Linear response theory has a large applicability in physics as it often gives the leading order response of a system to an external probe. We develop an extension of the theory to the domain of non-Hermitian quantum mechanics, where wave functions have a non-unitary dynamics. We exemplify the salient features of this theory through two examples which contain surprising predictions for the behavior of expectation values in the non-Hermitian realm: (1) finite electrical DC conductivity in a one-dimensional tachyon system, and (2) absence of Friedel oscillations due to an imaginary potential.
[1] D. Sticlet, B. Dora, C.P. Moca, Kubo formula for non-Hermitian systems and tachyon optical conductivity, arXiv:2104.02428 (2021).
[2] B. Dora, D. Sticlet, C.P. Moca, Non-Hermitian Lindhard function and Friedel oscillations, Phys. Rev. B 104, 125113 (2021).
