Einstein's quantum elevator: Hermitization of non-Hermitian Hamiltonians via a generalized vielbein formalism
Chia-Yi Ju, Adam Miranowicz, Fabrizio Minganti, Chuan-Tsung Chan, Guang-Yin Chen, Franco Nori
Abstract
The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbeinlike formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering the induced Hamiltonian to be Hermitian. In other words, any non-Hermitian Hamiltonian can be ``transformed'' into a Hermitian one without altering the physics. Thus we show how to find a reference frame (corresponding to Einstein's quantum elevator) in which a non-Hermitian system, equipped with a nontrivial Hilbert space metric, reduces to a Hermitian system within the standard formalism of quantum mechanics.