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arXiv 1111.1519cond-mat.supr-conmath-phmath.MP
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Richardson方法中宏观系统中对哈密顿量的精确期望值

Exact expectation values within Richardson's approach for the pairing Hamiltonian in a macroscopic system

Gregory Gorohovsky, Eldad Bettelheim

发表信息：
Physical Review B 84, 224503 (2011)
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摘要：

BCS超导性可以用一个简单的哈密顿量来解释，该哈密顿量描述了电子对之间的吸引配对相互作用。哈密顿量可以用平均场方法来处理，这足以研究平衡性质和各种非平衡效应。然而，在某些非平衡情况下，甚至在宏观而非微观超导体中，平均场论的应用可能是无效的。在这种情况下，我们可以求助于哈密顿量的完全解，如Richardson在1960年代给出的。最近，基于非平衡态量子不稳定性的存在，指出了Richardson解与宏观非平衡态超导体的相关性。然后，它是感兴趣的，以获得精确的本征值之间的配对哈密顿量的Richardson方法的宏观系统的期望值的解析表达式。我们在本文件中承担这项任务。应该注意的是，理查森的方法产生了哈密顿量的全部特征值，而BCS理论只产生了一个子集。然后，这里得到的结果推广了熟悉的BCS表达式（例如，对于电子占据或配对相关）到激发谱偏离BCS理论的情况（例如，在频谱呈现多个间隙的情况下）。

英文摘要：

BCS superconductivity is explained by a simple Hamiltonian describing an attractive pairing interaction between pairs of electrons. The Hamiltonian may be treated using a mean-field method, which is adequate to study equilibrium properties and a variety of nonequilibrium effects. Nevertheless, in certain nonequilibrium situations, even in a macroscopic rather than a microscopic superconductor, the application of mean-field theory may not be valid. In such cases, one may resort to the full solution of the Hamiltonian, as given by Richardson in the 1960s. The relevance of Richardson's solution to macroscopic nonequilibrium superconductors was pointed out recently based on the existence of quantum instabilities out of equilibrium. It is then of interest to obtain analytical expressions for expectation values between exact eigenvalues of the pairing Hamiltonian within the Richardson approach for macroscopic systems. We undertake this task in the current paper. It should be noted that Richardson's approach yields the full set of eigenvalues of the Hamiltonian, while BCS theory yields only a subset. The results obtained here, then, generalize the familiar BCS expressions (e.g., for the electron occupation or pairing correlations) to cases where the spectrum of excitations diverges from BCS theory (e.g., in cases where the spectrum exhibits multiple gaps).

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