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CS - Dr Lennart Dabelow

Typicality approach for open quantum system dynamics

Supervisor: Dr Lennart Dabelow

Project description:

Everyday experience tells us that we can understand and describe the behavior of macroscopic objects without knowing the exact details of all their microscopic constituents (e.g., atoms and molecules). This is essentially the key idea behind the use of ensembles in statistical mechanics. For example, the precise microstate of an isolated system in equilibrium may be unknown, but since nearly all microstates with the same energy, volume and particle number exhibit the same macroscopically observable properties, we can predict these properties by averaging over all those microstates, i.e., the microcanonical ensemble. The average properties are typical as they agree with those of the overwhelming majority of individual ensemble members.

Similar ideas have been developed to describe the dynamics of closed many-body quantum systems that evolve unitarily in time. For instance, Refs. [1, 2] have adopted suitable ensembles of randomized Hamiltonians to obtain an analytical theory for the nonlinear response of closed systems to parametrically time-dependent perturbations. However, many systems of current interest are not perfectly isolated or closed, but are instead open, e.g., because of continuous (weak) measurements or remnant environmental influences, resulting in non-unitary dynamics. Interest in such systems arises from applications in the development of quantum technologies as well as a variety of intriguing novel effects that are absent in closed systems.

In this project, the student will explore how typicality and random-matrix methods can be applied to describe and predict the nonequilibrium dynamics of open many-body quantum systems. To this end, they will combine existing and develop new tools from random matrix theory, large deviations theory, statistical mechanics, and non-Hermitian many-body physics. The starting point will be setups described by non-Hermitian Hamiltonians. Later, we will aim at extending the approach to quantum master equations.

Successful candidates will have

  • a first or upper second class (or equivalent) degree in mathematics, physics, or a related discipline (by September 2026);
  • good foundational knowledge of probability theory and statistics;
  • good foundational knowledge of quantum and statistical mechanics;
  • experience with computer programming in a multi-purpose language, for instance C/C++ or Python.

Informal enquiries are encouraged and should be directed to Dr Lennart Dabelow (l.dabelow@qmul.ac.uk).

References:

[1]  L. Dabelow and P. Reimann, Stalled response near thermal equilibrium in periodically driven systems, Nat. Commun. 15, 294 (2024), arXiv:2401.04645

[2]  L. Dabelow and P. Reimann, Random matrix approach to time-dependent forcing in many-body quanutm systems, Phys. Rev. B 110, 144308 (2024), arXiv:2409.10052

Funding Notes:

This project is open to candidates applying for EPSRC/Underrepresented Studentships and self-funded candidates.

Further information: 
How to apply 
Entry requirements 
Fees and funding

PhD Information Session 2026:
On Wednesday 14 January, we will be holding a short information session about PhD studies in Mathematics at QMUL. For full details about the event, please visit: https://www.qmul.ac.uk/maths/postgraduate/postgraduate-research/phd-information-session-2026/

 

As one of the UK’s most diverse universities, QMUL fosters an inclusive and supportive academic community.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award, we offer family-friendly benefits and support part-time study.  

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