Starting from common knowledge in quantum mechanics, this talk will introduce a simplified version of the quantum formalism. More precisely, I will recall basic facts about the wave function, the observables and the Schrödinger equation, and explain how in specific cases, one can solve quantum mechanical problems using finite dimensional linear algebra.
The second purpose of this talk is to apply this simplified formalism to a specific problem : the Linear Response Theory and the Entropic Fluctuations of Repeated Interaction Systems. Physically speaking, one can think of a beam of atoms whose temperatures are non-equal. This beam goes through a cavity which is filled with an electromagnetic field. In mean, this electromagnetic field will take energy from the hottest atoms and give energy to the coldest ones. Some well-known physical results of thermodynamics can be proved on a particular form in this situation.