Coherent states for a system of an electron moving in a plane: case of discrete spectrum

In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfies.

Back-to-Back Performance of the Full Spectrum Nonlinear Fourier Transform and Its Inverse

In this paper, data-transmission using the nonlinear Fourier transform for jointly modulated discrete and continuous spectra is investigated. A recent method for purely discrete eigenvalue removal at the detector is extended to signals with additional continuous spectral support. At first, the eigenvalues are sequentially detected and removed from the jointly modulated received signal. After each successful removal, the time-support of the resulting signal for the next iteration can be narrowed, until all eigenvalues are removed. The resulting truncated signal, ideally containing only continuous spectral components, is then recovered by a standard NFT algorithm. Numerical simulations without a fiber channel show that, for jointly modulated discrete and continuous spectra, the mean-squared error between transmitted and received eigenvalues can be reduced using the eigenvalue removal approach, when compared to state-of-the-art detection methods. Additionally, the computational complexity for detection of both spectral components can be decreased when, by the choice of the modulated eigenvalues, the time-support after each removal step can be reduced. Numerical simulations are also carried out for transmission over a Raman-amplified, lossy SSMF channel. The mutual information is approximated and the eigenvalue removal method is shown to result in achievable rate improvements.

Repetitive emissions of rising-tone chorus waves in the inner magnetosphere

Chorus waves are well known for their significant roles in the radiation belts of the Earth and other magnetized planets, including acceleration of electrons to relativistic energies, and precipitation of energetic electrons into the ionosphere to produce diffuse and pulsating aurora. They typically occur in the form of discrete and repetitive quasi-monochromatic emissions with a frequency chirping, which was discovered more than 50 years ago. However, until now there is still no satisfactory explanations for repetitive emissions of chorus waves. In this report, chorus emissions excited by energetic electrons with a temperature anisotropy are studied by both a one-dimensional \(\delta f\) simulation and theoretical model in a dipole magnetic field. The two models have unanimously demonstrated that a continuous injection of energetic electrons caused by an azimuthal drift is essential for the repetitive emissions of chorus waves. Consistent with satellite observations, both discrete and continuous spectra can be reproduced. An intense injection of energetic electrons will lead to a decrease of the time separation between the chorus elements, and the chorus emissions evolve from a discrete to a continuous spectrum when the injection is sufficiently strong.