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Open Quantum Systems Decoherence

Short-time Fourier transform of the pointwise product of two functions with application to the nonlinear Schrödinger equation

arXiv
Authors: Nuno Costa Dias, João Nuno Prata, Nenad Teofanov

Year

2021

Paper ID

62461

Status

Preprint

Abstract Read

~2 min

Abstract Words

107

Citations

N/A

Abstract

We show that the short-time Fourier transform of the pointwise product of two functions f and h can be written as a suitable product of the short-time Fourier transforms of f and h. The same result is then shown to be valid for the Wigner wave-packet transform. We study the main properties of the new products. We then use these products to derive integro-differential equations on the time-frequency space equivalent to, and generalizing, the cubic nonlinear Schrödinger equation. We also obtain the Weyl-Wigner-Moyal equation satisfied by the Wigner-Ville function associated with the solution of the nonlinear Schrödinger equation. The new equation resembles the Boltzmann equation.

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  • We show that the short-time Fourier transform of the pointwise product of two functions f and h can be written as a suitable product of the short-time Fourier transforms of f...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2108.04985 [2] arXiv https://arxiv.org/abs/2108.04985 [3] Publisher https://arxiv.org/abs/2108.04985

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