Entanglement Entropy in a Triangular Billiard

Abstract

Abstract: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.

Morphology of three-body quantum states from machine learning

“…Our choice provides us with a simple parametrization of triangles in terms of the mass ratio, κ = m I /m, where m I (m) is the mass of the impurity (fermions). Furthermore, it allows us to shed light on the problem of three particles in a ring with broken integrability [37][38][39].…”

Breakdown of separability due to confinement

“…Inside the boundary the potential behaves like the bidimensional harmonic oscillator, but in the billiard case, the particle has a free motion inside the triangular shaped domain. The brief review on the triangular billiard geometry problems is given, for example, in [31]. In this paper, we study four different shapes of the potential.…”