Engineering of Non-Hermitian Trajectories and Phase Structure in an Open Bose-Hubbard Model via Rate Operator Transformations
Abstract
Non-Hermitian evolution can be realized through post-selection on stochastic pure-state trajectories arising in continuously monitored open quantum systems. The rate operator formalism provides a versatile and systematic framework for unraveling a master equation into stochastic pure-state evolutions, offering enhanced control over the resulting non-Hermitian dynamics. In the present work, we explore the applicability of the rate operator formalism as a tool for engineering non-Hermitian dynamics. Specifically, we apply this approach to the Bose-Hubbard model subject to environmental dephasing, examining its consequences for controlled state manipulation. Our analysis is framed within the broader contexts of quantum state engineering and measurement-induced phase transitions. We demonstrate that the rate operator formalism enables the construction of effective non-Hermitian Hamiltonians exhibiting a unique steady state-even in regimes where the standard Monte Carlo wavefunction method fails to produce one. Furthermore, we show that this framework facilitates transitions between distinct steady-state phases, governed by tunable parameters such as the interaction strength and a non-Hermiticity control parameter introduced via the rate operator formalism.
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BibTeX
@misc{luomala2026engineering,
title = {{Engineering of Non-Hermitian Trajectories and Phase Structure in an Open Bose-Hubbard Model via Rate Operator Transformations}},
author = {Jaakko Luomala and Kimmo Luoma and Iiro Vilja and Jyrki Piilo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02490},
eprint = {2609.02490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02490},
}
RIS
TY - UNPB
TI - Engineering of Non-Hermitian Trajectories and Phase Structure in an Open Bose-Hubbard Model via Rate Operator Transformations
AU - Jaakko Luomala
AU - Kimmo Luoma
AU - Iiro Vilja
AU - Jyrki Piilo
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02490
UR - https://arxiv.org/abs/2609.02490
AB - Non-Hermitian evolution can be realized through post-selection on stochastic pure-state trajectories arising in continuously monitored open quantum systems. The rate operator formalism provides a versatile and systematic framework for unraveling a master equation into stochastic pure-state evolutions, offering enhanced control over the resulting non-Hermitian dynamics. In the present work, we explore the applicability of the rate operator formalism as a tool for engineering non-Hermitian dynamics. Specifically, we apply this approach to the Bose-Hubbard model subject to environmental dephasing, examining its consequences for controlled state manipulation. Our analysis is framed within the broader contexts of quantum state engineering and measurement-induced phase transitions. We demonstrate that the rate operator formalism enables the construction of effective non-Hermitian Hamiltonians exhibiting a unique steady state-even in regimes where the standard Monte Carlo wavefunction method fails to produce one. Furthermore, we show that this framework facilitates transitions between distinct steady-state phases, governed by tunable parameters such as the interaction strength and a non-Hermiticity control parameter introduced via the rate operator formalism.
ER -