtex, submitted to J. Phys.
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
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
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
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