First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP8083597, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
SC2443, Degree course structure A.Y. 2018/19, A.Y. 2018/19
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination MODELS OF THEORETICAL PHYSICS
Website of the academic structure
Department of reference Department of Physics and Astronomy
E-Learning website
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge AMOS MARITAN FIS/03
Other lecturers MARCO BAIESI FIS/02

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses FIS/02 Theoretical Physics, Mathematical Models and Methods 6.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 01/10/2018
End of activities 18/01/2019

Examination board
Board From To Members of the board
1 Commissione Models of Theoretical Physics 2018/2019 01/10/2018 30/11/2019 MARITAN AMOS (Presidente)
BAIESI MARCO (Membro Effettivo)

Prerequisites: Good knoledge of mathematical analysis, calculus, elementary quantum mechanics and basic physics.
Target skills and knowledge: 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 felds
ranging from “classical” subjects like difusionn quantum mechanics andn more in
generaln to the physics of complex systems. Particular emphasis will be placed on the
relationships between diferent topics allowing for a unifed 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 problemn the modeling and the solution thereofn 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 universalityn stochastic processes and emergent
phenomenan which justify the use of feld theoretical models of interacting systems. 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 systemsn which fnd applications even outside
the physical context in which they arose.
Examination methods: Final examination based on: Written and oral examination and weekly exercises proposed during the course
Assessment criteria: Critical knowledge of the course topics. Ability to present the studied material.
Discussion of the student project.
Course unit contents: Introduction; "The Unreasonable Efectiveness of Mathematics in the Natural Sciences
(Wigner 1959)"; Gaussian integralsn Wick theorem
Perturbation theoryn connected contributionsn Steepest descent
Legendre transformationn Characteristic/Generating functions of general probability
The Wiener integraln geometric characteristics of Brownian paths and Hausdorf/fractal
Brownian paths and polymer physicsn biopolymer elasticity. The random walk
generating functionn the Gaussian feld theory and coupled quantum harmonic
Levy walksn 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
Perturbative expansionn Universalityn critical dimensions
Generalized difusion and stochastic diferential equations
Path integrals representation of stochastic processes with general difusion operator
(Brownian motion in curved spaces)
The Feynman-Kac formula: difusion with sinks and sources
Quantum mechanics (solvable modeln harmonic oscillatorn free particle)
Feynman path integrals and the quantum version of the Feynman-Kac formula.
Quantum vs stochastic phenomena: quantum tunneling and stochastic tunneling
Stochastic amplifcation and stochastic resonance
Nonperturbative methods, instantons
Difusion in random media and anomalous difusion
Quantum Mechanics in a random potentialn 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
Planned learning activities and teaching methods: Lecture supported by tutorial, assignment, analytical and numerical problems
Textbooks (and optional supplementary readings)

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Problem based learning
  • Problem solving