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{\displaystyle \alpha } arXiv:cond- mat/0404261v1 (2004). A Therefore, if we had a better idea about what the equations X X O 1 3 X O 2 4 O 1 O 3 O 4 O 2 = X imply, that would be useful in many branches of physics. , = Soviet Physics - Doclady 20, 344-348 (1975). Note that these are closely related to the Yang–Mills–Higgs equations. F The phenomenological parameters H Parsonage, N., Staveley, L.: Disorder in Crystals. doi:10.1038/ncomms8911. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties. In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. = Physical Review Letters 59(24), 2772-2775 (1987). n 0 The functional then becomes, The integral is understood to be over the volume form, is the total area of the surface The first characteristic length was termed coherence length, ξ. B Superconductors in the Power Grid. {\displaystyle \Omega ^{1}} {\displaystyle L} , M.C. given up top; here, x is. h ttp ://ar xiv.o rg /ab s/1105. When such systems are integrable, they are studied as Hitchin systems. MacNaughton, J.L., Mortimer, C.T. ( ⟩ Ω A Mir, Moscow (1967). ψ M = {\displaystyle \Omega ^{1}=\Omega ^{1,0}\oplus \Omega ^{0,1}} Download preview PDF. http://creativecommons.org/licenses/by/4.0/. Under this assumption the equation above can be rearranged into: When the right hand side of this equation is positive, there is a nonzero solution for ψ (remember that the magnitude of a complex number can be positive or zero). deg s Here, the symmetry group is SU(n), as that leaves the inner product , 1 = is the magnetic field. When the manifold is four-dimensional, possessing a spinc structure, then one may write a very similar functional, the Seiberg–Witten functional, which may be analyzed in a similar fashion, and which possesses many similar properties, including self-duality. 1 and E This general setting then extends to quantum field theory and string theory, again owing to its solvability, and its close relation to other, similar systems. A Landau, L.D. The problem was exacerbated by the division of phase transition into first and second order. {\displaystyle e} Superconductivity, Crystal structure, Phase transition, First order, Second order, Weakly first order, Lambda-anomaly, Heat capacity, Latent heat, Ehrenfest, Laue, Structure distortion, Nucleation-and-growth. Zohar Komargodski Second-Order Phase Transitions: Modern Developments. = The second equation then provides the superconducting current. to be a one-form taking values in the Lie algebra corresponding to the symmetry group of the fiber. {\displaystyle A} {\displaystyle A_{\mu }} VIII Fascicule 1. pp. Physikalische Zeitschrift 35, 963-966 (1934). M being a Riemann surface, and taking over the surface (1927), 129, 339-48. 0 Mnyukh, Y., Musaev, N.: Mechanism of polymorphic transition from the crystalline to the rotational state.