Non-Hermitian Quantum Mechanics I: Instantaneous Self-Energy

Abstract

Starting from the unitary evolution of a closed quantum system, we rigorously demonstrate that the projection of the global wavefunction onto an arbitrary local subsystem is governed by an exact, time-dependent non-Hermitian Schrödinger equation. Crucially, the derivation does not rely on conventional approximations such as the Born approximation, the Markov approximation, or the wide-band limit. The central quantity is the \textit{instantaneous self-energy}, a time-dependent and generally non-Hermitian operator that encodes environmental backaction and, together with the subsystem Hamiltonian, forms the exact time-local generator of the projected dynamics. By benchmarking the conventional non-Hermitian approximation against this exact framework, we systematically expose its limitations. These results provide a rigorous microscopic foundation for the emergence of effective non-Hermitian dynamics in quantum systems.

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BibTeX RIS

BibTeX

@misc{liu2026nonhermitian,
  title = {{Non-Hermitian Quantum Mechanics I: Instantaneous Self-Energy}},
  author = {Lingfeng Liu and Wei-Wei Yang and Jiangping Hu and Zhesen Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23426},
  eprint = {2609.23426},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23426},
}

RIS

TY  - UNPB
TI  - Non-Hermitian Quantum Mechanics I: Instantaneous Self-Energy
AU  - Lingfeng Liu
AU  - Wei-Wei Yang
AU  - Jiangping Hu
AU  - Zhesen Yang
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23426
UR  - https://arxiv.org/abs/2609.23426
AB  - Starting from the unitary evolution of a closed quantum system, we rigorously demonstrate that the projection of the global wavefunction onto an arbitrary local subsystem is governed by an exact, time-dependent non-Hermitian Schrödinger equation. Crucially, the derivation does not rely on conventional approximations such as the Born approximation, the Markov approximation, or the wide-band limit. The central quantity is the \textit{instantaneous self-energy}, a time-dependent and generally non-Hermitian operator that encodes environmental backaction and, together with the subsystem Hamiltonian, forms the exact time-local generator of the projected dynamics. By benchmarking the conventional non-Hermitian approximation against this exact framework, we systematically expose its limitations. These results provide a rigorous microscopic foundation for the emergence of effective non-Hermitian dynamics in quantum systems.
ER  -

Abstract

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