19,184 research outputs found
Quaternionic Root Systems and Subgroups of the
Cayley-Dickson doubling procedure is used to construct the root systems of
some celebrated Lie algebras in terms of the integer elements of the division
algebras of real numbers, complex numbers, quaternions and octonions. Starting
with the roots and weights of SU(2) expressed as the real numbers one can
construct the root systems of the Lie algebras of SO(4),SP(2)=
SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the
division algebras. The roots themselves display the group structures besides
the octonionic roots of E_{8} which form a closed octonion algebra. The
automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the
largest crystallographic group in 4-dimensional Euclidean space, is realized as
the direct product of two binary octahedral group of quaternions preserving the
quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such
as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed
as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic
subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192
with different conjugacy classes occur as maximal subgroups in the finite
subgroups of the Lie group of orders 12096 and 1344 and proves to be
useful in their constructions. The triality of SO(8) manifesting itself as the
cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used
to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and
F_{4} respectively
Radiation damage in GaAs solar cells
Recent results of electron and proton irradiation and annealing of GaAs solar cells are presented along with some implications of these results. A comparison between the energy-levels produced by protons and by electrons which are not stopped in the material indicate that the damage produced by protons and electrons may be qualitatively different. Thus, annealing of proton damage may be very different from the annealing of electron damage
New Duality Relations for Classical Ground States
We derive new duality relations that link the energy of configurations
associated with a class of soft pair potentials to the corresponding energy of
the dual (Fourier-transformed) potential. We apply them by showing how
information about the classical ground states of short-ranged potentials can be
used to draw new conclusions about the nature of the ground states of
long-ranged potentials and vice versa. They also lead to bounds on the T=0
system energies in density intervals of phase coexistence, the identification
of a one-dimensional system that exhibits an infinite number of ``phase
transitions," and a conjecture regarding the ground states of purely repulsive
monotonic potentials.Comment: 11 pages, 2 figures. Slightly revised version that corrects typos.
This article will be appearing in Physical Review Letters in a slightly
shortened for
Fluid-solid transition in hard hyper-sphere systems
In this work we present a numerical study, based on molecular dynamics
simulations, to estimate the freezing point of hard spheres and hypersphere
systems in dimension D = 4, 5, 6 and 7. We have studied the changes of the
Radial Distribution Function (RDF) as a function of density in the coexistence
region. We started our simulations from crystalline states with densities above
the melting point, and moved down to densities in the liquid state below the
freezing point. For all the examined dimensions (including D = 3) it was
observed that the height of the first minimum of the RDF changes in an almost
continuous way around the freezing density and resembles a second order phase
transition. With these results we propose a numerical method to estimate the
freezing point as a function of the dimension D using numerical fits and
semiempirical approaches. We find that the estimated values of the freezing
point are very close to previously reported values from simulations and
theoretical approaches up to D = 6 reinforcing the validity of the proposed
method. This was also applied to numerical simulations for D = 7 giving new
estimations of the freezing point for this dimensionality.Comment: 13 pages, 10 figure
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