Random physics

Alberto Verga, research notebook

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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.