Open PhD-position: Nonequilibrium critical dynamics of a Kosterlitz-Thouless-transition
If you are interested, please contact me by email or phone.
Project: Using a colloidal ensemble in two dimensions, the formation of topological defects should be investigated while pushing the system far from thermal equilibrium through a continuous phase transition.
In equilibrium, melting of two-dimensional (2D) mono-crystals is described by the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young scenario (KTHNY-Theory), awarded with the Nobel-Price 2016 for Michael Kosterlitz and David Thouless. Following the theory, the continuous Phase transitions are driven by topological defects – proofed by previous experiments in our group. The typical view is, that spontaneous symmetry breaking occurs globally.
For non-zero cooling rates, this is not true but topological defects as monopoles, grain boundaries or strings have to be incorporated in the symmetry broken phase. Spontaneous symmetry breaking serves identically values of the order parameter only locally. Beyond equilibrium, the scenario is described by the Kibble-Zurek mechanism, originally developed by Tom Kibble to describe the defect density of the primordial Higgs-field during the expansion of the early universe shortly after Big Bang. Regions, separated far enough in space such that they cannot communicate even with the speed of light, cannot gain the same order-parameter during spontaneous symmetry breaking.
W. Zurek transferred the idea to condensed matter and quantum fluids. Due to the critical slowing down of order parameter fluctuations during cooling (correlation times tend to infinity), the system must fall out of equilibrium, incorporating topological defects into the low temperature phase.
In this project, those phenomena will be investigated with a colloidal monolayer of micrometer sized super-paramagnetic particles, which perform Brownian motion and are confined to an absolutely flat interface. Unlike “real” atoms, particles are large AND slow enough that they can easily be monitored with video-microscopy on single particle level at any relevant time scale. We can quench our ensembles on time scales, orders of magnitudes faster than the shortest intrinsic time scale given by the Brownian time (~ sec). Even for quantum fluids, such unrivalled fast cooling rates cannot be realized. This way, structure formation in non-equilibrium situations can be investigated in the laboratory, once discussed to be relevant in Big-Bang theory.