Transport is the defining property of states of matter, but often the most difficult to understand. Strongly interacting Fermi gases are especially challenging, despite their ubiquitous presence across many fields of physics, from atomic nuclei to high-temperature superconductors and neutron stars. Experiments on ultracold fermionic atoms allow the direct measurement of transport properties in ideal model systems where the Hamiltonian is precisely known, while transport properties are difficult to calculate theoretically. In this talk I will present our experiments on two systems: The unitary Fermi gas, where interactions are tuned to be as strong as quantum mechanics allows, and the Fermi-Hubbard lattice gas, believed to hold the key for our understanding of high-temperature superconductivity. Locally resolved sound and heat transport can distinguish superfluid and normal flow regimes in the unitary gas. Our observation of spin transport in the Fermi-Hubbard system reveals the mechanism governing quantum magnetism.
The trajectories of diffusion processes are continuous but nondifferentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only events with nonzero probability are measurable. We bridge this gap by considering the probability of diffusive trajectories to remain within a tube of small but finite radius around a smooth path. This probability can be measured in experiment, via the rate at which trajectories exit the tube for the first time, thereby establishing a link between path probabilities and physical observables. In my talk I will show how this link can be used to both measure ratios of path probabilities, and to extend the theoretical stochastic action from individual paths to tubes.
Coherent structures have a strong impact on transport and mixing processes in fluids flows. Their computational study has received considerable scientific interest for the past two decades, in particular in the context of atmospheric and oceanic flows. From a probabilistic point of view, coherent sets are regular regions in the physical domain of the flow that move about with minimal dispersion. Coherent sets can be efficiently identified via leading eigenvectors of transfer operators or by using trajectory-based spectral clustering methods. We will review these approaches and apply them to a number of example systems such as the Bickley jet and the Antarctic polar vortex.
Many systems in nature, e.g. atoms, molecules and planetary motion, can be described as Hamiltonian systems. In such systems, the transport between different regions of phase space determines some of their most important properties like the stability of the solar system and the rate of chemical reactions. While the transport in lower-dimensional systems with two degrees of freedom is well understood, much less is known for the higher-dimensional case. A central new feature in higher-dimensional systems are transport phenomena due to resonance channels. In this thesis, we clarify the complex geometry of resonance channels in phase space and identify a turnstile mechanism that dominates the transport out of such channels. To this end, we consider the coupled standard map for numerical investigations as it is a generic example for 4d symplectic maps. At first, we visualize resonance channels in phase space revealing their highly non-trivial geometry. Secondly, we study the transport away from such channels. This is governed by families of hyperbolic 1D-tori and their stable and unstable manifolds. We provide an approach to measure the volume of a turnstile in higher dimensions as well as the corresponding transport. From the very good agreement of the two measurements we conclude that these structures are a suitable generalization of the well-known 2d turnstile mechanism to higher dimensions.
Many body localization allows quantum systems to evade thermalization owing to the emergence of extensive number of local conserved quantities. Many-body localized (MBL) systems exhibit universal dynamics, qualitatively distinct from dynamics in ergodic systems. Despite being subject of intense theoretical and experimental studies, many aspects of MBL remain to be understood. In this talk, after reviewing the basic properties of MBL phase, I will focus on recent progress in understanding the theory of MBL transition and on the issue of existence of the many-body mobility edges. I will conclude with an overview of open questions and promising methods that may enable a further progress in understanding of MBL.
Deep learning is very powerful at a variety of tasks, including self-driving cars and playing go beyond human level. Despite these engineering successes, why deep learning works remains unclear; a question with many facets. I will discuss two of them: (i) Deep learning is a fitting procedure, achieved by defining a loss function which is high when data are poorly fitted. Learning corresponds to a descent in the loss landscape. Why isn’t it stuck in bad local minima, as occurs when cooling glassy systems in physics? What is the geometry of the loss landscape? (ii) in recent years it has been realised that deep learning works best in the over-parametrised regime, where the number of fitting parameters is much larger than the number of data to be fitted, contrarily to intuition and to usual views in statistics. I will propose a resolution of these two problems, based on both an analogy with the energy landscape of repulsive particles and an analysis of asymptotically wide nets.