1,031 research outputs found
Eigenfunctions of the Laplace-Beltrami Operator on Hyperboloids
Eigenfunctions of the Laplace-Beltrami operator on a hyperboloid are studied
in the spirit of the treatment of the spherical harmonics by Stein and Weiss.
As a special case, a simple self-contained proof of Laplace's integral for a
Legendre function is obtained.Comment: 5 page
Inductive Algebras for Finite Heisenberg Groups
A characterization of the maximal abelian sub-algebras of matrix algebras
that are normalized by the canonical representation of a finite Heisenberg
group is given. Examples are constructed using a classification result for
finite Heisenberg groups.Comment: 5 page
Steady state behaviour in atomic three-level lambda and ladder systems with incoherent population pumping
The steady state in three-level lambda and ladder systems is studied. It is
well-known that in a lambda system this steady state is the coherent population
trapping state, independent of the presence of spontaneous emission. In
contrast, the steady state in a ladder system is in general not stable against
radiative decay and exhibits a minimum in the population of the ground state.
It is shown that incoherent population pumping destroys the stability of the
coherent population trapping state in the lambda system and suppresses a
previously discovered sharp dip in the steady state response. In the ladder
system the observed minimum disappears in the presence of an incoherent pump on
the upper transition.Comment: 4 pages, RevTex, 5 figures, to appear in Phys. Rev.
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