Dr. Elmer V. H. Doggen
What is the connection between the microscopic world of quantum mechanics and our everyday experience of the macroscopic world? This question is at the core of theoretical condensed matter physics. A key problem is the connection between the deterministic evolution of small quantum systems and the (inherently?) random, statistical description of statistical physics and quantum wave function collapse.
My work aims to answer these fundamental questions. In general, many-body systems are expected to show ergodic behaviour familiar from the ensembles of statistical physics. That is, the particular microscopic details of the system are irrelevant, the system effectively loses memory of any local perturbations to it, and the system can be described by a handful of thermodynamic variables such as the temperature, pressure, and so on.
Some quantum systems, however, are not ergodic, even in the presence of many-body interactions between the particles. Disorder in the system leads to a recently discovered localized phase of matter: the many-body localized (MBL) phase. MBL is exceptionally difficult to study, because strong interactions and strong disorder together imply that simple, approximate theories break down. This means that the properties and stability of this phase are still debated.
Disorder is not an essential ingredient for inhibiting ergodicity. Constrained systems are another example, for instance a system wherein a potential gradient effectively inhibits large-scale transport. In the non-interacting case this leads to Wannier-Stark localization. Non-ergodicity survives the introduction of interactions to this sytem, because local bottlenecks create insurmountable energy barriers.
An exciting new development is the study of quantum measurement transitions, where we study the breakdown of quantum correlations and entanglement due to local measurements. This leads to a phase diagram with a transition between an entangling and disentangling phase. Thus, we hope to achieve a better understanding of the century-old question: what is a quantum measurement, really?
To help answer these questions, we can use the power of modern computers not available to the pioneers of quantum mechanics. The use of tensor network-based algorithms, in particular matrix product states, has been a tremendous asset for studying quantum many-body systems. Even in the simplest general case, a lattice system with two degrees of freedom (say, either a particle is there or it's not), the computational complexity of the problem increases exponentially with the size of the system. Tensor network-based algorithms use a smart way to mitigate this problem, leading to "only" a polynomial growth of complexity. We have only scratched the surface of what we can learn with these powerful algorithms.
Publication profile: see Google Scholar
Slow Many-Body Delocalization beyond One Dimension, Phys. Rev. Lett. 125, 155701 (2020)
Stark many-body localization: Evidence for Hilbert-space shattering, Phys. Rev. B 103, L100202 (2021) - selected as an Editor's Suggestion
Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization, arXiv:2104.10451
Interested in joining our group and contributing to these research projects? Inquire about open Master, PhD and postdoc positions with Prof. Dr. Alexander D. Mirlin.
2017-present: Postdoctoral Researcher, Karlsruhe Institute of Technology, Germany
2015-2017: Postdoctoral Researcher, Université Paul Sabatier (Toulouse III), France
2011-2015: PhD student, Aalto University, Finland