Statistical-Mechanical Theory of Nonlinear Density Fluctuations near the Glass Transition
* SPEAKERS
Name
Affiliation
E-mail
Michio Tokuyam
Tohoku University
tokuyama(at)tagen.tohoku.ac.jp
* HOST(Applicant)
Name
Affiliation
E-mail
YongSeok Jho
APCTP
ysjho(at)apctp.org
* DATE / TIME
2013-11-04, 4PM
* PLACE
512 Seminar Room
* ABSTRACT
The Tokuyama-Mori type projection-operator method is employed to study the dynamics of nonlinear density fluctuations near the glass transition. A linear non-Markov time-convolutionless equation for the scattering function Fα(q, t) is first derived from the Newton equation with the memory function ψα(q, t), where α = c for the coherent-intermediate scattering function and s for the selfintermediate scattering function. In order to calculate ψα(q, t), the Mori type projection-operator method is then used and a linear non-Markov time-convolution equation for ψα(q, t) is derived with the memory function ϕα(q, t). In order to calculate ϕα(q, t), the same binary approximation as that used in the modecoupling theory (MCT) is also employed and hence ϕα(q, t) is shown to be identical with that obtained by MCT. Thus, the coupled equations are finally derived to calculate the scattering functions, which are quite different from the so-called ideal MCT equation. The most important difference between the present theory and MCT appears in the Debye-Waller factor fα(q). In MCT it is given by fα(q) = Γα(q)/(Γα(q) + 1), where Γα(q) is the long-time limit of the memory function ϕα(q, t). On the other hand, in the present theory it is given by fα(q) = exp[−1/Γα(q)]. Thus, it is expected that the critical temperature Tc of the present theory would be much lower than that of MCT. The other differences are also discussed.
