Corsi di Laurea Corsi di Laurea Magistrale Corsi di Laurea Magistrale
a Ciclo Unico
Scuola di Scienze
PHYSICS OF DATA
Insegnamento
MODELS OF THEORETICAL PHYSICS
SCP8083597, A.A. 2019/20

Informazioni valide per gli studenti immatricolati nell'A.A. 2019/20

Principali informazioni sull'insegnamento
Corso di studio Corso di laurea magistrale in
PHYSICS OF DATA
SC2443, ordinamento 2018/19, A.A. 2019/20
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Crediti formativi 6.0
Tipo di valutazione Voto
Denominazione inglese MODELS OF THEORETICAL PHYSICS
Sito della struttura didattica http://physicsofdata.scienze.unipd.it/2019/laurea_magistrale
Dipartimento di riferimento Dipartimento di Fisica e Astronomia "Galileo Galilei"
Sito E-Learning https://elearning.unipd.it/dfa/course/view.php?idnumber=2019-SC2443-000ZZ-2019-SCP8083597-N0
Obbligo di frequenza No
Lingua di erogazione INGLESE
Sede PADOVA
Corso singolo È possibile iscriversi all'insegnamento come corso singolo
Corso a libera scelta È possibile utilizzare l'insegnamento come corso a libera scelta

Docenti
Responsabile AMOS MARITAN FIS/03
Altri docenti MARCO BAIESI FIS/02
GIACOMO GRADENIGO

Mutuazioni
Codice Insegnamento Responsabile Corso di studio
SCP8083597 MODELS OF THEORETICAL PHYSICS AMOS MARITAN SC2382

Dettaglio crediti formativi
Tipologia Ambito Disciplinare Settore Scientifico-Disciplinare Crediti
CARATTERIZZANTE Teorico e dei fondamenti della fisica FIS/02 6.0

Organizzazione dell'insegnamento
Periodo di erogazione Primo semestre
Anno di corso I Anno
Modalità di erogazione frontale

Tipo ore Crediti Ore di
didattica
assistita
Ore Studio
Individuale
LEZIONE 6.0 48 102.0

Calendario
Inizio attività didattiche 30/09/2019
Fine attività didattiche 18/01/2020
Visualizza il calendario delle lezioni Lezioni 2019/20 Ord.2018

Commissioni d'esame
Commissione Dal Al Membri
1 Commissione Models of Theoretical Physics 2018/2019 01/10/2018 30/11/2019 MARITAN AMOS (Presidente)
BAIESI MARCO (Membro Effettivo)
SUWEIS SAMIR SIMON (Supplente)

Syllabus
Prerequisiti: Good knowledge of mathematical analysis, calculus, elementary quantum mechanics and basic physics.
Conoscenze e abilita' da acquisire: The purpose of the course is to provide the student with a wide vision on how
theoretical physics can contribute to understand phenomena in a variety of fields
ranging from “classical” subjects like difusionn quantum mechanics and more in
general to the physics of complex systems. Particular emphasis will be placed on the
relationships between different topics allowing for a unified mathematical approach
where the concept of universality will play an important role. The course will deal with
a series of paradigmatic physical systems that have marked the evolution of
theoretical physics in the last century including the most recent challenges posed by
disordered systems with applications to machine learning and neural networks. Each
physical problem the modeling and the solution thereof will be described in detail
using powerful mathematical techniques.
The frst part of the course will provide the basic mathematical tools necessary to deal
with most of the subjects of our interest. The second part of the course will be
concerned with the key concepts of universality stochastic processes and emergent
phenomena which justify the use of field theoretical models of interacting systems and tools like the renormalization group techniques. In
the third part it will be shown how solutions of quantum systems can be mapped in
solutions of difusion problems and vice versa using common mathematical
techniques. The last part will deal with the most advanced theoretical challenges
related to non-homogenous/disordered systems, which find applications even outside
the physical context in which they arose.
Modalita' di esame: Final examination based on: Written and oral examination and weekly exercises proposed during the course
Criteri di valutazione: Critical knowledge of the course topics. Ability to present the studied material.
Discussion of the student project.
Contenuti: Introduction; "The Unreasonable Effectiveness of Mathematics in the Natural Sciences
(Wigner 1959)"; Gaussian integrals Wick theorem
Perturbation theory connected contributions Steepest descent
Legendre transformation Characteristic/Generating functions of general probability
distributions/measures
The Wiener integral geometric characteristics of Brownian paths and Hausdorff/fractal
dimension
Brownian paths and polymer physics biopolymer elasticity. The random walk
generating function, the Gaussian field theory and coupled quantum harmonic
oscillators
Levy walks violation of universality
Field theories as models of interacting systems
O(n) symmetric Phi^4– theory. The large n limit: Spherical (Berlin-Kac) model and 1/n
expansion.

Perturbative expansion. Introduction to renormalization group techniques and universality.

Generalized diffusion and stochastic differential equations. The Feynman-Kac formula: diffusion with sinks and sources
Feynman path integrals and the quantum version of the Feynman-Kac formula.
Quantum mechanics (solvable model: free particle, harmonic oscillator)
Quantum vs stochastic phenomena: quantum tunneling and stochastic tunneling
Stochastic amplification and stochastic resonance
Non-perturbative methods: instantons
Diffusion in random media and anomalous diffusion
Quantum Mechanics in a random potential localization and random matrices
Statistical physics of random spin systems and the machine-learning problem
Random energy model, replica trick
Cavity method, Random Field Ising Model
Attivita' di apprendimento previste e metodologie di insegnamento: Lecture supported by tutorial, assignment, analytical and numerical problems
Eventuali indicazioni sui materiali di studio:
Testi di riferimento:

Didattica innovativa: Strategie di insegnamento e apprendimento previste
  • Lecturing
  • Problem solving

Didattica innovativa: Software o applicazioni utilizzati
  • Moodle (files, quiz, workshop, ...)