• Heriot-Watt University Featured PhD Programmes
  • University of Birmingham Featured PhD Programmes
  • King Abdullah University of Science and Technology (KAUST) Featured PhD Programmes
  • University College London Featured PhD Programmes
  • FindA University Ltd Featured PhD Programmes
  • University of Manchester Featured PhD Programmes
  • University of Warwick Featured PhD Programmes
University of Strathclyde Featured PhD Programmes
University of Southampton Featured PhD Programmes
King’s College London Featured PhD Programmes
Queen Mary University of London Featured PhD Programmes
University of Reading Featured PhD Programmes

Resonant state expansion for relativistic and non-relativistic wave equations (physics)

Project Description

The resonant state expansion (RSE) is a rigorous perturbative method recently invented in Cardiff School of Physics and Astronomy. The RSE has been developed and used for relativistic wave equations describing such open systems as planar, cylindrical and spherical optical resonators with various perturbations. The method was demonstrated to be particularly suitable for calculating highquality
modes in such open system and efficient and accurate in calculating their perturbations. It has been shown that the RSE is a few orders of magnitude quicker computational tool as compared to existing commercial software packages like ComSol or Lumerical.
One of the main aims of the project is to apply the RSE to non-relativistic wave equations and develop a theory of resonant states in quantum-mechanical systems. In particular, the RSE will be applied to Schrödinger’s wave equation describing an electron/exciton in various nanostructures with effectively one-, two- and/or three-dimensional potentials and various perturbations. The efficiency and the quality of the new method will be investigated and tested against the existing finite difference methods and ab initio calculations. The concept of resonant states will also be used to investigate the short and long-time behaviour of quantum states and to calculate a non-quadratic (non-exponential) decay of the survival probability of quantum states at short (long) times.
The project will also consider some further applications of the RSE in relativistic problems. This may include calculation of eigenstates in optical planar waveguides and photonic crystal fibres where everlasting waveguide modes contribute to expansions of the Green’s function. Finally, there will be made attempts towards generalisation of the RSE for relativistic Dirac wave equation with a
potential application of the method to narrow-band semiconductor nanostructures.

Funding Notes

This project is available for self-funded or sponsored students only.

How good is research at Cardiff University in Physics?

FTE Category A staff submitted: 19.50

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

Email Now

Insert previous message below for editing? 
You haven’t included a message. Providing a specific message means universities will take your enquiry more seriously and helps them provide the information you need.
Why not add a message here
* required field
Send a copy to me for my own records.

Your enquiry has been emailed successfully

Share this page:

Cookie Policy    X