Regensburg 2010 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 27: CE: Poster Session

TT 27.49: Poster

Mittwoch, 24. März 2010, 14:00–18:00, Poster D1

Perturbative theory of isosbestic points — •Markus Greger, Marcus Kollar, and Dieter Vollhardt — Theoretische Physik III, Zentrum für elektronische Korrelationen und Magnetismus, Universität Augsburg

A family of non-monotonic curves, obtained by plotting a quantity f(x,y) as a function of one of its variables (say, x) for different values of y, will in general intersect, leading to crossing points of the curves. In physics, chemistry and biology the crossing of a family of curves is the rule rather than the exception. Sometimes these crossing points are found to be confined to a remarkably narrow region, or are even located at a single point, thus leading to a conspicuous feature often called isosbestic point. Here we consider a perturbative expansion in the variable y. For an exact isosbestic point x^⋆, the dependence of f(x,y) on y is then described by the first term of the expansion in y. For approximate isosbestic points higher order terms are responsible for the finite width of the crossing region. This approach describes approximate isosbestic points in various unrelated quantities such as the optical conductivity σ(ω,n) in the Falicov-Kimball model, the photoemission spectra A(ω,T) of VO₂/TiO₂, the reflectivity R(ω,T) of CaCu₃Ti₄O₁₂, and the Raman response χ″(ω,T) of HgBa₂CuO_4.16.