# Random physics

Alberto Verga, research notebook


# Classical and Quantum Chaos

Graduate course on classical chaos, plasmas, and quantum chaos. The approach is phenomenological, with a brief presentation of the theoretical concepts in parallel with computations (mostly numerical) of specific systems.

## Summary

1. Maps
• dyadic map and the sensitivity to initial conditions
• logistic map, stable and instable orbits, bifurcations, periodic orbits, chaotic orbits
• Hamiltonian formalism: Liouville, KAM and PB theorems.
• standard map: a chaotic Hamiltonian system, fixed points and Chirikov stochasticity criterion; quasilinear diffusion.
• Stability and bifurcation of dynamical systems
2. Plasmas
• Vlasov equation, Landau damping
• Numerical simulation of the collisionless plasma (particle in cell)
• Quasilinear diffusion
3. Quantum chaos

# Statistical Physics

First master course on statistical mechanics.