83,425 research outputs found
Monte Carlo Studies of the Fundamental Limits of the Intrinsic Hyperpolarizability
The off-resonant hyperpolarizability is calculated using the dipole-free
sum-over-stats expression from a randomly chosen set of energies and transition
dipole moments that are forced to be consistent with the sum rules. The process
is repeated so that the distribution of hyperpolarizabilities can be
determined. We find this distribution to be a cycloid-like function. In
contrast to variational techniques that when applied to the potential energy
function yield an intrinsic hyperpolarizability less than 0.71, our Monte Carlo
method yields values that approach unity. While many transition dipole moments
are large when the calculated hyperpolarizability is near the fundamental
limit, only two excited states dominate the hyperpolarizability - consistent
with the three-level ansatz.Comment: 7 pages, 5 figure
Gravity from a Modified Commutator
We show that a suitably chosen position-momentum commutator can elegantly
describe many features of gravity, including the IR/UV correspondence and
dimensional reduction (`holography'). Using the most simplistic example based
on dimensional analysis of black holes, we construct a commutator which
qualitatively exhibits these novel properties of gravity. Dimensional reduction
occurs because the quanta size grow quickly with momenta, and thus cannot be
"packed together" as densely as naively expected. We conjecture that a more
precise form of this commutator should be able to quantitatively reproduce all
of these features.Comment: 8 pages; Honorable Mention in the 2005 Gravity Research Foundation
Essay Competition; v2: acknowledgments adde
The Stability of Noncommutative Scalar Solitons
We determine the stability conditions for a radially symmetric noncommutative
scalar soliton at finite noncommutivity parameter . We find an
intriguing relationship between the stability and existence conditions for all
level-1 solutions, in that they all have nearly-vanishing stability eigenvalues
at critical . The stability or non-stability of the system may then
be determined entirely by the coefficient in the potential. For
higher-level solutions we find an ambiguity in extrapolating solutions to
finite which prevents us from making any general statements. For these
stability may be determined by comparing the fluctuation eigenvalues to
critical values which we calculate.Comment: 12 pages, corrected typo
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