Learning objectives
At the end of the course the student is expected to be able to:
- Know the Path Integral formulation of quantum mechanics and apply it to concrete problems, either through exact solutions, when possible, or by using approximation methods.
- Know the different definitions of entropy, statistics and thermodynamics, and the relationship between entropy and information;
- Know and apply entropy calculation methods to problems of non-equilibrium thermodynamics and physical and interdisciplinary systems;
- Being able to find bibliographical references on frontier topics and to assess the quality of scientific articles;
- Ability to prepare and present scientific seminars on contemporary research topics.
- Being able to self-evaluate one's knowledge in the necessarily broad context of modern theoretical physics, differentiating conceptual aspects from more technical ones.
Prerequisites
Quantum Mechanics and Basic Statistical Physics
Course unit content
The lectures provide an overview on results and methods of modern Theoretical Physics.
This year, the course will be organised in two sections:
- Path Integral formulation of Quantum Mechanics and applications, given by Prof. Luca Griguolo.
- Theormodynamical Entropy, Statistical Entropy and Information, given by Prof. Raffaella Burioni.
Full programme
First part:
- Path Integral Path formalism;
- Functional and Euclidean methods;
- The semiclassical approximation.
Second part:
- Thermodynamical Entropy and Statistical Entropy
- Irreversibility and the H theorem
- Relations between entropy and information;
- Variational principles of maximum entropy and statistical inference;
- Applications to Data science and learning.
Bibliography
A detailed literature will be provided, integrated by lecture notes when available.
Teaching methods
Blackboard lectures and slides.
Assessment methods and criteria
Oral examination. The student will prepare a short seminar on a subject agreed with the lecturers. This will be the initial part of the examination, which will go on with questions on the rest of the subjects taught during the course. The oral examination will last about 30 minutes. The evaluation will be agreed between the lecturers, and will be communicated to the student immediately after the end of the interview.
Other information
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