56 research outputs found
Exact propagators on the lattice with applications to diffractive effects
The propagator of the discrete Schr\"odinger equation is computed and its
properties are revealed through a Feynman path summation in discrete space.
Initial data problems such as diffraction in discrete space and continuous time
are studied analytically by the application of the new propagator. In the
second part of this paper, the analogy between time propagation and 2D
scattering by 1D obstacles is explored. New results are given in the context of
diffraction by edges within a periodic medium. A connection with tight-binding
arrays and photonic crystals is indicated.Comment: Final version with two appendices. Published in J. Phys. A: Math.
Theo
Decoherence at constant excitation
We present a simple exactly solvable extension of of the Jaynes-Cummings
model by adding dissipation. This is done such that the total number of
excitations is conserved. The Liouville operator in the resulting master
equation can be reduced to blocks of matrices
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