372 research outputs found
Designing bound states in a band as a model for a quantum network
We provide a model of a one dimensional quantum network, in the framework of
a lattice using Von Neumann and Wigner's idea of bound states in a continuum.
The localized states acting as qubits are created by a controlled deformation
of a periodic potential. These wave functions lie at the band edges and are
defects in a lattice. We propose that these defect states, with atoms trapped
in them, can be realized in an optical lattice and can act as a model for a
quantum network.Comment: 8 pages, 10 figure
Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition
We study the quantum Hamilton-Jacobi (QHJ) equation of the recently obtained
exactly solvable models, related to the newly discovered exceptional
polynomials and show that the QHJ formalism reproduces the exact eigenvalues
and the eigenfunctions. The fact that the eigenfunctions have zeros and poles
in complex locations leads to an unconventional singularity structure of the
quantum momentum function , the logarithmic derivative of the wave
function, which forms the crux of the QHJ approach to quantization. A
comparison of the singularity structure for these systems with the known
exactly solvable and quasi-exactly solvable models reveals interesting
differences. We find that the singularities of the momentum function for these
new potentials lie between the above two distinct models, sharing similarities
with both of them. This prompted us to examine the exactness of the
supersymmetric WKB (SWKB) quantization condition. The interesting singularity
structure of and of the superpotential for these models has important
consequences for the SWKB rule and in our proof of its exactness for these
quantal systems.Comment: 10 pages with 1 table,i figure. Errors rectified, manuscript
rewritten, new references adde
Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the
complex domain, to a number of complex Hamiltonians, characterized by discrete
parity and time reversal (PT) symmetries and obtain their eigenvalues and
eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials
are analyzed and the subtle differences, in the singularity structures of their
quantum momentum functions, are pointed out. The role of the PT symmetry in the
complex domain is also illustrated.Comment: 11 page
Wave attenuation and dispersion due to floating ice covers
Experiments investigating the attenuation and dispersion of surface waves in
a variety of ice covers are performed using a refrigerated wave flume. The ice
conditions tested in the experiments cover naturally occurring combinations of
continuous, fragmented, pancake and grease ice. Attenuation rates are shown to
be a function of ice thickness, wave frequency, and the general rigidity of the
ice cover. Dispersion changes were minor except for large wavelength increases
when continuous covers were tested. Results are verified and compared with
existing literature to show the extended range of investigation in terms of
incident wave frequency and ice conditions
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