非扩展的二次格林函数与谱密度法 量子统计力学

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摘要翻译：
我们将热力学二次格林函数的形式推广到非扩展量子统计力学。在最优拉格朗日乘子表示下，给出了两个泛型算子($q=1$)的两次$q$%格林函数及其相关的$q$-谱密度($q$度量非可拓度）的直接计算方法和$q$-谱性质，并与广义算子($q=1$)进行了严格的类比，给出了两个泛型算子的两次$q$%格林函数的最优Lagrangian乘子表示的最优Lagrangian乘子表示的最优Lagrangian乘子表示的最优Lagrangian乘子表示法。一些重点放在非广泛版本的谱密度方法上，它在探索各种系统的平衡和输运性质方面的有效性已经在传统的经典和量子多体物理中得到了很好的证实。为了考察运动方程和谱密度方法在研究非平凡多体问题中的Q$诱导非伸展性效应时的作用，我们着重研究了具有强粒子间引力的高密度玻色气体的二次量子化模型的平衡性质，该模型在广泛的条件下有精确的结果。值得注意的是，在低温区域内，通过克服$q$巨配分函数的计算，显式地计算了$q$诱导的非伸缩性对几个热力学量的贡献。
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英文标题：
《Two-time Green's functions and spectral density method in nonextensive
  quantum statistical mechanics》
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作者：
A. Cavallo, F. Cosenza, L. De Cesare
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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：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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英文摘要：
  We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multipliers representation, the $q$-spectral properties and the methods for a direct calculation of the two-time $q$% -Green's functions and the related $q$-spectral density ($q$ measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive ($q=1$) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the $q$-induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the $q$-induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the $q$ grand-partition function.
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PDF链接：
https://arxiv.org/pdf/710.5695

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关键词：统计力学 谱密度 Conventional Presentation Contribution 函数 有效性 最优 性质 效应