“Quantum” chaos and stability condition of soliton-like waves of nuclear burning in neutron-multiplicating media

Abstract

We show that the stability сondition 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.