DOI

The spatial correlation functions of the thermal fluctuations in systems with smoothly varying structure are calculated by means of the WKB method. As a particular physical problem we consider the behavior of director fluctuations in cholesteric liquid crystals possessing one-dimensional spatial periodicity. The problem leads to the solution of set of two second order differential equations with periodic coefficients. It is shown that in this physical system there exist regions where the WKB approximation is not valid. The analysis of these regions is similar to that of the turning points in quantum mechanics. Contrary to standard approach in our problem the turning point has fourth-order singularity and only decaying solutions have physical sense. We find WKB solutions for normal modes of director fluctuations in cholesteric liquid crystals far from the turning point as well as in its vicinity. We obtain that two fluctuating modes interact in the vicinity of the turning point, but any of these modes does not produce another. The amplitudes of modes change in such a way the product of amplitudes is constant. As a result we obtain explicit expressions for spatial correlation function in cholesteric liquid crystals with the large pitch which are valid in the entire domain. Finally we discuss the use of the correlation function in light scattering experiments
Язык оригиналаанглийский
Страницы (с-по)2420-2446
Число страниц27
ЖурналJournal of Mathematical Physics
Том45
Номер выпуска6
DOI
СостояниеОпубликовано - 17 мая 2004

    Предметные области Scopus

  • Физика конденсатов
  • Математическая физика

ID: 39217223