Nanotechnology Engineering

1) Lagrangian and Hamiltonian mechanics N particles systems; generalized coordinates and conjugate momenta; phase space: micro-state and macro-state of a system; Lagrangian function and the Lagrangian equations of motion. The Hamiltonian function and the Hamiltonian equations of motion. 2) Introduction to statistical mechanics Statistical ensamble; the Gibbs hypothesis; distribution function; the measure of a physical quantity; the Liouville theorem and its consequences. Microcanonical ensamble: distribution and partition functions; entropy; therma, mechanical and chemical equilibrium; statistical macroscopic quantities: temperature, pressure, chemical potential. Intensive and extensive observables; the link with classical physics. Canonical ensamble: distribution and partition functions; energy probability density and density of states; the partition function of an ideal gas; the Helmoltz free energy; Maxwell and Maxwell-Boltzmann distributions; The equipartition theorem; Grand-Canonical Ensamble: Distribution and partition functions; the ideal gas in the granmd-canonical ensamble; quantum partition functions; the Bose-Einstein and the Fermi-Dirac distributions. 3) Monte-Carlo and statistical mechanics Monte-Carlo integration; pseudo-random numbers. Random numbers generators, casuality tests; The Lehmer generator; importance sampling: inversion and rejection; Markov chains; the Metropolis-Monte-Carlo algorithm; technicalities: interaction potentials; periodic boundary conditions; truncation and shift etc.; orientational moves for polyatomic molecules; Metropolis Monte-Carlo in the micro-canonical and grand canonical ensambles.

Class notes and textbook from the teacher. a deeper understanding from: 1) first and second chapters: C. Kittel “Elementary Statistical Physics” John Wiley & Sons 2) third and fourth chapters Frenkel-Smit “Understanding Molecular Simulation”; Academic Press; Allen; Tildsley “Computer Simulation of Liquids”; Ed. Oxford Science;