Microscopic models UGA - WPMNMMI2

Goal(s)

This course is an introduction to the second quantization. This ultimate formulation of quantum mechanics is nowadays used in all fields. This course introduces the concepts and mathematical elements leading to the solution of N-body problems in quantum mechanics (correlations).

Content(s)

• Reminder on operators, switches. Indiscernibility and N-particle wave function (Slatter determinant).

• Formalism of the second quantization: operators in second quantization, elementary properties, field generator and expression of usual operators.

• Hartree approximation, exchange integral, correlations and mean field

• Some examples: jellium model, electron-phonon interaction, BCS model (treated as a TD)

The second part of the course aims at introducing the notions necessary to model and simulate the quantum properties of electronic systems with or without interactions. Theoretical exercises as well as practical work aiming at the manipulation of simple algorithms will be considered in the context of concrete examples such as band structures, metal/insulator transition, the role of electronic correlations, quantum magnetism, the notion of frustration or quantum and thermal melts.

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It is strongly advised to have a solid base in quantum mechanics. Similarly, the basic notions of programming must be acquired (writing simple code, using conditions and loops, etc.). It is recommended to be familiar with the basics of the Python language in order to better understand the teaching