Atomic inertial sensors constitute highly controllable and scalable platforms for precision measurements of inertial effects, particularly acceleration. In this talk, I will present and analyze a theoretical proposal for an atomtronic angular accelerometer based on an angularly ac?shaken ring lattice. I will show how supercurrents of ultracold atoms circulating in the ring can be harnessed to achieve high?precision measurements of angular acceleration.

In this system, a significant net atomic current emerges when the lattice driving frequency is tuned to integer fractions of the system’s Bloch frequency. These resonances give rise to directed transport, with the resulting supercurrents encoding information about the external angular acceleration.

Within the Bose–Hubbard model, I will discuss  two main regimes: the single-particle regime and the weakly interacting many-body regime. In the single-particle limit, I will demonstrate analytically that the resonance width scales inversely with the measurement time, thereby imposing a Fourier limited bound on the achievable precision in angular-acceleration estimation. By contrast, weak onsite interactions modify this behavior. Numerical simulations will show that interactions can lead to a pronounced sharpening of the resonances. As a result, the sensitivity to the angular acceleration can surpass the Fourier limited scaling of the non-interacting case, improving the measurement precision by several orders of magnitude.

We explore examples of Dirac operators on bounded domains exhibiting an interval of essential spectrum. In particular, we consider three-dimensional Dirac operators on Lipschitz domains with critical electrostatic and Lorentz scalar shell interactions supported on a compact smooth surface. Unlike typical bounded-domain settings where the spectrum is purely discrete, the criticality of these interactions can generate a nontrivial essential spectrum interval, whose position and length are explicitly controlled by the coupling constants and surface curvatures.

Based on joint work with J. Behrndt (TU Graz), M. Holzmann (TU Graz), and K. Pankrashkin (Univ. Oldenburg).

Higher dimensional abelian quantum double models have been shown to be well defined in any finite dimension and exhibit the characteristic behavior of SPT phases models. In this talk, we will introduce the formalism of these models in a pedagogical manner, focusing on the characterization of the topological ground state subspace and briefly presenting its classification scheme. We will discuss the connection of these models with pressing problems in condensed matter physics and quantum computation.

I will first show that for general 2d random ergodic one-body magnetic Schrödinger operators the bulk magnetization equals the total edge current at any temperature. Moreover, the celebrated bulk-edge correspondence between quantum transport indices will be obtained as a corollary of our result by imposing a gap condition and by taking a "zero temperature" limit. After that, I will show how to extend the equality of bulk magnetization and total edge current to lattice fermion systems with finite-range interactions satisfying local indistinguishability of the Gibbs state, a condition known to hold for sufficiently high temperatures. In the interacting framework, an important intermediate result is a new version of Bloch's theorem for two-dimensional systems, stating that persistent currents vanish in the bulk.

The talk is based on joint works with Horia Cornean, Jonas Lampart, Stefan Teufel and Tom Wessel.