Testing Catability and Coherent Superposition of $2\mathcal{D}$ Graphene via Lie Algebra

TL;DR

This paper introduces a theoretical framework combining Lie algebra and Green function methods to analyze superposed coherent states and interference effects in graphene quantum systems.

Contribution

It develops a novel approach to quantify phase-sensitive coherence and interference stability in graphene using Lie algebra and Green function techniques.

Findings

Quantifies interference stability via phase-dependent measures.

Extends formalism with Lie algebra to capture symmetry in graphene states.

Provides a systematic method for analyzing quantum correlations in graphene.

Abstract

We develop a theoretical framework for describing superposed coherent states in graphene quantum systems using the concept of catability as a phase-sensitive metric functional measure. In this case, the formalism quantifies interference stability and coherence structure via phase-dependent contributions of quantum superposition states. Catability is defined as a functional measure sensitive to relative phase variations within coherent state combinations, serving as a diagnostic tool for quantum interference effects in graphene-based systems. Also, the formulation is extended using Lie algebra techniques, where the underlying symmetry structure of graphene quantum states is represented through operator algebras governing state transformations in quantum space. In this context, to describe nonlocal propagation and phase-resolved dynamics, a Green function approach is incorporated, enabling systematic treatment of quantum correlations in a spatially extended structures framework. A unified framework is constructed by combining Lie algebraic symmetry analysis with Green function propagation theory, yielding a consistent description of phase-sensitive catability in complex graphene quantum configurations within the framework approach. Results provide a structured route for testing coherence, interference stability, and quantum state control in low-dimensional quantum materials systems.