30558 - STATISTICAL AND QUANTUM PHYSICS

Being familiar with elementary mechanics, as well as with basic linear algebra and probabilities will be of help for students to better understand the topics, and to solve problems

Quantum and statistical physics are the two pillars of modern physics. The scope of the course is to provide the basic conceptual and methodological tools which form the basis of quantum mechanics and statistical physics. The course will introduce the main concepts, provide the necessary mathematical formalism, and work out many examples of applications.

Part A: Quantum Physics

1-    Why quantum mechanics? Introduction to quantum phenomena

2-    Schrödinger equation

3-    Quantum measurements

4-    Energy quantization

5-    Principle of quantum mechanics

6-    Two state systems

7-    Approximation methods

8-    Angular momentum

9-    Quantum description of atoms

10- Entanglement, Einstein-Podolsky-Rosen paradox, Bell’s inequalities

11- Introduction to quantum computing

Part B: Statistical Physics

1-    Why statistical physics? From microscopics to macroscopics

2-    Statistical descriptions

3-    Thermodynamics seen from the statistical physics viewpoint

4-    Ideal gas

5-    Interacting systems, phase transitions, ferromagnetism

6-    Dynamics and equilibrium

7-    Statistical physics and Data Dcience

8-    Statistical physics and Machine Learning

- understand the description of quantum systems

- understand  quantum spins

- understand the quantum theory of atomic structure

- understand the concepts of entanglement and quantum measurement

- understand the principles of statistical physics and their relations to thermodynamics

- understand the theory of ideal gases

- understand the notion of phase transition

- undestand the dynamics of statistical physics systems and the approach to equilibrium

- understand the principles of application of statistical physics in data science and machine learning

- Study quantum properties of particles in external potentials

- Use perturbative methods

- Study quantum properties of spin 1/2 particles

- Study properties of ideal gases, classical, fermions and bosons

- Study phase transitions using mean-field theory

- Understand the dynamical properties of simple many-body systems

- Use the simplest mean-field methods in data analysis and inverse problems

• Face-to-face lectures
• Exercises (exercises, database, software etc.)

Exercises are an important part of the course. Regularly, a part of the lectures time will be dedicated to exercises in  the class, illustrating and complementing the lectures.

The total grade has a maximum of 32 points. 

The grade of 30 cum laude corresponds to 31 or 32 points

In order to pass the exam, the students must obtain a grade of 18 points at least.

The exam is not open-book. Any material apart from the one provided by the instructors is forbidden. A sheet contianing basic formulas and fundamental constants will be provided.

-       Quantum mechanics, J-L Basdevant and J. Dalibard, Springer

-       Fundamentals of Statistical and Thermal Physics, Frederick Reif, Mac Graw Hill  (optional)

-       “From statistical physics to data-driven modelling”, Simona Cocco, Rémi Monasson and Francesco Zamponi, Oxford University Press 2023

Exercises will be provided, as well as additional teaching material when needed