Induced tunneling in quantum field theory: Soliton creation in collisions of highly energetic particles

We consider tunneling transitions between states separated by an energy barrier in a simple field theoretical model. We analyze the case of soliton creation induced by collisions of a few highly energetic particles. We present a semiclassical, but otherwise first principle, study of this process at all energies of colliding particles. We find that direct tunneling to the final state occurs at energies below the critical value Ec, which is slightly higher than the barrier height. Tunneling probability grows with energy in this regime. Above the critical energy, the tunneling mechanism is different. The transition proceeds through creation of a state close to the top of the potential barrier (sphaleron) and its subsequent decay. At a certain limiting energy, El, tunneling probability ceases to grow. At higher energies, the dominant mechanism of transition becomes the release of energy excess E-El by the emission of a few particles and then tunneling at effectively lower energy E=El via the limiting semiclassical configuration. The latter belongs to a class of “real-time instantons,” semiclassical solutions saturating the inclusive probability of tunneling from initial states with a given number of particles. We conclude that the process of collision-induced tunneling is exponentially suppressed at all energies.