AbstractSolving multiscale PDEs is difficult in high dimensional and/or convection dominant cases. The Lagrangian computation, interacting particle method, is shown to outperform solving PDEs directly (Eulerian). Examples include computing effective diffusivities, KPP front speed, and asymptotic transport properties in topological insulators. However the particle simulation takes long before co...
AbstractThis talk focuses on the simulation of fermionic systems on arbitrary graphs, including two-dimensional lattices. We start by examining the one-dimensional Jordan-Wigner transformation and its expansion to two-dimensional exact bosonization. This method is crucial for simulating fermions using emergent fermions in the ℤ2 toric code. We then discuss how fermionic observables and Pauli m...