Efimov-Like Behaviour in Low-Dimensional Polymer Models

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• 作者：Federica Mura ; Somendra M. Bhattacharjee ; Jaya Maji…
• 刊名：Journal of Low Temperature Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：185
• 期：1-2
• 页码：102-121
• 全文大小：1,201 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Condensed Matter
  Characterization and Evaluation Materials
  Magnetism and Magnetic Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-7357
• 卷排序：185

文摘

In the quantum Efimov effect, identical bosons form infinitely many bound trimer states at the bound dimer dissociation threshold, with their energy spectrum obeying a universal geometrical scaling law. Inspired by the formal correspondence between the possible trajectories of a quantum particle and the possible conformations of a polymer chain, the existence of a triple-stranded DNA bound state when a double-stranded DNA is not stable was recently predicted by modelling three directed polymer chains in low-dimensional lattices, both fractal (\(d<1\)) and euclidean (\(d=1\)). A finite melting temperature for double-stranded DNA requires in \(d\le 2\) the introduction of a weighting factor penalizing the formation of denaturation bubbles, that is non-base paired portions of DNA. The details of how bubble weighting is defined for a three-chain system were shown to crucially affect the presence of Efimov-like behaviour on a fractal lattice. Here we assess the same dependence on the euclidean \(1+1\) lattice, by setting up the transfer matrix method for three infinitely long chains confined in a finite size geometry. This allows us to discriminate unambiguously between the absence of Efimov-like behaviour and its presence in a very narrow temperature range, in close correspondence with what was already found on the fractal lattice. When present, however, no evidence is found for triple-stranded bound states other than the ground state at the two-chain melting temperature.KeywordsEfimov effectTriplex DNAPoland–Scheraga modelTransfer matrix