Research students

Present and former research students

Present research students

Former research students

Some potential topics for PhD projects

Interplay of mutation and selection in population genetics

Population genetics describes biological evolution in mathematical terms. Methods of statistical mechanics can be employed to investigate certain models of sequence evolution of DNA sequences, which can be mapped onto classical or quantum spin systems. There is a close collaboration to groups in Germany, both in mathematics and in biology. One aspect of the work is the implementation of the DMRG (density matrix renormalisation group) method that allows efficient numerical treatment of finite systems of reasonable size.

Spectral properties of aperiodic Schrödinger operators

Aperiodically ordered quantum systems are of interest in the theoretical description of quasicrystals, a particular kind of ordered solid lacking the periodic structure of ordinary crystals. Such systems exhibit rather unusual spectral properties, including singular continuous spectra and multifractal eigenfunctions. The work aims at unravelling the connection between spectral properties on the one hand and quantum diffusion on the other hand, employing a combination of analytical and numerical techniques.

Stastistical mechanics of aperiodically ordered and disordered systems

The properties of a system at, or close to, a second-order phase transition are assumed to be universal. Roughly, this means that they do not depend on any particular details of the system. However, aperiodic order or disorder, either in the coupling constants or in the underlying discrete structure, may influence the critical behaviour. The work comprises the investigation of the effects of aperiodic order and disorder in classical and quantum spin models, particularly the Ising model.

Any student who is interested to join me on one of the above topics, or would like to know more about my research interests, is cordially invited to contact me!

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Uwe Grimm
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