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## 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)

## Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

Luis L. Sanchez-Soto, Juan J. Monzon

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Mobius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.

http://arxiv.org/abs/1405.4791

Quantum Physics (quant-ph)