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 Poland-Scheraga model for a directed DNA-like polymer, double-stranded first and triple-stranded later. Within the Poland-Scheraga 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 free-energy of the system from matrix eigenvalues. Studying them at the critical point of the unzipped-zipped 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 2-body 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 Poland-Scheraga model for a directed DNA-like polymer, double-stranded first and triple-stranded later. Within the Poland-Scheraga 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 free-energy of the system from matrix eigenvalues. Studying them at the critical point of the unzipped-zipped 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 2-body problem.
2014-09
60
File in questo prodotto:
File Dimensione Formato  
Mura_Federica.pdf

accesso aperto

Dimensione 1.66 MB
Formato Adobe PDF
1.66 MB Adobe PDF Visualizza/Apri

The text of this website © Università degli studi di Padova. Full Text are published under a non-exclusive license. Metadata are under a CC0 License

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/18703