[2605.10967] Testing Catability and Coherent Superposition of $2mathcal{D}$ Graphene Quantum system

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Summary:We develop a theoretical framework for describing superposed coherent states in graphene quantum programs utilizing the idea of catability as a phase-sensitive metric practical measure. On this case, the formalism quantifies interference stability and coherence construction by way of phase-dependent contributions of quantum superposition states. Catability is outlined as a practical measure delicate to relative part variations inside coherent state mixtures, serving as a diagnostic software for quantum interference results in graphene-based programs. Additionally, the formulation is prolonged utilizing Lie algebra methods, the place the underlying symmetry construction of graphene quantum states is represented by means of operator algebras governing state transformations in quantum house. On this context, to explain nonlocal propagation and phase-resolved dynamics, a Inexperienced operate method is included, enabling systematic remedy of quantum correlations in a spatially prolonged buildings framework. A unified framework is constructed by combining Lie algebraic symmetry evaluation with Inexperienced operate propagation concept, yielding a constant description of phase-sensitive catability in advanced graphene quantum configurations inside the framework method. Outcomes present a structured route for testing coherence, interference stability, and quantum state management in low-dimensional quantum supplies programs.