无序系统普遍关系的 "琐碎性

V. Pastukhov
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引用次数: 0

摘要

讨论了在淬火无序状态下具有接触相互作用的自旋$1/2$费米子的普遍关系。无序由具有高斯分布和 $\delta$-liketwo 点相关函数的随机外部势来模拟。利用简单的标度论证、理论的正则化以及赫尔曼-费曼定理,我们确定了粒子分布的大动量尾部以及在任意维度 $d\ge2$ 下具有无序性的多费米子系统的类似谭氏能量相关性。结果表明,能量-压力关系在二维和三维中表现出一种尺度反常。
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`Triviality' of universal relations for disordered systems
The universal relations for spin-$1/2$ fermions with contact interaction in the presence of quenched disorder are discussed. The disorder is modeled by a random external potential with the Gaussian distribution and $\delta$-like two-point correlation function. Utilizing simple scaling arguments, the renormalizability of the theory, and the Hellmann-Feynman theorem we identified the large-momentum tail of particle distribution and analog of Tan's energy relation for many-fermion systems with disorder in arbitrary dimension $d\ge 2$. It is shown that the energy-pressure relation manifests a kind of scale anomaly in two and three dimensions.
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