Quantum Hierarchical Fokker-Planck Equations with U(1) Gauge Fields (U(1)-QHFPE): A Computational Framework for Aharonov-Bohm Effects
- URL: http://arxiv.org/abs/2509.11195v1
- Date: Sun, 14 Sep 2025 09:48:18 GMT
- Title: Quantum Hierarchical Fokker-Planck Equations with U(1) Gauge Fields (U(1)-QHFPE): A Computational Framework for Aharonov-Bohm Effects
- Abstract summary: We introduce U(1)-QHFPE, a non-Markovian and non-perturbative open quantum dynamics software package for solving quantum Fokker-Planck equations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We introduce U(1)-QHFPE, a non-Markovian and non-perturbative open quantum dynamics software package for solving quantum Fokker-Planck equations incorporating gauge fields within the Hierarchical Equations of Motion (HEOM) formalism. The framework rigorously preserves gauge invariance and rotational symmetry, enabling accurate simulations of transport phenomena such as the Aharonov-Bohm effect under strong system-bath coupling. In this regime, quantum entanglement between the system and bath emerges naturally. Demonstration programs include calculations of symmetric and antisymmetric correlation functions in Aharonov-Bohm ring geometries, showcasing the code's ability to resolve topological quantum interference in dissipative open systems.
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