发表机构
University of Sassari; Università di Padova; INFN Sezione di Padova（萨萨里大学; 帕多瓦大学; 意大利国家核物理研究所帕多瓦分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过引入非局域分数阶算子推广Popov作用，证明二维超导体中涡旋相互作用呈幂律约束，抑制热涨落并稳定有限温度长程有序，进而提出分数阶London方程统一描述非局域电动力学。
AI 中文摘要
我们通过将局域仅相位Popov作用推广到利用非局域分数阶算子的框架，提出了二维（2D）超导体中相位涨落和拓扑转变的非局域场论描述。通过用Riesz分数阶拉普拉斯算子$-(-\nabla^2)^{\alpha/2}$（其中$1<\alpha<2$）替换标准空间拉普拉斯算子，我们证明了涡旋-反涡旋相互作用从对数约束转变为更强的幂律约束，形式为$V(r)\propto r^{2-\alpha}$。通过推广的Kosterlitz-Thouless能量-熵分析，我们证明这种非局域约束严格抑制了热涡旋增殖。由于非局域算子将系统安全地置于Mermin-Wagner限制严格有效域之外，这种幂律约束在有限温度下自然稳定了真正的长程有序。最后，通过构造规范不变的分数阶作用，我们提出了分数阶London方程。该方法产生了一个实空间幂律核，直接映射到具有长相干长度的超导体的反常Pippard极限，为非局域电动力学提供了一个统一的现象学动机框架。
英文摘要
We formulate a non-local, field-theoretic description of phase fluctuations and topological transitions in two-dimensional (2D) superconductors by generalizing the local only-phase Popov action to a framework utilizing non-local fractional operators. By replacing the standard spatial Laplacian with the Riesz fractional Laplacian $-(-\nabla^2)^{α/2}$ (where $1<α<2$), we prove that the vortex-antivortex interaction transitions from logarithmic confinement to a stronger power-law confinement of the form $V(r)\propto r^{2-α}$. Through a generalized Kosterlitz-Thouless energetic-entropic analysis, we demonstrate that this non-local confinement strictly suppresses thermal vortex proliferation. Because the non-local operator safely places the system outside the strict domain of validity of the Mermin-Wagner restriction, this power-law confinement natively stabilizes true long-range order at finite temperatures. Finally, by constructing a gauge-invariant fractional action, we formulate a fractional London equation. This approach yields a real-space power-law kernel that maps directly onto the anomalous Pippard limit of superconductors with long coherence lengths, providing a unified phenomenologically motivated framework for non-local electrodynamics.
Comments8 pages, 0 figures, submitted to Physical Review B
