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QEM-4: Topological Domain-Wall and Stationary Interference Texture in Multi-Body Entanglement

Wangyoufu

Published Nov 6, 2025• 0 citations
Publisher

Abstract

The QEM-4 paper extends the Quantum Entanglement Mechanics (QEM) framework by introducing the concept of topological domain-walls emerging from mirror-coupled entanglement layers. These domain-walls act as internal interfaces where sequential flip-waves form stationary interference textures, analogous to internal double-slit patterns within the entanglement lattice. Analytical φ⁴-type solutions and critical-layer scaling relations are derived, providing testable predictions in coupled-qubit, ion-chain, and optical-lattice systems.

DOI
10.5281/zenodo.17540434

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arXiv:1610.08919•Physical Review A•Dec 29, 2016•2 citations
The QEM-4 paper extends the Quantum Entanglement Mechanics (QEM) framework by introducing the concept of topological domain-walls emerging from mirror-coupled entanglement layers. These domain-walls act as internal interfaces where sequential flip-waves form stationary interference textures, analogous to internal double-slit patterns within the entanglement lattice. Analytical φ⁴-type solutions and critical-layer scaling relations are derived, providing testable predictions in coupled-qubit, ion-chain, and optical-lattice systems.
We present QEM-8³, a hierarchical mirror-lattice framework for multi-body quantum entanglement. Non-commutativity of measurement order and basis rotation jointly induce Sequential Trigger Flips (STF), whose propagation forms Flip-Waves across nested mirror layers. We derive a coupled flip-wave equation, identify a Critical Layer (mirror–basis resonance), define the symmetry group G_{8^3} and a topological invariant T_{8^3}, and predict quasi-time-crystalline spectral oscillations, time-reversal echoes, and critical entanglement peaks.
Abstract (EN):We introduce the Mirror-Flip Unit (MFU) as the minimal structural cell that realizes and stabilizes multi-body entanglement within the QEM framework. The MFU is a dual-layer mirror lattice supporting Σ/Δ collective modes with a controllable Δ-domain-wall profile that confines coherence. We derive governing equations near stationary textures, obtain the scaling ξ ~ |θ−θc|^{-1/2}, and predict falsifiable signatures: π-echo, sech^2 standing envelopes, and a causal front bounded by v_max ≈ (J ξ)/ħ. Protocols are provided for wall-fit (ξ), front-tracking (v_max), and stability-window mapping. Series note: This work is part of the Quantum Entanglement Mechanics (QEM) series by Youfu Wang (2025). 中文摘要 (ZH):本文在 QEM 框架下提出“镜像翻转单元(MFU)”作为多体纠缠的最小结构元。MFU 由支持 Σ/Δ 集体模的双层镜像格架构成,其 Δ-畴壁用于相干约束。我们在稳态纹理附近给出动力学方程,得到相关长度缩放律 ξ ~ |θ−θc|^{-1/2},并给出可验证指纹:π 回声、sech² 驻波包络、以及由 v_max ≈ (J ξ)/ħ 限定的因果前沿。文末附有实验流程:畴壁拟合 ξ、前沿追踪 v_max 与稳定窗口测量。系列说明:本作属于王有福(Youfu Wang)在 2025 年提出的 QEM 系列研究。
Abstract (EN):We unify QEM-4–7 into a single field framework for hierarchical mirror lattices. Starting from a variational functional for Σ/Δ modes with a domain-wall order parameter, we derive coarse-grained equations across layers, an RG-like flow for effective couplings, and a universal causal-cone bound that collapses to QEM-5 locally and to an array form in QEM-7. The coherence length scales as ξ ~ |θ−θc|^{-1/2} at each level. We provide falsifiable predictions and cross-level protocols. Series note: This work is part of the Quantum Entanglement Mechanics (QEM) series by Youfu Wang (2025). 中文摘要 (ZH):我们把 QEM-4–7 统一到层级镜像格的场论框架中:从变分泛函出发得到跨层粗粒化方程与“类重整化”的耦合流;统一的因果锥上限在局域退化为 QEM-5,在阵列退化为 QEM-7。相关长度在各层满足 ξ ~ |θ−θc|^{-1/2};重整后的参数把约束向上层级传递,给出芯片级时序预算、扇出与稳定窗口。并给出跨层可检验流程与普适性指纹(π 回声、sech² 包络、前沿速度塌缩律)。
This work extends the Quantum Entanglement Mechanics (QEM) framework to explore the upper propagation limit of flip-waves within multi-body entanglement systems. We introduce a causal-cone model that defines the boundary of correlation spread and demonstrate that flip-wave coherence cannot propagate faster than the intrinsic coupling velocity of the phase lattice. This finding bridges the topology of entanglement, the structure of causal boundaries, and the limits of quantum-information transmission. Series note: This work is part of the Quantum Entanglement Mechanics (QEM) series by Youfu Wang (2025).
This paper introduces QEM-8^3, a three-dimensional extension of the QEM-8 entanglement framework. The model treats each entangled pair (A↔B and C↔D) as both an individual binary relation and part of a larger lattice system. By stacking the eight directional entanglement modes along vertical, horizontal, and depth axes, the structure forms a stable entanglement square lattice. The transitions between AB|CD and AD|BC are explained through measurement sequence, basis switching, and stability reconfiguration. The result is a discrete algebraic lattice that preserves absolute duality and relational symmetry across multi-quantum entanglement systems.
We study the domain walls which form when Bose condensates acquire a double-well dispersion. Experiments have observed such domain walls in condensates driven across a Z2{\mathbb{Z}}_{2}Z2​ symmetry-breaking phase transition in a shaken optical lattice. We derive a generic model to describe the dispersion and to compute the wave functions and energies of the domain walls. We find two distinct regimes which demand different physical pictures. In the weak-coupling regime, where interactions are weak compared to the kinetic-energy barrier, ``density-wave domain walls'' form that support an extended density wave and a series of phase steps. These features can be understood as the quantum interference between domains with distinct momenta. In the strong-coupling regime where interaction dominates, the system forms ``phase domain walls'' which have the minimum width allowed by the uncertainty principle and suppressed density modulation. Analytic results for the domain-wall wave functions are obtained in the two regimes. The energy of domain walls behaves similarly to that of topological defects in paradigmatic field theories.