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Quantum Coherence Percolation Threshold (QCPT): A Network Phase Transition Theory of Many-Body Quantum Coherence

Jincheng Zhang

Published Aug 11, 2026• 0 citations
Publisher

Abstract

The macroscopic manifestation of quantum coherence in complex many-body systems remains one of the most profound and challenging frontiers in modern physics. While traditional percolation theory successfully describes classical connectivity phase transitions in disordered media, and quantum phase transitions typically focus on zero-temperature Hamiltonian parameter variations, the interplay between network topology and quantum coherence propagation lacks a unifying macroscopic framework. In this paper, we propose the theory of Quantum Coherence Percolation Threshold (QCPT), introducing the concept that quantum coherence can undergo a sudden, non-analytic macroscopic percolation transition across complex networks. We formally define the coherence connection probability, denoted as p_C, and demonstrate that when p_C exceeds a critical threshold p_C*, a global coherent cluster abruptly emerges, characterized by a non-zero macroscopic global coherence measure C_global > 0. By formulating the density matrix evolution, local coherence sharing, and topological constraints over complex graph structures, we establish the analytical foundation for this network-mediated quantum phase transition. This framework bridges quantum information theory, statistical mechanics, and network science, offering a foundational blueprint for understanding macroscopic quantum states in complex environments.

DOI
10.5281/zenodo.21888292

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