Second-order different ial equations are ubiquitous in physics\, but every once in a while there are special cases where the order of these equations may be reduced. One e xample of such a reduction is the quantum harmonic oscillator as solved by P. Dirac. Dirac introduced the annihilation and creation operators\, whic h permit solving of the second-order problem presented by the linear Schr& ouml\;dinger equation by reduction to a first-order linear equation. In th e context of superconductivity\, a system of non-linear second-order diffe rential equations describing vortex lines in superconductors may be reduce d to first-order at a particular value of the Ginzburg-Landau parameter. T his reduction can be achieved by two procedures. One approach uses an inge nious minimization of the Ginzburg-Landau free energy functional tailored to the presence of a topological defect (the Bogomol&rsquo\;nyi procedure) . The other uses the Ginzburg-Landau equations and operators analogous to Dirac&rsquo\;s annihilation and creation operators (the Sarma procedure). The Bogomol&rsquo\;nyi procedure leads to the famous Bogomol&rsquo\;nyi eq uations\, published in 1976. The Sarma procedure was never published in a journal but is hinted at in P. G. de Gennes&rsquo\;s 1966 classic Supercon ductivity of Metals and Alloys. \; \;We will show that\, in the pa rticular case of the vortex line\, the Sarma procedure recovers the Bogomo l&rsquo\;nyi equations and that the Sarma procedure is in fact more genera l\, as to be applicable it does not rely upon the presence of a topologica l defect.

\n DTSTART:20240905T193000Z LOCATION:Physics\, Room 338 SUMMARY:Sarma and Bogomol'nyi Equations in Superconductivity END:VEVENT END:VCALENDAR