A new real-space formulation of crystal properties in closed formReport as inadecuate

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Abstract : As a new approach to describe perfect crystal properties, the mathematical study of cyclic matrices initiated recently J. Physique 42 1981 903 by the author is pursued in the present article. A very natural formulation of vibrational, electronic, magnetic

. crystal properties is offered by calculating the elements of some functions of interatomic interaction matrices, whose dimensions are infinite. These functions can be handled by a drastic reduction of the matrix variable order, which is based on relations linking cyclic matrices and orthogonal polynomials. Exact expressions are obtained in the form of multiple integrals. They are valid for functions describing experimentally measured properties, any thermodynamic function, Green-s function, density of states, etc. Their derivation does not require a prior spectral analysis of the problem. A detailed study of the density of states is undertaken, and a simple closed expression is given for this quantity.

Keywords : crystal properties electronic density of states lattice dynamics matrix algebra

Author: Ph. Audit

Source: https://hal.archives-ouvertes.fr/


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