Geiger–Nuttall law for Schrödinger solitons

Abstract

Based on the formal analogy between soliton tunneling through a classically forbidden potential barrier and –particle tunneling and decay we introduce a ‘toy solitonic model of a nucleus’ and show that the analog of the Geiger–Nuttall law can be discovered for Schrödinger solitons. We reveal and explain the analogy with virtual particle–antiparticle pair production and annihilation mechanisms and show how the nonlinear particle-like wave packet is being ‘dressed in a coat of virtual pairs’ and transformed into the soliton. In computational experiments with different soliton parameters and for different profiles of the barriers, including the charged sphere Coulomb potential, we demonstrate how the scaling symmetry breaking reveals the hidden role of the soliton self-interaction (binding) energy in the soliton scattering on external potentials and its dramatic impact on the wave-particle duality of solitons.

Keywords:

• nonlinear Schrödinger equation
• soliton self-interaction energy
• soliton binding energy
• soliton tunneling
• soliton scattering
• Geiger–Nuttall law for Schrödinger solitons

Acknowledgements

The authors gratefully acknowledge useful conversations and illuminating discussions with Professor J.R. Taylor from Imperial College, London.