Wigner distribution of Sine Gordon and Kink solitons

TL;DR

This paper derives and analyzes the Wigner distributions for Kink and Sine-Gordon solitons, enabling phase space analysis of their charge, current, and quantum speed limits.

Contribution

It provides the first derivation of Wigner distributions for these solitons using the Schrödinger wave-functional, linking phase space analysis with soliton quantum properties.

Findings

Wigner distributions for Kink and Sine-Gordon solitons are analytically derived.

Charge and current densities are calculated from the distributions.

Quantum speed limit bounds are established for the solitons.

Abstract

Wigner distributions play a significant role in formulating the phase space analogue of quantum mechanics. The Schrodinger wave-functional for solitons is needed to derive it for solitons. The Wigner distribution derived can further be used for calculating the charge distributions, current densities and wave function amplitude in position or momentum space. It can be also used to calculate the upper bound of the quantum speed limit time. We derive and analyze the Wigner distributions for Kink and Sine-Gordon solitons by evaluating the Schrodinger wave-functional for both solitons. The charge, current density, and quantum speed limit for solitons are also discussed which we obtain from the derived analytical expression of Wigner distributions.