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 and exemplify the salient features of this theory through two examples: (1) a one-dimensional tachyon under the effect of electric field-like perturbations and (2) a free electron gas perturbed by non-Hermitian scalar potentials. We show that these contain striking predictions for the behavior of expectation values in the non-Hermitian realm such as a finite electrical DC conductivity in (1) and suppression of Friedel oscillations in (2).

 

References:

[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).