12,904 research outputs found
Statistics of the Eigenvalues of a Noisy Multi-Soliton Pulse
For Nonlinear-Frequency Division-Multiplexed (NFDM) systems, the statistics
of the received nonlinear spectrum in the presence of additive white Gaussian
noise (AWGN) is an open problem. We present a novel method, based on the
Fourier collocation algorithm, to compute these statistics.Comment: Accepted for presentation at European Conference on Optical
Communications (ECOC) 201
A Short Note on the Infinite Decision Puzzle
This work draws on the Supertask literature1 in order to better understand the conceptual and physical possibility of an infinite decision puzzle presented by Barrett and Arntzenius (1999, 2002). The first section presents the puzzle and two possible objections documented in the literature. The next section argues that cardinality and tracking considerations play a key role in understanding the puzzle. The work concludes with a discussion about some implications for the decision theory.supertask infinite decision puzzle
Comment on: 'A simple analytical expression for bound state energies for an attractive Gaussian confining potential'
We discuss a recently proposed analytical formula for the eigenvalues of the
Gaussian well and compare it with the analytical expression provided by the
variational method with the simplest trial function. The latter yields
considerably more accurate results than the former for the energies and
critical parameters
Eigenvalues and eigenfunctions of the anharmonic oscillator
We obtain sufficiently accurate eigenvalues and eigenfunctions for the
anharmonic oscillator with potential by means of three
different methods. Our results strongly suggest that the spectrum of this
oscillator is discrete in agreement with early rigorous mathematical proofs and
against a recent statement that cast doubts about it
On two different kinds of resonances in one-dimensional quantum-mechanical models
We apply the Riccati-Pad\'{e} method and the Rayleigh-Ritz method with
complex rotation to the study of the resonances of a one-dimensional well with
two barriers. The model exhibits two different kinds of resonances and we
calculate them by means of both approaches. While the Rayleigh-Ritz method
reveals each set at a particular interval of rotation angles the Riccati
Pad\'{e} method yields both of them as roots of the same Hankel determinants
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