Pair correlation

Analytical expressions for the anharmonic effective potential, local force constant, Displacement-displacement Correlation Function (DCF) CR and Debye-Waller factor described by the Mean Square Relative Displacement (MSRD) σ2 and by the Mean Square Displacement (MSD) u2of bcc crystals in the X-ray Absorption Fine Structure (XAFS) have been derived. The effective interatomic potential of the system has been considered by taking into account the influences of nearest atomic neighbors, and it contains the Morse potential characterizing the interaction of each pair of atoms.

8p 12120609 01-06-2020 13 2   Download

Under explicit diophantine conditions on (α, β) ∈ R2 , we prove that the local two-point correlations of the sequence given by the values (m − α)2 + (n−β)2 , with (m, n) ∈ Z2 , are those of a Poisson process. This partly confirms a conjecture of Berry and Tabor [2] on spectral statistics of quantized integrable systems, and also establishes a particular case of the quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms of signature (2,2). The proof uses theta sums and Ratner’s classification of measures invariant under unipotent flows. ...

54p tuanloccuoi 04-01-2013 56 8   Download