Engineering of Non-Hermitian Trajectories and Phase Structure in an Open Bose-Hubbard Model via Rate Operator Transformations

• URL: http://arxiv.org/abs/2609.02490v1
• Date: Wed, 02 Sep 2026 11:58:42 GMT
• Title: Engineering of Non-Hermitian Trajectories and Phase Structure in an Open Bose-Hubbard Model via Rate Operator Transformations
• Abstract summary: Rate operator formalism provides a versatile and systematic framework for unraveling a master equation into pure-state evolutions.<n>In the present work, we explore the applicability of the rate operator formalism as a tool for engineering non-Hermitian dynamics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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