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From BdG to DVR: A Pathwise Diagnostic Framework for Decoherence and Dislocation in Topological Quantum Systems

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Preprints.org
DOI
10.20944/preprints202506.0464.v1

The Bogoliubov--de Gennes (BdG) formalism provides a powerful spectral framework for understanding excitations in topological superconductors. However, its assumptions of unitarity and coherence limit its capacity to detect the early onset of decoherence or internal quantum dislocation. In this work, we apply the recently introduced Difference-based Variational Reconstruction (DVR) framework to analyze the structure of BdG-derived eigenmodes, particularly Majorana bound states, under controlled decoherence.We demonstrate that while BdG spectra remain stable, DVR contrast residuals sharply rise in spin--position dislocation scenarios, exposing hidden coherence breakdown. This extends our previous findings [1] on DVR's detection of wave-particle duality transitions and the Quantum Cheshire Cat effect, where DVR contrast residuals notably revealed sharp dislocation between spin and trajectory mid-path, even as global coherence was preserved. Here, we build on those findings by showing that DVR can act as a dynamic structural diagnostic layered over BdG-based eigenmodes, detecting decoherence and spin dislocation even before spectral features change. The DVR contrast residual framework provides a new pathwise lens for open quantum systems, complementing Hamiltonian-based models with localized, contrast-sensitive diagnostics.

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