Dynamics of superfluids

Abstract

The Ginzburg Landau equation can also be used to study the dynam- ics of super uids apart from the superconductors.The GL equation is a non-linear equation. Some of the simplest solutions of GL equations for super uids consist of the tan hyperbolic function. Also we can use dif- ferent methods to nd the solution for this kind of di erential equation such as the method of separation of variables. By nding the cylindri- cally symmetric solutions for this equation something can be physically concluded about the geometry of the vortices in super uids.There must be a speci c reason as to why the vortices always appear to be formed in a hexagonal pattern rather than square or any other. This can be concluded by looking at the free energy equations of this system.