Entanglement Entropy in a Triangular Billiard

The Schrödinger equation for a quantum particle in a two-dimensional triangular billiard can be written as the Helmholtz equation with a Dirichlet boundary condition. We numerically explore the quantum entanglement of the eigenfunctions of the triangle billiard and its relation to the irrationality of the triangular geometry. We also study the entanglement dynamics of the coherent state with its center chosen at the centroid of the different triangle configuration. Using the von Neumann entropy of entanglement, we quantify the quantum entanglement appearing in the eigenfunction of the triangular domain. We see a clear correspondence between the irrationality of the triangle and the average entanglement of the eigenfunctions. The entanglement dynamics of the coherent state shows a dependence on the geometry of the triangle. The effect of quantum squeezing on the coherent state is analyzed and it can be utilize to enhance or decrease the entanglement entropy in a triangular billiard.