Basic Theoretical Physics: A Concise Overview P39. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | Ginzburg-Landau Theory of Superconductivity 397 Similar to Lagrangian formalism in classical mechanics minimizing the free energy with respect to provides the following Euler-Langrange equation for the variation problem 1_ -inv - qeA 2 r a T - To p 2 . 0 . 2mff Minimizing with respect to does not give anything new only the complex conjugate result. Minimizing F with respect to A on the other hand leads to the Maxwell equation curl curl A xoj s since B p0 H curl A and thus curlH js . Solving equation for A 0 assuming spatially homogeneous states and neglecting higher terms one obtains for T To the trivial result 0 while for T 0 the non-trivial expression a2 I V T - T 2P results. In the first case the free energy is zero while in the second case it is given by F T V - To - T 2 . 4p On passing through To the heat capacity C d2F dT2 therefore changes discontinuously by an amount ac v aß. At T To a continuous phase change13 thus takes place as for the case of Bose-Einstein condensation in which the order parameter F increases smoothly from zero for T To to finite values for T To whereas the heat capacity increases discontinuously as mentioned. Two characteristic lengths result from the Ginzburg-Landau theory of superconductivity. These are a the so-called coherence length T of the order parameter and b the so-called penetration depth X T of the magnetic induction. 13 A discontinuous change of the specific heat is allowed by a continuous phase transition. It is only necessary that the order parameter changes continuously. 398 53 Applications I Fermions Bosons Condensation Phenomena One obtains the coherence length T for the density of Cooper pairs by assuming that ty ty0 Sty r where as above A 0 and ty0 y t t0 - t Using we obtain - 2 eff dx2 T - T0 3 0 2 5 0 which by assuming Sty r k ex leads to e T J 4meB I. V H2a To - T On the other hand one obtains the penetration depth X T of the magnetic field assuming A 0 and ty ty0. Thus .
