Scattering properties of $\cal{PT}$-symmetric quantum systems

Details Scattering properties of $\cal{PT}$-symmetric quantum systems Scattering properties of $\cal{PT}$-symmetric quantum systems

2011-09-14

arxiv.org/abs/1109.3113v1

Physics

Quantum Physics

9 pages

Scientific paper

Properties of the scattering matrix for 1-D $\cal{PT}$-symmetric systems have been analyzed. In the context of the continuum states, conservation properties are utilized to extract physical conclusions. Asymptotic states are shown to have necessarily broken $\cal{PT}$-symmetry, leading to restricted boundary conditions, some resembling the proposed $\cal{PT}$ CPA laser \cite{Longhi}, with absorption/emission during the scattering process. It is noted that transmission is possible, only if incidence takes place from both sides of the system, which is unique to a $\cal{PT}$-symmetric quantum mechanical system. $\cal{PT}$-symmetric systems require additional conditions for scattering and transfer matrices, indicating a unique algebraic structure. The S-matrix is found to be \textit{Hermitian}, instead of being unitary, and to satisfy a `duality' condition, having known optical analogues \cite{Dual}. Finally, a suggestive approach towards a `physical' $\cal{PT}$-symmetric norm is made.

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