Mechanics - Physics

•  1^st year course/Mechanics: basics of continuum mechanics
•  1^st year course/Physics: statistical physics and quantum physics parts.
•  1^st year course/Waves and Signal: Maxwell, wave and Helmholtz equations, paraxial propagation, signal processing.
•  Basics of group theory.

•  Use the 1^st year programme to discover fundamental notions:
  -- dynamics in mechanics;
  -- in the case of optics, the formation of images and the transmission/retrieval of information using light;
  -- in addition to the above, the course will also cover the following topics: - the concept of symmetry and variational calculus in relation to the Lagrange and Hamilton formalisms, for quantum physics.
  -- fluctuations and critical phenomena for statistical physics.
•  Know how to put a problem into equations using different tools.
•  Know how to calculate theoretically or numerically the solutions of the different problems formulated.
•  Know how to analyse the solutions obtained.

The programme is divided into three parts of equal volume: mechanics, optics, and physics (quantum and statistical).
Mechanics:
•  Equation tools:
  -- Virtual power theorem and opening to the finite element method
  -- Hamilton's principle and Lagrange's equations
•  Resolution and analysis:
  -- Transient and stationary regimes
  -- Modes
  -- Stability and bifurcations
Optics:
•  Matrix methods for rays and waves, Collins formula and phase space
•  Types of optical system (imaging, afocal, Fourier transforming), aberrations and optical resolution
•  Waveguides (metallic, dielectric and gradient index)
•  Lasers: stimulated emission, coherence, cavities, modes, short pulses, amplification of chirps
Quantum physics:
•  Infinitesimal symmetries, Lie algebra of generators: Lorentz group, spinorial transformations of the SU2 group seen as a representation of the group of rotations in R3
•  Density matrix for qubits (Bloch vector), coherence and purity of a quantum state, links with optics
•  Principle of least action
Statistical physics:
•  Distribution theory and applications in physics
•  Random fields applied to physics
•  Equilibrium fluctuations and phase transitions

•  Know the links and similarities between different disciplines
•  Know how to put a large number of complex systems into equations
•  Know how to solve a system of equations analytically
•  Know the basics of numerical methods for solving the systems encountered
•  Know how to analyse the solutions obtained
•  Be able to solve simple problems as seen in courses or similar to them
•  Deepen basic concepts such as the principle of symmetry

CC1: written (42%)
CC2: written (42%)
CC3: mini-project in optics (8 %)
CC4: short tests at the beginning of each tutorial class (8 %)

•  PDF version of slides, PDF and CDF notes
•  Physics:
  -- D. Griffith, Introduction to Quantum Mechanics, Wiley (available in electronic and paper version at the centre de documentation) plus polycopie available on Moodle
  -- Ph. Réfrégier, Noise theory and application to physics, Springer, 2003
  -- J.M. Yeomans, Statistical Mechanics of Phase Transitions, Oxford Science Publications,1992

Optics: Miguel Alonso, Luis Arturo Aleman Castaneda, Frédéric Lemarquis, Laurent Gallais-During
Quantum physics: Thomas Durt et Marc Jaeger
Statisical physics: Philippe Réfrégier, Georges Bérardi, Muriel Roche, Julien Fade
Mechanics: Emmanuelle Sarrouy, Bruno Cochelin, Régis Cottereau, Thierry Désoyer, Cédric Maury