## Is space-time symmetry a suitable generalization of parity-time symmetry?

Paolo Amore, Francisco M. Fernández, Javier Garcia

We discuss space-time symmetric Hamiltonian operators of the form $$H=H_{0}+igH^{\prime}$$, where $$H_{0}$$ is Hermitian and $$g$$ real. $$H_0$$ is invariant under the unitary operations of a point group $$G$$ while $$H^\prime$$ is invariant under transformation by elements of a subgroup $$G^\prime$$ of $$G$$. If $$G$$ exhibits irreducible representations of dimension greater than unity, then it is possible that $$H$$ has complex eigenvalues for sufficiently small nonzero values of $$g$$. In the particular case that $$H$$ is parity-time symmetric then it appears to exhibit real eigenvalues for all $$0<g<g_c$$, where $$g_{c}$$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether $$H$$ may exhibit real or complex eigenvalues for $$g>0$$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.

http://arxiv.org/abs/1405.5234
Quantum Physics (quant-ph)