Linking matrices in systems with Periodic Boundary Conditions

Using the Gauss linking number, we define a new measure of entanglement, the linking matrix, for a collection of closed or open chains in 3-space. Periodic Boundary Conditions (PBC) are often used in the simulation of physical systems of filaments. Using the periodic linking number, defined in [24], we define the periodic linking matrix to study entanglement of closed or open chains in systems employing PBC. We study the properties of the periodic linking matrix as a function of cell size. We provide analytical results concerning the eigenvalues of the periodic linking matrix and show that some of them are invariant of cell-size. linking matrix, linking number, periodic boundary conditions, entanglement 57M99,57M25,15B99,0072,00A69,68U20