Goldstone-mode instability leading to fragmentation in a spinor Bose-Einstein condensate

We apply the number-conserving Bogoliubov theory to spinor Bose-Einstein condensates and show that the Goldstone magnon causes instability leading to fragmentation. Unlike the dynamical instability, where modes with complex eigenfrequencies grow exponentially, here the zero-energy mode exhibits algebraic growth. We also point out that a small fraction of thermally excited atoms enhances the fragmentation dynamics.