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arXiv 0909.3675cond-mat.dis-nncond-mat.stat-mech
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低温玻璃的量子统计物理

Quantum Statistical Physics of Glasses at Low Temperatures

J. van Baardewijk, R. Kuehn

摘要:

本文对低温下结构玻璃的微观平均场模型进行了量子统计分析。该模型可以被认为是由完全相互作用势的随机玻恩冯卡门展开引起的。这个问题被减少到一个单网站的理论制定的时间路径积分使用副本来处理的混乱。我们研究了系统在热力学平衡下的物理性质,并发展了微扰和非微扰方法来求解模型。微扰理论被制定为一个环展开的两个粒子的不可约图,并进行到三圈秩序的有效行动。的非微扰描述研究在两个方面,(i)使用静态近似,和(ii)通过量子蒙特卡罗模拟。在双圈阶微扰理论下得到的松原关联与量子蒙特卡罗模拟的结果符合得很好。特征低温异常的比热再现,无论是在非微扰静态近似,并从一个三圈微扰评价的自由能。在后一种情况下,结果到目前为止依赖于使用松原相关性在两个循环的自由能的三个循环的表达式,在三个循环顺序的自洽松原相关性仍然不可用。我们建议,以证明这两个回路松原相关性的良好协议,通过量子蒙特卡罗模拟获得的非微扰。

英文摘要:

We present a quantum statistical analysis of a microscopic mean-field model of structural glasses at low temperatures. The model can be thought of as arising from a random Born von Karman expansion of the full interaction potential. The problem is reduced to a single-site theory formulated in terms of an imaginary-time path integral using replicas to deal with the disorder. We study the physical properties of the system in thermodynamic equilibrium and develop both perturbative and non-perturbative methods to solve the model. The perturbation theory is formulated as a loop expansion in terms of two-particle irreducible diagrams, and is carried to three-loop order in the effective action. The non-perturbative description is investigated in two ways, (i) using a static approximation, and (ii) via Quantum Monte Carlo simulations. Results for the Matsubara correlations at two-loop order perturbation theory are in good agreement with those of the Quantum Monte Carlo simulations. Characteristic low-temperature anomalies of the specific heat are reproduced, both in the non-perturbative static approximation, and from a three-loop perturbative evaluation of the free energy. In the latter case the result so far relies on using Matsubara correlations at two-loop order in the three-loop expressions for the free energy, as self-consistent Matsubara correlations at three-loop order are still unavailable. We propose to justify this by the good agreement of two-loop Matsubara correlations with those obtained non-perturbatively via Quantum Monte Carlo simulations.

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