Calculating the Superconducting Superheating Field and Critical Wavelength Using Automatic Differentiation within Ginzburg-Landau Theory

For many physical systems the stability and equations of motion are derived by calculating variations of a free energy. We show how automatic differentiation simplifies the task of evaluating these variations while avoiding tedious calculations performed by hand or through symbolic computation. We illustrate its usefulness by recalculating the superconducting superheating field and critical wavelength of type-II superconductors within Ginzburg-Landau theory.