Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism

• URL: http://arxiv.org/abs/2107.11910v2
• Date: Fri, 22 Apr 2022 06:33:25 GMT
• Title: Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Authors: Chia-Yi Ju, Adam Miranowicz, Fabrizio Minganti, Chuan-Tsung Chan, Guang-Yin Chen, Franco Nori
• Abstract summary: We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones. In other words, any non-Hermitian Hamiltonian can be "transformed" into a Hermitian one without altering the physics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbein-like 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 non-trivial Hilbert space metric, reduces to a Hermitian system within the standard formalism of quantum mechanics.

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