Talks

In this lecture I will cover the developments in the area which followed our work and finally lead Isett to the resolution of the Onsager conjecture. If time allows I will give a glimpse of the challenges that lie ahead if one would like to give a rigorous justification that some dissipative solutions of the Euler equations are indeed limit of classical solutions of Navier-Stokes.

Many physical phenomena may be modeled by first order symmetric hyperbolic equations with degenerate dissipative or diffusive terms. This is the case in gas dynamics, where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or damping (relaxation) term.
Such so-called partially dissipative or diffusive systems have been extensively studied by S .Kawashima in his PhD thesis from 1984. For a rather general class of systems he pointed out a simple necessary condition for the global existence of solutions in the vicinity of constant solutions.
This condition that is nowadays named (SK) condition has been revisited in a number of research works. In particular, K. Beauchard and E. Zuazua proposed in 2010 an explicit method for constructing a Lyapunov functional allowing to refine Kawashima’s results and to establish global existence results in some situations that were not covered before. Very recently, advances have been made by T. Crin-B...

The flow associated to a given smooth vector field $u(t,x)$ is well-defined, it is smooth, and it can be used to solve the classical linear PDEs associated to $u$, namely the transport and the continuity equations. The situation is substantially different when $u$ is not smooth (e.g. when $u$ is not Lipschitz continuous in the space variable, but only Sobolev or BV). Goal of the lecture is to provide an overview on classical and recent results about flow maps and PDEs associated to non-smooth vector fields.

In the recent resolution of the strong Onsager’s conjecture in L^3 framework, so-called wavelet-inspired Nash’s iteration has been developed. In this lecture, we will sketch this new method and provide the necessary background. The lecture will be based on our recent joint work with Matthew Novack.

* Introduction to resonant light matter interaction (coherent and incoherent scattering, Rabi oscillations, Mollow triplets) * Origin of antibunching in resonance fluorescence (L. Hanschke et al. Phys. Rev. Lett. 125, 170402 (2020)) * Doubly-dressed Mollow triplets (C. Gustin et al. Phys. Rev. Research 3, 013044 (2021) * Dynamic Mollow triplets from Janes-Cummins systems (K. Fischer et al. Nature Photonics 10, 163–166 (2016)) * Dynamic Mollow triplets from two-level systems (K. Boos et al. arXiv:2305.15827 (2023) – accepted at PRL)

.Scalar quantum field theories can possess metastable vacuum states which decay through thermal and quantum fluctuations. In space, the decay of the metastable vacuum proceeds through the creation and subsequent expansion of bubbles containing a new phase, which coalesce and eventually complete the phase transition. Vacuum decay is a non-perturbative and non-linear dynamical problem, making it the perfect candidate for quantum simulators. Understanding this process has phenomenological implications for early Universe cosmology, including observables such as a stochastic gravitational wave background, meaning there may be novel ways to use quantum simulators to make predictions for observational cosmology. In this talk I will first describe theoretical work developing observables for vacuum decay, including nucleation site correlation functions and bubble nucleation pre-cursors. I will then describe experimental efforts within the Quantum Simulators for Fundamental Physics consortium to develop analog quantum simulators of vacuum decay with cold atomic gasses. Such experiments will allow us to empirically test early Universe physics in tabletop experiments.