Second quantization, Green's functions. Weakly interacting bosonic and fermionic systems. Tight binding approximation,Hubbard model. Systems of electrons and phonons. Superfluidity and superconductivity. BCS theory. Superconducting-insulating tunneling, Josephson effect. Superconducting quantum computers. Simulation of many-body systems in quantum computers. Ising model, Majorana fermions. Tensor networks
The aim of this course is to provide the basic theoretical tools to study quantum many-particle systems. These tools will be applied to study superconductivity, superfluidity and magnetism. Finally, modern tools will be introduced to simulate these systems in classical and quantum computers.
Prerequisites
Quantum mechanics. Statistical mechanics.
Teaching Methods
theoretical lessons in the classroom
Further information
Flexible reception hours, contact the lecturers
Type of Assessment
The oral exam consists in the discussion of an in-depth study on a topic carried out in the program, as well as possible questions on the course program. The in-depth topic is assigned by the lecturers at least two weeks before the test.
Course program
Second quantization, Green's functions. Weakly interacting bosonic and fermionic systems. Tight binding approximation,Hubbard model. Systems of electrons and phonons. Superfluidity and superconductivity. BCS theory. Superconducting-insulating tunneling, Josephson effect. Superconducting quantum computers. Simulation of many-body systems in quantum computers. Ising model, Majorana fermions. Tensor networks