  Pattern formation in ultra-cold quantum systems has recently received a great
deal of attention.In this work, we investigate a two-dimensional model system
accounting for the dynamics of trapped ions. We find a novel spiral wave which
is rigidly rotating but with a peculiar core region in which adjacent ions
oscillate in anti-phase. The formation of this novel spiral wave is ascribed to
the novel excitability reported by Lee and Cross. The breakup of the novel
spiral wave is probed and, especially, one extraordinary scenario of the
disappearance of spiral wave caused by spontaneous expansion of the anti-phased
core is unveiled.
