The aim of this thesis is to investigate, using simplified lattice models, whether the Efimov effect, well known in quantum mechanics, can arise in polymer physics too, particularly in a triple stranded DNA system. Such effect consists in the formation of stable trimer bound states when dimer bound states are not stable. We base strand interaction rules on a PolandScheraga model for a directed DNAlike polymer, doublestranded first and triplestranded later. Within the PolandScheraga scheme, only interactions between base pairs with the same monomer indexes along the strands are permitted. Thus, the identification of the monomer index with imaginary time allows the formal mapping to the quantum problem in which particles interact at the same time. According to the transfer matrix method, we are able to extract information about the freeenergy of the system from matrix eigenvalues. Studying them at the critical point of the unzippedzipped phase transition we look for the similarities between the bound states in the polymer model and those predicted by Efimov theory for a three particle quantum system. In particular, in Efimov theory, an infinite series of trimer energy levels, with a constant ratio between consecutive levels, is found at the critical point of the 2body problem.
Efimov bound states in polymer physics
Mura, Federica
2014/2015
Abstract
The aim of this thesis is to investigate, using simplified lattice models, whether the Efimov effect, well known in quantum mechanics, can arise in polymer physics too, particularly in a triple stranded DNA system. Such effect consists in the formation of stable trimer bound states when dimer bound states are not stable. We base strand interaction rules on a PolandScheraga model for a directed DNAlike polymer, doublestranded first and triplestranded later. Within the PolandScheraga scheme, only interactions between base pairs with the same monomer indexes along the strands are permitted. Thus, the identification of the monomer index with imaginary time allows the formal mapping to the quantum problem in which particles interact at the same time. According to the transfer matrix method, we are able to extract information about the freeenergy of the system from matrix eigenvalues. Studying them at the critical point of the unzippedzipped phase transition we look for the similarities between the bound states in the polymer model and those predicted by Efimov theory for a three particle quantum system. In particular, in Efimov theory, an infinite series of trimer energy levels, with a constant ratio between consecutive levels, is found at the critical point of the 2body problem.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/18703