EXAM PROGRAM (2019/2020) 

1) Introduction to thermodynamics. Thermodynamic potentials.
Extensive and intensive quantities. Chemical potential of the ideal gas.

2) Microcanonical ensemble.

3) Canonical ensemble, isobaric-isothermal ensemble, grand-canonical
ensemble.

4) Average kinetic energy and equipartition theorem. 
Pair distribution function. Structure factor. Virial pressure.

5) Metropolis algorithm, general theory. 
Applications to monoatomic systems in the canonical,
isobaric/isothermal ensemble and in the grand-canonical ensemble.
Ising model canonical simulations. Computation of the chemical potential
in the canonical ensemble.

6) Fluctuation relations, data reweighting methods, umbrella sampling 
and simulated tempering.

7) Basics of MD simulations. Verlet updates: basic properities, time 
reversal, momentum conservation, phase-space volume conservation.
Verlet update for the harmonic oscillator. 
Liouvillian formulation of the dynamics. 
Verlet update in the Liouville approach.
Properties of Liouvillians and existence of a conserved
Hamiltonian. Leap-frog algorithm.

8) Dynamics in the presence of constraints and hybrid algorithms.

9) Molecular dynamics in the presence of a Gaussian noise. Langevin equation.