Search Talks

In these two lectures we will go over some applications of nonlinear algebra to physics. In the first lecture we will take a look at the CHY scattering equations in order to see what algebraic statistics and theoretical physics have in common. In the second lecture, we will consider a classical algebraic variety, the Grassmannian. We will discuss its basic properties and see several contexts in which the Grassmannian appears in positive geometry and physics.

Scattering amplitudes in N=4 supersymmetric Yang-Mills theory can be computed using the BCFW recursion. There are many ways of running the recursion and hence many formulas for a single amplitude. The amplituhedron, defined by Arkani-Hamed and Trnka, is a remarkable geometric object which encodes N=4 SYM amplitudes and their many formulas. I will give an introduction to the (tree-level) amplituhedron and the mathematics behind it, such as the positive Grassmannian. Time permitting, I will discuss recent developments involving the structure of the amplituhedron, such as the surprising "cluster adjacency" phenomenon.

The question of the long-time behavior of quantum trajectories has been recently solved in the finite-dimensional case. In infinite dimension, the problem is still open. In this talk, we consider the particular model of the "one-atom maser," an infinite-dimensional system with many applications in quantum mechanics. We completely describe its long-time behavior by comparing it with a classical birth-and-death process. This is a joint work with T. Benoist and L. Bruneau.

Hundred years ago Stern and Gerlach demonstrated that spin-1/2 particles moving through a very high magnetic field gradient showed spin-path entanglement. Here, we show there that one can describe the emergence of the spin state and path variable’s entanglement as a dynamical feature in Stern-Gerlach experiments using open quantum system approach. This novel approach also gives broadening of the spots on the detector as well as the collapse of the wavefunction.

Reference: 

Das, G., & Bhattacharyya, R. (2024). Irreversibility of a Stern-Gerlach experiment. Physical Review A, 110(6), 062211. (DOI: https://doi.org/10.1103/PhysRevA.110.062211)