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摘要翻译：
我们系统地研究了一维不可穿透任意子气体的格林函数。我们证明了单粒子密度矩阵是Toeplitz矩阵的行列式，其大N渐近性由Fisher-Hartwig猜想给出。我们对该行列式给出了一个详细的数值分析，详细地说明了玻色子和费米子之间的交叉以及动量分布函数奇异性的重组。我们证明了单粒子密度矩阵满足Painleve VI微分方程，然后用该微分方程导出小距离和大动量展开式。我们发现，该展开式中的第一个非消失项总是K^{-4}，这对Lieb-Liniger气体中的所有耦合都是成立的，这可以追溯到哈密顿量中存在δ函数相互作用。
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英文标题：
《One-particle density matrix and momentum distribution function of
one-dimensional anyon gases》
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作者：
Raoul Santachiara and Pasquale Calabrese
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Mesoscale and Nanoscale Physics 介观和纳米物理
分类描述：Semiconducting nanostructures: quantum dots, wires, and wells. Single electronics, spintronics, 2d electron gases, quantum Hall effect, nanotubes, graphene, plasmonic nanostructures
半导体纳米结构：量子点、线和阱。单电子学，自旋电子学，二维电子气，量子霍尔效应，纳米管，石墨烯，等离子纳米结构
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：High Energy Physics - Theory 高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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英文摘要：
We present a systematic study of the Green functions of a one-dimensional gas of impenetrable anyons. We show that the one-particle density matrix is the determinant of a Toeplitz matrix whose large N asymptotic is given by the Fisher-Hartwig conjecture. We provide a careful numerical analysis of this determinant for general values of the anyonic parameter, showing in full details the crossover between bosons and fermions and the reorganization of the singularities of the momentum distribution function. We show that the one-particle density matrix satisfies a Painleve VI differential equation, that is then used to derive the small distance and large momentum expansions. We find that the first non-vanishing term in this expansion is always k^{-4}, that is proved to be true for all couplings in the Lieb-Liniger anyonic gas and that can be traced back to the presence of a delta function interaction in the Hamiltonian.
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PDF链接：
https://arxiv.org/pdf/802.1913
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