The understanding of the fermionic sector of the world-volume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory like, for example, the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper, we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in the absence of fluxes. A non-zero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry.
The calculations of thermal expansion coefficients have been carried out using ab-initio molecular dynamics with a small cell containing only eight atoms that is a suitable calculation in size for materials design. Si, Ge, and GaP crystals were selected as the reference materials for comparison between calculation and experiment. The calculated lattice constants were in good agreement with experimental ones. The thermal expansion coefficients of three crystals were obtained from the temperature dependence of the lattice constants. There was reasonable agreement between the calculation and the experiment. Furthermore, even in use of the smaller cells containing two atoms for Ti, Cr, Fe, and four atoms for Al, Co, Ni crystals, the calculated thermal expansion coefficients were in good agreement with experiments. Our results proved firmly that there is a good possibility of obtaining the thermal expansion coefficients by ab-initio molecular dynamics even in use of a small cell for the calculations. #
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