Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recursion formulas for nonlinear density fluctuations near the glass
  transition   The time-convolutionless mode-coupling (TMCT) equation for the intermediate
scattering function $f_{\alpha}(q,t)$ derived recently by the present author is
transformed into a simple nonlinear recursion formula for a generating function
$\Omega_{\alpha}(\bm{q},t)(=-\ln[f_{\alpha}(q,t)]/q^2)$, where $\alpha=c$
stands for a collective case and $\alpha=s$ for a self case. By employing the
same simplification on the nonlinear memory function as that proposed by the
mode-coupling theory (MCT), the simplified asymptotic recursion formula is then
derived and is numerically analyzed for different temperatures under the
initial conditions obtained from the simulation. In a liquid state the
numerical results are shown to recover the simulation results well. Although
they can describe the simulation results well in the $\beta$-relaxation stage
even for lower temperatures, they do not agree with those in the so-called
$\alpha$-relaxation stage because of the simplified model. The coupling
parameter $\lambda^{(\alpha)}$ dependence of the Debye-Waller factor
$f_{\alpha}$ is also discussed. The critical point is found as
$\lambda_c^{(c)}=2e(\simeq 5.43656)$ and $f_c=e^{-1/2}(\simeq 0.60653)$, while
MCT gives $\lambda_c^{(c)}=4.0$ and $f_c=1/2$. Then, the critical temperature
$T_c$ is shown to be definitely lower than that predicted by MCT. Thus, it is
emphasized that the present theory can improve the high $T_c$ problem appeared
in MCT. The time evolution of the memory function and that of the diffusion
coefficient are also investigated within asymptotic formulas.

17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org