On the Dynamics of Non-Relativistic Flavor-Mixed Particles

Abstract

Evolution of a system of interacting non-relativistic quantum flavor-mixed particles is considered both theoretically and numerically. It was shown that collisions of mixed particles not only scatter them elastically, but can also change their mass eigenstates thus affecting particles' flavor composition and kinetic energy. The mass eigenstate conversions and elastic scattering are related but different processes, hence the conversion $S$-matrix elements can be arbitrarily large even when the elastic scattering $S$-matrix elements vanish. The conversions are efficient when the mass eigenstates are well-separated in space but suppressed if their wave-packets overlap; the suppression is most severe for mass-degenerate eigenstates in flat space-time. The mass eigenstate conversions can lead to an interesting process, called `quantum evaporation,' in which mixed particles, initially confined deep inside a gravitational potential well and scattering only off each other, can escape from it without extra energy supply leaving nothing behind inside the potential at $t\to \infty$. Implications for the cosmic neutrino background and the two-component dark matter model are discussed and a prediction for the direct detection dark matter experiments is made.