  We show that information about scattering data of a quantum field theory can
be obtained from studying the system at finite density and low temperatures. In
particular we consider models formulated on the lattice which can be exactly
dualized to theories of conserved charge fluxes on lattice links. Apart from
eliminating the complex action problem at nonzero chemical potential mu, these
dualizations allow for a particle world line interpretation of the dual fluxes
from which one can extract data about the 2-particle wave function. As an
example we perform dual Monte Carlo simulations of the 2-dimensional O(3) model
at nonzero mu and finite volume, whose non-perturbative spectrum consists of a
massive triplet of particles. At nonzero mu particles are induced in the
system, which at sufficiently low temperature give rise to sectors of fixed
particle number. We show that the scattering phase shifts can be obtained
either from the critical chemical potential values separating the sectors or
directly from the wave function in the 2-particle sector. We find that both
methods give excellent agreement with the exact result. We discuss the
applicability and generality of the new approaches.
