Non-Destructive Quantum Topological Sorting and Multiplexing Effect via Non-Hermitian Coherent Tunneling in Continuous Atomic Media 基于连续原子介质非厄米相干隧穿的无损量子拓扑分拣&合束效应 Non-Hermitian Mode Tunneling in Continuous Atomic Media (NSMTE)(N-HMTCAM) 非厄米空间模式隧穿效应 (NSMTE) ： 连续原子介质中的非厄米模式隧穿 耗散梯度诱导的普适隧穿法则 Universal Tunneling Law Induced by Dissipation Gradients 耗散梯度诱导的普适隧穿法则 Universal Tunneling Law Induced by Dissipation Gradients
This archive documents the foundational framework for the Non-Hermitian Selection (𝓢ₙₕ) Principle, the proposed energetic engine driving coherent self-organization in open quantum systems. The work presents: Core Theoretical Contribution: The ₙₕ principle posits that stability in complex systems emerges not from energy minimization alone, but from the selective dissipation of incoherent phase-modes, actively filtering a quantum system toward higher global coherence. Key Numerical Prediction: Analysis of a simplified two-mode non-Hermitian BEC model predicts a +9.7% enhancement in Ramsey contrast (from ~78.3% to ~86.7%), corresponding to a potential improvement in atomic clock stability. Proposed Physical Mechanism: The enhancement is hypothesized to be driven by the stabilization effect of a Phase-Entropy Gradient (𝚫𝚽(r)), defined as 𝚫𝚽(r) = ρ(r) · v(r). Regions with minimal 𝚫𝚽 are predicted to exhibit maximal coherence gain. Complete Experimental Protocol: A detailed, falsifiable protocol is provided to test this ΔΦ mechanism in a real ⁸⁷Rb BEC setup, using spatially modulated dissipation via photoassociation/Raman pumping. Theoretical Context: This work provides the energetic mechanism for the Coherence-Surface Energy Minimization (CSEM) principle, which yields the energy-length scaling law E ∝ L⁻² and the golden-ratio (ϕ) stability in quasicrystals. Together, these principles form the basis of the Theory of Rendered Information (TRI). Status: This is an archived theoretical proposal and numerical exploration. The effects described are predictions awaiting experimental validation.
We introduce a driven-dissipative Floquet model in which a single harmonic oscillator, with both frequency and decay rate modulated, realizes a non-Hermitian synthetic lattice with an effective electric-field gradient in frequency space. Using the Floquet-Green's function and the doubled Hamiltonian representation of non-Hermitian matrices, we show that the linear response of this system is characterized by a local winding number. Nontrivial values of the winding number induce directional amplification in the synthetic dimension, thereby converting input signals to different frequencies. The underlying mode structure is well described by a Jackiw-Rebbi-like continuum theory with Dirac cones and solitonic topological zero modes in synthetic frequency. Our results establish a simple and experimentally feasible route to non-Hermitian topological amplification, naturally implementable in current quantum technologies such as superconducting circuits.
We propose a generalization of the Filoche--Mayboroda localization landscape that extends the theory well beyond the static, elliptic and Hermitian settings while preserving its geometric interpretability. Using the positive operator
H†H, we obtain a landscape that predicts localization across non-Hermitian, Floquet, and topological systems without computing eigenstates. Singular-value collapse reveals spectral instabilities and skin effects, the Sambe formulation captures coherent destruction of tunneling, and topological zero modes emerge directly from the landscape. Applications to Hatano--Nelson chains, driven two-level systems, and driven Aubry--André--Harper models confirm quantitative accuracy, establishing a unified predictor for localization in equilibrium and driven quantum matter.
我们建议为为在三个远洞套住的多重原子的纠缠的状态的产生的一个计划由二相同单个模式的纤维连接了。与以前的计划相比，建议计划的明显的优点是：首先，在建议协议的所有洞能自由地与对方一起交往，它在量通讯和分布式的量计算是重要的。第二，在计划，原子，洞，和纤维，模式在回声。因此，要求的相互作用时间是短的，鉴于 decoherence，它是重要的。原则上，建议计划能被扩大产生 n 原子纠缠的状态。[从作者抽象]