Nonlinear Schrodinger Equation Solitons on Quantum Droplets

TL;DR

This paper models azimuthal nonlinear waves on quantum liquid drops using the nonlinear Schrödinger equation, combining analytical solutions with quantum energy level calculations to match experimental nuclear data.

Contribution

It introduces a novel approach combining nonlinear Schrödinger equation solutions with Bethe ansatz for nuclear cluster dynamics.

Findings

Theoretical energy spectra match experimental data on alpha clustering nuclei.

Dark solitons modeled by elliptic functions describe wave behavior on quantum droplets.

Quantum regime analysis provides insights into nuclear surface dynamics.

Abstract

Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum and parity for alpha particle clustering nuclei.