381 research outputs found
On Exactness Of The Supersymmetric WKB Approximation Scheme
Exactness of the lowest order supersymmetric WKB (SWKB) quantization
condition , for certain
potentials, is examined, using complex integration technique. Comparison of the
above scheme with a similar, but {\it exact} quantization condition, , originating from the quantum Hamilton-Jacobi
formalism reveals that, the locations and the residues of the poles that
contribute to these integrals match identically, for both of these cases. As
these poles completely determine the eigenvalues in these two cases, the
exactness of the SWKB for these potentials is accounted for. Three non-exact
cases are also analysed; the origin of this non-exactness is shown to be due
the presence of additional singularities in , like branch
cuts in the plane.Comment: 11 pages, latex, 1 figure available on reques
A New Look at Mode Conversion in a Stratified Isothermal Atmosphere
Recent numerical investigations of wave propagation near coronal magnetic
null points (McLaughlin and Hood: Astron. Astrophys. 459, 641,2006) have
indicated how a fast MHD wave partially converts into a slow MHD wave as the
disturbance passes from a low-beta plasma to a high-beta plasma. This is a
complex process and a clear understanding of the conversion mechanism requires
the detailed investigation of a simpler model. An investigation of mode
conversion in a stratified, isothermal atmosphere, with a uniform, vertical
magnetic field is carried out, both numerically and analytically. In contrast
to previous investigations of upward-propagating waves (Zhugzhda and Dzhalilov:
Astron. Astrophys. 112, 16, 1982a; Cally: Astrophys. J. 548, 473, 2001), this
paper studies the downward propagation of waves from a low-beta to high-beta
environment. A simple expression for the amplitude of the transmitted wave is
compared with the numerical solution.Comment: 14 pages, 6 figure
The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism
The generalized Sinh-Gordon potential is solved within quantum Hamiltonian
Jacobi approach in the framework of PT symmetry. The quasi exact solutions of
energy eigenvalues and eigenfunctions of the generalized Sinh-Gordon potential
are found for n=0,1 states.Comment: 10 pages appear to in IJT
Faster Approximate String Matching for Short Patterns
We study the classical approximate string matching problem, that is, given
strings and and an error threshold , find all ending positions of
substrings of whose edit distance to is at most . Let and
have lengths and , respectively. On a standard unit-cost word RAM with
word size we present an algorithm using time When is
short, namely, or this
improves the previously best known time bounds for the problem. The result is
achieved using a novel implementation of the Landau-Vishkin algorithm based on
tabulation and word-level parallelism.Comment: To appear in Theory of Computing System
Compressed Subsequence Matching and Packed Tree Coloring
We present a new algorithm for subsequence matching in grammar compressed
strings. Given a grammar of size compressing a string of size and a
pattern string of size over an alphabet of size , our algorithm
uses space and or time. Here
is the word size and is the number of occurrences of the pattern. Our
algorithm uses less space than previous algorithms and is also faster for
occurrences. The algorithm uses a new data structure
that allows us to efficiently find the next occurrence of a given character
after a given position in a compressed string. This data structure in turn is
based on a new data structure for the tree color problem, where the node colors
are packed in bit strings.Comment: To appear at CPM '1
Towards surface quantum optics with Bose-Einstein condensates in evanescent waves
We present a surface trap which allows for studying the coherent interaction
of ultracold atoms with evanescent waves. The trap combines a magnetic Joffe
trap with a repulsive evanescent dipole potential. The position of the magnetic
trap can be controlled with high precision which makes it possible to move
ultracold atoms to the surface of a glass prism in a controlled way. The
optical potential of the evanescent wave compensates for the strong attractive
van der Waals forces and generates a potential barrier at only a few hundred
nanometers from the surface. The trap is tested with Rb Bose-Einstein
condensates (BEC), which are stably positioned at distances from the surfaces
below one micrometer
Orbital Tests of Relativistic Gravity using Artificial Satellites
We reexamine non-Einsteinian effects observable in the orbital motion of
low-orbit artificial Earth satellites. The motivations for doing so are
twofold: (i) recent theoretical studies suggest that the correct theory of
gravity might contain a scalar contribution which has been reduced to a small
value by the effect of the cosmological expansion; (ii) presently developed
space technologies should soon give access to a new generation of satellites
endowed with drag-free systems and tracked in three dimensions at the
centimeter level. Our analysis suggests that such data could measure two
independent combinations of the Eddington parameters (beta - 1) and (gamma - 1)
at the 10^-4 level and probe the time variability of Newton's "constant" at the
d(ln G)/dt ~ 10^-13 yr^-1 level. These tests would provide well-needed
complements to the results of the Lunar Laser Ranging experiment, and of the
presently planned experiments aiming at measuring (gamma -1). In view of the
strong demands they make on the level of non- gravitational perturbations,
these tests might require a dedicated mission consisting of an optimized
passive drag-free satellite.Comment: 17 pages, IHES/P/94/22 and CPT-94/P.E.302
PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation
PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and
generalized harmonic oscillator potentials with the position-dependent mass. A
general point canonical transformation is applied by using a free parameter.
Three different forms of mass distributions are used. A set of the energy
eigenvalues of the bound states and corresponding wave functions for target
potentials are obtained as a function of the free parameter.Comment: 13 page
Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility
We propose an analysis technique for the exceptional points (EPs) occurring
in the discrete spectrum of open quantum systems (OQS), using a semi-infinite
chain coupled to an endpoint impurity as a prototype. We outline our method to
locate the EPs in OQS, further obtaining an eigenvalue expansion in the
vicinity of the EPs that gives rise to characteristic exponents. We also report
the precise number of EPs occurring in an OQS with a continuum described by a
quadratic dispersion curve. In particular, the number of EPs occurring in a
bare discrete Hamiltonian of dimension is given by ; if this discrete Hamiltonian is then coupled to continuum
(or continua) to form an OQS, the interaction with the continuum generally
produces an enlarged discrete solution space that includes a greater number of
EPs, specifically , in which
is the number of (non-degenerate) continua to which the discrete sector is
attached. Finally, we offer a heuristic quantum phase transition analogy for
the emergence of the resonance (giving rise to irreversibility via exponential
decay) in which the decay width plays the role of the order parameter; the
associated critical exponent is then determined by the above eigenvalue
expansion.Comment: 16 pages, 7 figure
Kaon-Nucleon Scattering Amplitudes and Z-Enhancements from Quark Born Diagrams
We derive closed form kaon-nucleon scattering amplitudes using the ``quark
Born diagram" formalism, which describes the scattering as a single interaction
(here the OGE spin-spin term) followed by quark line rearrangement. The low
energy I=0 and I=1 S-wave KN phase shifts are in reasonably good agreement with
experiment given conventional quark model parameters. For Gev
however the I=1 elastic phase shift is larger than predicted by Gaussian
wavefunctions, and we suggest possible reasons for this discrepancy. Equivalent
low energy KN potentials for S-wave scattering are also derived. Finally we
consider OGE forces in the related channels K, KN and K,
and determine which have attractive interactions and might therefore exhibit
strong threshold enhancements or ``Z-molecule" meson-baryon bound states.
We find that the minimum-spin, minimum-isospin channels and two additional
K channels are most conducive to the formation of bound states.
Related interesting topics for future experimental and theoretical studies of
KN interactions are also discussed.Comment: 34 pages, figures available from the authors, revte
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