Strongly-out-of-equilibrium thermalisation and transport
- Perturb material and it'll try to go back to equilibrium - fentosecond laser pulses to precision punch materials (by choosing frequency of the laser pulse) to activate certain types of transitions
- Take a "snapshot" to see what excited state it is in right after the first laser pulse
- Can we describe as precisely as possible the behaviour of the material during this thermalisation of the material (if the behaviour isn't Fermi Dirac and has been perturbed away from this behaviour)
- Boils down to solving numerically the Boltzmann Equation (partial differential equation). Calculate the time propogation of this. f[t,x,k] and also band index
- Scattering term is the most complicated (non-linear operator. high dimension. shape of it is rather complicated (contains dirac deltas, etc))
- TORTOISE: C++ Library (2 projects related to building pieces of this library)
- Project 1: Gauss integration for scattering integrals
- Project 2: Spectra Integration and convolution (discretise a certain type of integral)
- Skills needed: C++ programming skills (OOP, Template, Eigen library), Analytical Skills (Numerical Math)

- Project 3: Dielectric response of metallic carbon nanotubes for plasmonic applications
- plasmon: collective longitudinal excitation of the electrons in a system
- bulk plasmons vs localised surface plasmons: LSP couple to light because of electrons confinement in nanostructures, contribute to light absorbing spectrum
- Modelling plasmons 1: drude model and drude smith model (further scattering elements with the boundaries of the system)
- Modelling plasmons 2: maxwell (laplace) equation
- Modelling plasmons 3: RPA dielectric function (dielectric response calculated using random phase approximation)
- Project 4: Envelope functions approximation for low-dimension semiconductor devices
- Description of band structure / wave function of bulk material
- Decouple spatial components
- solve SE in the bulk
- solve envelope function approximation
- compute interesting quantities from the wave functions (absorption, diffusion, scattering elements)

- Project 5: Numerous simulation
- Existing discontinuous Galerkin code for non-linear reaction-diffusion equation
- Extend existing code to 7 unknown variables
- Solve governing equation for the reaction-diffusion Malaria model for initial conditions
- FORTRAN 90 based programming

- Nonlinear Schrodinger Equation
- Solutions: solitons, breathers, rogue waves (applications in hydrodynamics and optics)
- For systems that have a lot of nonlinear properties (like the sea)
- Project 6: Perturb the equation including similar types of terms and how they affect the above mentioned solutions.
- Can be solved both analytically and numerically

- Project 7: Transfer Matrix
- Do experiment
- Use code to fit experimental values
- Use the fitting to extract several properties about the spintronics