"Quantum" Chaos and Stability Condition of Soliton-like Waves of Nuclear Burning in Neutron-Multiplicating Media

TL;DR

This paper investigates the stability of soliton-like nuclear burning waves in neutron-multiplicating media, linking it to quantum statistical conditions derived from Bohr-Sommerfeld quantization and Wigner ensemble statistics.

Contribution

It introduces a novel stability criterion for nuclear burning waves based on quantum chaos theory and statistical mechanics, connecting nuclear physics with quantum chaos concepts.

Findings

Stability depends on the relationship between equilibrium and critical isotope concentrations.

The Bohr-Sommerfeld quantization condition influences the necessary stability criterion.

Wigner quantum statistics determine the sufficient stability condition.

Abstract

We show that the stability condition for the soliton-like wave of nuclear burning in neutron-multiplicating medium is determined in general by two conditions. The first condition (necessary) is determined by relationship between the equilibrium concentration and critical concentration of active (fissile) isotope, that is a consequence of the Bohr-Sommerfeld quantization condition. The second condition (sufficient) is set by the so-called Wigner quantum statistics, or more accurately, by a ststistics of the Gaussian simplectic ensembles with respect to the parameter that describes the squared width of burning wave front of nuclear fuel active component.