Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point

Understand

We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian.

• We first consider a two-level system and give an elementary derivation of the asymptotics of the transition probability when the tuning parameter slowly changes in the finite range.
• Then we apply this perturbation theory to many-particle systems with low energy spectrum characterized by quasiparticle excitations.
• Within this approach we derive the scaling of various quantities such as the density of generated defects, entropy and energy.