Scattering properties of PT - symmetric quantum systems

Abstract

Properties of the scattering matrix for 1-D PT -symmetric systems have been analyzed. In the context of the continuum states, conservation properties are utilized to extract physical conclu- sions. Asymptotic states are shown to have necessarily broken PT -symmetry, leading to restricted boundary conditions, some resembling the proposed PT CPA laser [1], 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 PT -symmetric quantum mechanical system. PT -symmetric systems require additional conditions for scattering and transfer matrices, indicating a unique algebraic structure. The S-matrix is found to be Hermitian, instead of being unitary, and to satisfy a 'duality' condition, having known optical analogues [2]. Finally, a suggestive approach towards a 'physical' PT -symmetric norm is made.