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The Lorentz force on a charged particle moving in a magnetic field leads to the unique topological features of quantum Hall systems, including precisely quantized Hall conductance, topologically protected edge [...], Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties (1-5). Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science (6-8). Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip (9). This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock-Darwin Hamiltonian for photons in a magnetic field and harmonic trap (10). Using spatial- and energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit (10,11), we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen-Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space (12-15). This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids (16,17) and direct detection of anyons (18,19).

Aiming at a micromagnetic model that describes the macroscopic material behavior starting from microstructural features, there is a need for efficient time stepping schemes for the integration of Landau-Lifshitz-equation in material samples with dimensions of order [micro]m. This paper presents two related semianalytical time schemes. The time stepping algorithms are compared with other explicit time stepping schemes. Here, memory efficiency, time efficiency, convergence, and precision are checked. Further, special attention goes to 1) preservation of the magnetization magnitude in each FD cell; 2) a nonincrease of the free energy when applying a constant field; and 3) conservation of the systems free energy in the case of zero damping. Index Terms--Hysteresis, Landau-Lifshitz equation, micromagnetics, semianalytical integration.