8,616 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
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
Fast algorithms for computing defects and their derivatives in the Regge calculus
Any practical attempt to solve the Regge equations, these being a large
system of non-linear algebraic equations, will almost certainly employ a
Newton-Raphson like scheme. In such cases it is essential that efficient
algorithms be used when computing the defect angles and their derivatives with
respect to the leg-lengths. The purpose of this paper is to present details of
such an algorithm.Comment: 38 pages, 10 figure
Inelastic Collapse of Three Particles
A system of three particles undergoing inelastic collisions in arbitrary
spatial dimensions is studied with the aim of establishing the domain of
``inelastic collapse''---an infinite number of collisions which take place in a
finite time. Analytic and simulation results show that for a sufficiently small
restitution coefficient, , collapse can
occur. In one dimension, such a collapse is stable against small perturbations
within this entire range. In higher dimensions, the collapse can be stable
against small variations of initial conditions, within a smaller range,
.Comment: 6 pages, figures on request, accepted by PR
A Tunable Kondo Effect in Quantum Dots
We demonstrate a tunable Kondo effect realized in small quantum dots. We can
switch our dot from a Kondo impurity to a non-Kondo system as the number of
electrons on the dot is changed from odd to even. We show that the Kondo
temperature can be tuned by means of a gate voltage as a single-particle energy
state nears the Fermi energy. Measurements of the temperature and magnetic
field dependence of a Coulomb-blockaded dot show good agreement with
predictions of both equilibrium and non-equilibrium Kondo effects.Comment: 8 pages, 4 figure
Spiking Neurons Learning Phase Delays
Time differences between the two ears are an important cue for animals to azimuthally locate a sound source. The first binaural brainstem nucleus, in mammals the medial superior olive, is generally believed to perform the necessary computations. Its cells are sensitive to variations of interaural time differences of about 10 μs. The classical explanation of such a neuronal time-difference tuning is based on the physical concept of delay lines. Recent data, however, are inconsistent with a temporal delay and rather favor a phase delay. By means of a biophysical model we show how spike-timing-dependent synaptic learning explains precise interplay of excitation and inhibition and, hence, accounts for a physical realization of a phase delay
Theory of a Continuous H Normal-to-Superconducting Transition
I study the transition within the Ginzburg-Landau model, with
-component order parameter . I find a renormalized fixed point free
energy, exact in limit, suggestive of a nd-order
transition in contrast to a general belief of a st-order transition. The
thermal fluctuations for force one to consider an infinite set of
marginally relevant operators for . I find , predicting
that the ODLRO does not survive thermal fluctuations in . The result is
a solution to a critical fixed point that was found to be inaccessible within
-expansion, previously considered in E.Brezin, D.R.Nelson,
A.Thiaville, Phys.Rev.B {\bf 31}, 7124 (1985), and was interpreted as a
st-order transition.Comment: 4 pages, self-unpacking uuencoded compressed postscript file with a
figure already inside text; to appear in Phys. Rev. Lett
Determination of air content of hardened concrete using image analysis.
Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1983 .M493. Source: Masters Abstracts International, Volume: 40-07, page: . Thesis (M.A.Sc.)--University of Windsor (Canada), 1983
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