  In this paper, we provide a theoretical analysis of strongly interacting
quantum systems confined by a time-dependent external potential in one spatial
dimension. We show that such systems can be used to simulate spin chains
described by Heisenberg Hamiltonians in which the exchange coupling constants
can be manipulated by time-dependent driving of the shape of the external
confinement. As illustrative examples, we consider a harmonic trapping
potential with a variable frequency and an infinite square well potential with
a time-dependent barrier in the middle.
