Benjamin Lees, Ph.D.

Age: 27

Area of research: from Quantum statistical mechanics to spatial random permutations

Name of my Research Institute:

University of Warwick, U.K.

Research period at the TU Darmstadt: May 2017 to April 2019 (AvH Research Fellowship for Postdoctoral Researchers)

Benjamin Lees, Ph.D.

Questionnaire to the Research Fellow

My field of research is fascinating. To laymen I would explain it in the following comprehensible manner:

Everyone is familiar with the freezing or boiling of water when the temperature is changed sufficiently. These phase transitions are not the only types possible of course. One such transition results in Bose-Einstein condensation, a state of ultra-cold bosons that was predicted by Einstein and created for the first time in 1995. This transition should be closely related to superfluidity and superconductivity but the precise links still remain to be worked out. My work closely concerns the theory behind this and other phase transitions of matter using links to probability theory.

My most important success in research to date is…

I was able to rigorously establish a connection between a class of quantum spin systems and a fascinating probabilistic model. Using this link one can prove that a phase transition occurs in the quantum system at low temperatures. This transition to a so-called antiferromagnetic phase allows a deeper understanding of the various compounds that exhibit this rather strange antiferromagnetic behaviour. The link with the probabilistic model also raises more questions and hope of exploiting similar techniques on many other models.

Benjamin Lees with his host Professor Dr. Volker Betz (front).
Benjamin Lees with his host Professor Dr. Volker Betz (front).

I’ve chosen the TU Darmstadt because of…

the strong Stochastic group here, which will allow me to further develop the connections between quantum systems and probabilistic models. As I come more from the quantum systems side of this connection the skills already present in Darmstadt will compliment my own well and allow for a mutually beneficial relationship. Professor Betz is renowned as an expert on both sides of this connection and the current state of the theory connecting these two important topics making Darmstadt a natural choice to carry out my research.

Guest of: Prof. Dr. Volker Betz

Department: Mathematics

My guest favourably impressed me by… Ben has done great work in connecting models of quantum statistical mechanics with random loop models of probability theory, and analysing the former through the latter. He is very enthusiastic and motivated, and has an excellent publication track record.

Our team and the TU Darmstadt benefit from his expertise…

Prof. Dr. Volker Betz.
Prof. Dr. Volker Betz.

in connecting quantum systems with probability systems, and his deep knowledge of quantum spin systems. This is precisely what we need at the current state of our research project on the probabilistic representation of Bose-Einstein condensation.