Liquid Glass Transition. A unified theory from the two band by Toyoyuki Kitamura

By Toyoyuki Kitamura

A glass is disordered fabric like a viscous liquid and behaves automatically like an excellent. a tumbler is generally shaped by way of supercooling the viscous liquid speedy adequate to prevent crystallization, and the liquid-glass transition happens in diversified manners counting on the fabrics, their background, and the supercooling tactics, between different components. The glass transition in colloids, molecular structures, and polymers is studied all over the world. This booklet provides a unified concept of the liquid-glass transition at the foundation of the 2 band version from statistical quantum box idea linked to the temperature Green’s functionality strategy. it's firmly unique in its method and should be of curiosity to researchers and scholars focusing on the glass transition around the actual sciences.

  • Examines key theoretical difficulties of the liquid-glass transition and similar phenomena
  • Clarifies the mechanism and the framework of the liquid-glass transition

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1 The Limitations of the Microscopic Classical Theory and the Roles of Quantum Statistics We have approached to the unified theory of the liquid–glass transition from the microscopic classical theory. Since the liquid–glass transition are prepared in the liquid state, sound, and the extra bubbles of intra-band and inter-band particle-hole pairs not constituting sound and phonons play an essential role in the liquid–glass transition. However, the microscopic classical theory of sound is only valid at higher temperatures β ω < 1 and in the long wavelength regime.

We show an example in the next section. 2 The Fock Space In order to construct quantum field theory countable, we consider the following subset denoted by [0]-set with a finite number of particles: [0]-set = {|n 1 , n 2 , . . ; n i = finite}. 7) i In actual experiments, only a finite number of quanta is excited, although the number can be arbitrally large. Therefore [0]-set is sufficient for actual physical processes. The [0]-set does not contain infinite states which had been in the original set {|n 1 , n 2 , .

Now we investigate the physical meaning of Eq. 17) [2]. 19) say that − 1 2 mn 1 2 δmn V (0) = mn M 2 M [−δmn V (0) + V (Rm − Rn )] = 2 M = 2 ωq 2 ηq† ηq , q ωq2 (1 + βV (q))ηq† ηq q 2 † ωsq ηq ηq . q Judging from the unified theory of the liquid–glass transition explained in Introduction, we can conclude that ωq is an elementary excitation associated with the intra-band particle-hole pairs, ηq and ηq† . Thus we can regard ωq as the frequencies of the bubbles of intra-band particle-hole pairs. As explained in Introduction, the sound wave ωsq is formed as the sum of an infinite series of interacting bubbles of intra-band particlehole pairs.

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