Classical signatures in the dynamics of two-particle coherent states

It is known that the time evolution of a given set of quantum states can be formulated in terms of classical dynamics over their projected effective phase space. We investigate this effective phase space and the associated Lagrangian dynamics by considering two-particle coherent states in the symmetric (bosonic) and anti-symmetric (fermionic) configurations. By applying this formalism to 1D scattering problems as well as quadratic potentials in Hall physics regimes, we show that the exchange statistics of the particles in question leave distinct signatures in their classical trajectories. Further, the particles are seen to experience an effective “statistical force” that is a classical manifestation of their quantum mechanical exclusion properties. We also show that this formalism is easily extended to many-body problems, and thus offers a way to extract classical trajectories in these complex and possibly chaotic systems.