We show how open strings cease to propagate when unstable D-branes decay. The<br />
information on the propagation is encoded in BSFT two-point functions for<br />
arbitrary profiles of open string excitations. We evaluate them in tachyon<br />
condensation backgrounds corresponding to (i) static spatial tachyon kink (=<br />
lower dimensional BPS D-brane) and (ii) homogeneous rolling tachyon. For (i)<br />
the propagation is restricted to the directions along the tachyon kink, while<br />
for (ii) all the open string excitations cease to propagate at late time and<br />
are subject to a collapsed light cone characterized by Carrol...