18,043 research outputs found
An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes
We will present a complete set of equations, in the form of an
Einstein-Bianchi system, that describe the evolution of generic smooth lattices
in spacetime. All 20 independent Riemann curvatures will be evolved in parallel
with the leg-lengths of the lattice. We will show that the evolution equations
for the curvatures forms a hyperbolic system and that the associated
constraints are preserved. This work is a generalisation of our previous paper
arXiv:1101.3171 on the Einstein-Bianchi system for the Schwarzschild spacetime
to general 3+1 vacuum spacetimes
Cruise Report 69-S-3: Pelagic fish and trawling survey of Santa Barbara oil spill
(PDF contains 5 pages
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
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
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
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 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
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