We investigate theoretically the time evolution of a one-dimensional system of spin-1/2 fermions in a harmonic trap after, initially, a spiral spin configuration far-from equilibrium is created. We predict a spin segregation building up in time already for weak interaction under realistic experimental conditions. The effect relies on the interplay between exchange interaction and the harmonic trap, and it is found for a wide range of parameters. It can be understood as a consequence of an effective, dynamically induced long-range interaction that is derived by integrating out the rapid oscillatory dynamics in the trap.
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