The Glasses Transition and Low Energy Excitations in Supercooled Metallic Liquid and Glasses
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I. Kanazawa
Department of Physics, Tokyo Gakugei University, Koganei-shi, Tokyo 184-8501, Japan ABSTRACT
We have introduced the theory of three-dimensional supercooled metallic liquids and glasses, which is based on the gauge invariant Lagrangian with spontaneous breaking, and discussed the viscosity of the three-dimensional supercooled metallic liquids. On the basis of the present theoretical formula, a qualitative picture of low energy excitations (the boson peak) is proposed. INTRODUCTION
For understanding the dynamics of supercooled liquids and the structural glass transition, we must study the short-range structures of the supercooled liquids and amorphous solids. There exists an important development in studies of the structures of supercooled liquid and glasses. Based on an important idea of Kleman and Sadoc [1], it has been proposed that the parameter (r; u) in two-dimensional and three-dimensional metallic glasses is speci ed by rigid-body rotation, which are related to gauge elds of SO(3) symmetry for S 2 and SO(4) symmetry for S 3 , respectively [2-4]. Extending the Sethna-Sachdev-Nelson formula [2-4], the present author [5-10] has proposed a theoretical formula based on the gauge-invariant Lagrangian density with spontaneous breaking in the two-dimensional metallic liquid and glass system, and introduced order parameter, which identi es the two-dimensional glass phase, by using the topological number of the frozen hedgehog-like soliton. Recently Kivelson et. al. [11, 12] present an interesting theoretical approach, which is refered as the frustration-limited domain (FLD) theory. In this theory, long-range interaction in Coulmbic form plays an important role in the properties of supercooled liquids. In this study, we will introduce a theoretical formula based on the gauge-invariant Lagrangian density with spontaneous breaking in three-dimensional metallic glass system, and present qualitative discussion of the viscosity of the three-dimensional supercooled metallic liquids. In addition, we will discuss a qualitative picture of low energy excitation (the boson peak) in glasses and supercooled liquids. THE MODEL FOR THREE-DIMENSIONAL METALLIC GLASSES
Now, we shall introduce a eld-theoretical model to treat three-dimensional liquids and glasses by using excited clusters (solitions). It has been proposed that the parameter (t; r; u) = (t; x; y; z; u) in three-dimensional liquids and glasses is speci ed by the rotation, which is related to the gauge elds of Aa for SO(4) symmetry for S3 [4, 13]. It has been required that the curvature can be represented by using a component, u, in the other-axis direction, when the three spatial dimensional axis are x, y and z ones. It is L12.5.1
preferable that we think of the anomalous density uctuation in the three-dimensional liquids as the hedgehog-like uctuation (cluster), taking account of the curvature. We adopt the parameter (r; u) a (a = 1; 2; 3; 4), which is similar to that in the Sachdev and Nelson model [4, 13]. The SO(4) quadruplet elds, Aa , are sp
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