Escape behavior of quantum two-particle systems with Coulomb interactions.

Quantum escapes of two particles with Coulomb interactions from a confined one-dimensional region to a semi-infinite lead are discussed by using the probability of finding all particles within the confined region, that is, the survival probability, in comparison with free particles. By taking into account the quantum effects of two identical particles, such as the Pauli exclusion principle, it is shown analytically that for two identical free fermions (bosons), the survival probability decays asymptotically in power ~t(-10) (~t(-6)) as a function of time t, although it decays in power ~t(-3) for one free particle. On the other hand, for two particles with attractive Coulomb interactions it is shown numerically that the survival probability decays in power ~t(-3) after a long time. Moreover, for two particles with repulsive Coulomb interactions it decays exponentially in time ~exp (-αt) with a constant α, which is almost independent of the initial energy of particles.