Evolution Generators for Complex Parameters
Abstract
Theoretical studies on how quantum systems are affected by external factors are often formulated through parameter changes in the system's Hamiltonian. Beyond Berry connections and phases, which focus on specific Hamiltonian eigenstates, recent studies inspired by non-Hermitian quantum formalisms provide a framework for obtaining general state evolution generators for real-valued parameters. This study extends the applicability of the evolution generator formalism to complex-valued parameters via Wirtinger derivatives. By treating a complex parameter and its conjugate as independent variables, the evolution equations are derived for both quantum states and the metric of the Hilbert space bundle. The analysis demonstrates that while state evolution with respect to a complex parameter is naturally governed by its corresponding evolution generator, metric evolution requires a coupled contribution from both the generator and its conjugate counterpart to preserve state normalization. Explicit examples are worked out to illustrate the implementation and physical consistency of the formalism.
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BibTeX
@misc{yeh2026evolution,
title = {{Evolution Generators for Complex Parameters}},
author = {Jen-Yin Yeh and Chia-Yi Ju},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29602},
eprint = {2608.29602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29602},
}
RIS
TY - UNPB
TI - Evolution Generators for Complex Parameters
AU - Jen-Yin Yeh
AU - Chia-Yi Ju
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29602
UR - https://arxiv.org/abs/2608.29602
AB - Theoretical studies on how quantum systems are affected by external factors are often formulated through parameter changes in the system's Hamiltonian. Beyond Berry connections and phases, which focus on specific Hamiltonian eigenstates, recent studies inspired by non-Hermitian quantum formalisms provide a framework for obtaining general state evolution generators for real-valued parameters. This study extends the applicability of the evolution generator formalism to complex-valued parameters via Wirtinger derivatives. By treating a complex parameter and its conjugate as independent variables, the evolution equations are derived for both quantum states and the metric of the Hilbert space bundle. The analysis demonstrates that while state evolution with respect to a complex parameter is naturally governed by its corresponding evolution generator, metric evolution requires a coupled contribution from both the generator and its conjugate counterpart to preserve state normalization. Explicit examples are worked out to illustrate the implementation and physical consistency of the formalism.
ER -