Probability distributions of line lattices in random media from the 1D Bose gas

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• 作者：Emig ; Thorsten ; Kardar ; Mehran
• 关键词：05.30.-d ; 05.70.-a ; 64.60.Cn ; 74.60.Ge
• 刊名：Nuclear Physics B
• 出版年：2001
• 出版时间：June 25, 2001
• 年：2001
• 卷：604
• 期：3
• 页码：479-510
• 全文大小：276 K

文摘

The statistical properties of a two-dimensional lattice of elastic lines in a random medium are studied using the Bethe ansatz. We present a novel mapping of the dilute random line lattice onto the weak coupling limit of a pure Bose gas with delta-function interactions. Using this mapping, we calculate the cumulants of the free energy in the dilute limit exactly. The relation between density and displacement correlation functions in the two models is examined and compared with existing results from renormalization group and variational ansätze.