## ECTS credits

4 credits

## Semester

Fall

## Prerequisites

• 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.

## Learning objectives

• 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.

## Description of the programme

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

## Generic central skills and knowledge targeted in the discipline

• 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

## How knowledge is tested

CC1: written (42%)

CC2: written (42%)

CC3: mini-project in optics (8 %)

CC4: short tests at the beginning of each tutorial class (8 %)

## Bibliography

• 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

## Teaching team

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

- Total hours of teaching72h
- Master class36h
- Directed work18h
- Practical work2h
- 14h
- 2h