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Application of renormalization group techniques to the solution of integrals and Schrodinger eigenvalue equations

Alberto Giuseppe Catalano

Application of renormalization group techniques to the solution of integrals and Schrodinger eigenvalue equations.

Rel. Arianna Montorsi, Andrea Trombettoni, Roberto Piazza. Politecnico di Torino, Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi), 2020

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Abstract:

The renormalization group (RG) consists of a set of concepts and methods which can be used to analyze phenomena in many different fields of mathematics and physics, ranging from probability theory and statistical mechanics, to nonequilibrium phenomena. These RG techniques are particularly useful in order to study fluctuations on top of a mean-field like solution. In the last two decades the development of the so-called functional renormalization group (FRG) method has provided a mathematically elegant and yet simple way of expressing Wilson’s idea of successive mode elimination in terms of a formally exact functional differential equation for the effective action (also known as the Ginzburg-Landau free energy in condensed matter contexts). The aim of the Thesis is to apply FRG tools to two problems: the study of non-trivial one variable and multivariable integrals, and the determination of the energy spectrum of the Schrödinger equation.

Relators: Arianna Montorsi, Andrea Trombettoni, Roberto Piazza
Academic year: 2020/21
Publication type: Electronic
Number of Pages: 99
Subjects:
Corso di laurea: Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi)
Classe di laurea: New organization > Master science > LM-44 - MATHEMATICAL MODELLING FOR ENGINEERING
Aziende collaboratrici: Sissa
URI: http://webthesis.biblio.polito.it/id/eprint/18673
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