62 research outputs found
-digit Benford converges to Benford
Using the sum invariance property of Benford random variables, we prove that
an -digit Benford variable converges to a Benford variable as approaches
infinity.Comment: 5 pages, 1 figur
Manifestly Supersymmetric Lax Integrable Hierarchies
A systematic method of constructing manifestly supersymmetric
-dimensional KP Lax hierarchies is presented. Closed expressions for the
Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy
equations being eigenfunction equations are shown to be automatically invariant
under the (extended) supersymmetry. The supersymmetric Lax models existing in
the literature are found to be contained (up to a gauge equivalence) in our
formalism.Comment: LaTeX, 10 pg
The motion of two identical masses connected by an ideal string symmetrically placed over a corner
We introduce a novel, two-mass system that slides up an inclined plane while
its center of mass moves down. The system consists of two identical masses
connected by an ideal string symmetrically placed over a corner-shaped support.
This system is similar to a double-cone that rolls up an inclined set of
V-shaped rails. We find the double-cone's motion easy to demonstrate but
difficult to analyze. Our example here is more straightforward to follow, and
the experimental observations are in good agreement with the theoretical
predictions.Comment: 10 pages, 7 figures; Accepted for publication in American Journal of
Physic
Generation of a Novel Exactly Solvable Potential
We report a new shape invariant (SI) isospectral extension of the Morse
potential. Previous investigations have shown that the list of "conventional"
SI superpotentials that do not depend explicitly on Planck's constant
is complete. Additionally, a set of "extended" superpotentials has been
identified, each containing a conventional superpotential as a kernel and
additional -dependent terms. We use the partial differential equations
satisfied by all SI superpotentials to find a SI extension of Morse with novel
properties. It has the same eigenenergies as Morse but different asymptotic
limits, and does not conform to the standard generating structure for
isospectral deformations.Comment: 9 pages, 3 figure
Coordinate Realizations of Deformed Lie Algebras with Three Generators
Differential realizations in coordinate space for deformed Lie algebras with
three generators are obtained using bosonic creation and annihilation operators
satisfying Heisenberg commutation relations. The unified treatment presented
here contains as special cases all previously given coordinate realizations of
and their deformations. Applications to physical problems
involving eigenvalue determination in nonrelativistic quantum mechanics are
discussed.Comment: 11 pages, 0 figure
New Solvable Singular Potentials
We obtain three new solvable, real, shape invariant potentials starting from
the harmonic oscillator, P\"oschl-Teller I and P\"oschl-Teller II potentials on
the half-axis and extending their domain to the full line, while taking special
care to regularize the inverse square singularity at the origin. The
regularization procedure gives rise to a delta-function behavior at the origin.
Our new systems possess underlying non-linear potential algebras, which can
also be used to determine their spectra analytically.Comment: 19 pages, 4 figure
Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace
We generalize the Drinfeld-Sokolov formalism of bosonic integrable
hierarchies to superspace, in a way which systematically leads to the zero
curvature formulation for the supersymmetric integrable systems starting from
the Lax equation in superspace. We use the method of symmetric space as well as
the non-Abelian gauge technique to obtain the supersymmetric integrable
hierarchies of the AKNS type from the zero curvature condition in superspace
with the graded algebras, sl(n+1,n), providing the Hermitian symmetric space
structure.Comment: LaTeX, 9 pg
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