Syllabus
Mechanics of molecular systems.
Statistical ensembles, random walks, discrete and continuous probability, maximal likelihood principle, temperature.
Liouville theorem and Liouville equation.
Introduction to molecular dynamics, microcanonical ensemble, classical virial theorem, thermal equilibrium.
Integration of equations of motion: finite difference methods, classical operator of time evolution and numerical integrators.
Classical time-dependent statistical mechanics and linear response theory.
Quantum models in biophysics and chemical physics: Nuclear spins. Molecular vibrations. Electronic states.
Density matrices: Populations and coherences. Wave function collapse. Liouville-von Neumann equation.
Quantum-classical mapping: Bloch sphere. Wigner density. Bohr-Sommerfeld quantization.
Quantum statistics at equilibrium: Canonical density matrices. Boson condensation. Gibbs paradox. Fermi-Dirac and Bose-Einstein distributions. Quasiparticles.
Emergence of relaxation: von Neumann entropy. Unitary evolution. Reduced density matrix. Random Hamiltonian. Decoherence. Liouville space, superoperators.
Quantum master equations: Quantum semigroups, Lindblad form, Stochastic Liouville equations, Open quantum systems. Secular dynamics. Thermodynamics of quantum relaxation.
Molecules in optical fields: Bloch equations. Absoption line shapes. Bayesian quantum statistics. Photon arrival trajectories. Dynamical spectroscopy.
Annotation
Introduction to the study of molecular systems by methods of classical and quantum statistical physics. The lecture aims to establish a solid foundations for the use of molecular dynamics and to introduce to the density matrix - the central concept of quantum statistics with the perspective to model electronic and vibrational coherence.
Thorough understanding of quantum-classical correspondence will be emphasized.