Theories of fundamental particles are tested against collider experiments by computing scattering predictions. The traditional Feynman diagram approach requires complicated integrals. Our method recursively constructs many-particle scattering results from few-particle ones, using basic calculus and combinatorics.
The interactions between consituents in quantum materials are hard to know exactly, and difficult to solve numerically. We incorporate random matrices to represent them and exploit their mathematical properties to facilitate computation.
Comparing the entanglement in two different quantum states is an important question. In general, quantum states are represented by a density matrix. They are big matrices, so such a description, despite being complete, can be unwieldly. Thus, we compute, from the density matrices, a single number measure. Such measure should faithfully reflect the property while being easy to compute, and for mixed-many body states is still elusive. We introduce a novel measure for this purpose, which bears meaning from quantum informational operation, that is not reflected in previous methods.