关联量子系统电导率的下界
Lower bounds for the conductivities of correlated quantum systems
摘要：
我们展示了如何可以获得一个下界的相关量子系统的电，自旋或热传导率所描述的形式H = H0 + g H1的哈密顿。这里H0是一个相互作用的哈密顿量，其特征在于守恒定律导致无限的电导率为g=0。小扰动g H1，然而，呈现有限的电导率在有限的温度。例如，H0可以是连续场论，其中动量守恒，或者是可积的一维模型，而H1可能描述弱无序的影响。在限制g为0，我们推导出相关的电导率的下限，并显示如何使用记忆矩阵形式主义系统地改善它们。此外，我们讨论了各种应用程序和调查在什么条件下，我们的下限可能成为准确的。
英文摘要：
We show how one can obtain a lower bound for the electrical, spin or heat conductivity of correlated quantum systems described by Hamiltonians of the form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by conservation laws which lead to an infinite conductivity for g=0. The small perturbation g H1, however, renders the conductivity finite at finite temperatures. For example, H0 could be a continuum field theory, where momentum is conserved, or an integrable one-dimensional model while H1 might describe the effects of weak disorder. In the limit g to 0, we derive lower bounds for the relevant conductivities and show how they can be improved systematically using the memory matrix formalism. Furthermore, we discuss various applications and investigate under what conditions our lower bound may become exact.
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