Non-Hermitian effective dynamics from post-selection protocols
Abstract
Multiple seemingly distinct frameworks are commonly proposed to explain the emergence of effective non-Hermitian dynamics in quantum systems coupled to an environment. Furthermore, it remains contested how to properly calculate expectation values or whether thermal equilibrium states exist in non-Hermitian systems. In this work, we show that Feshbach projection, the Lindblad master equation, and the ancilla approach can all be understood through the Kraus map formalism, leading to non-Hermitian time evolution if an appropriate post-selection procedure is enforced. After first deriving an exact expression for the conditional system dynamics, we discuss the approximations employed in each approach and the classes of non-Hermitian Hamiltonians that can be obtained. Within this framework, we physically justify the consistency of the right-right formalism (as opposed to the biorthogonal one) for calculating expectation values. Finally, we demonstrate that the traditional notion of thermodynamic equilibrium is not applicable to general non-Hermitian systems. Consequently, stationary states are characterized as non-equilibrium steady states, which should not be conflated with system-projected thermal states of the system-environment composite.
Related
- Fully Quantum Latent Diffusion for Synthetic Malware Records: Effective Denoising, Limited Class Information, and Costly Post-Selection
- Evolution dynamics of spinning binaries in effective-one-body theory to fifth Post-Minkowskian order
- Environmental Effects in Post-Minkowskian Dynamics: Effective Field Theory, Feynman Rules, and Ward Identities for Compact Objects in Relativistic Fluids
- Binary Black Holes in Einstein-Maxwell-Dilaton Theory: Second Post-Newtonian Dynamics from Effective Field Theory
- Effective Hamiltonians and non-Hermitian physics
BibTeX
@misc{siskou2026nonhermitian,
title = {{Non-Hermitian effective dynamics from post-selection protocols}},
author = {Apostolos Siskou and Volker Meden},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03910},
eprint = {2611.03910},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03910},
}
RIS
TY - UNPB
TI - Non-Hermitian effective dynamics from post-selection protocols
AU - Apostolos Siskou
AU - Volker Meden
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03910
UR - https://arxiv.org/abs/2611.03910
AB - Multiple seemingly distinct frameworks are commonly proposed to explain the emergence of effective non-Hermitian dynamics in quantum systems coupled to an environment. Furthermore, it remains contested how to properly calculate expectation values or whether thermal equilibrium states exist in non-Hermitian systems. In this work, we show that Feshbach projection, the Lindblad master equation, and the ancilla approach can all be understood through the Kraus map formalism, leading to non-Hermitian time evolution if an appropriate post-selection procedure is enforced. After first deriving an exact expression for the conditional system dynamics, we discuss the approximations employed in each approach and the classes of non-Hermitian Hamiltonians that can be obtained. Within this framework, we physically justify the consistency of the right-right formalism (as opposed to the biorthogonal one) for calculating expectation values. Finally, we demonstrate that the traditional notion of thermodynamic equilibrium is not applicable to general non-Hermitian systems. Consequently, stationary states are characterized as non-equilibrium steady states, which should not be conflated with system-projected thermal states of the system-environment composite.
ER -