Then, under the scaling relation µhα = ν rβ, the solution of the (scaled) coupled CTRW master (integral) equation, eq. (3), ph,r (x, t), weakly converges to the Green function of the fractional diffusion equation, u(x, t), for h → 0 and r → 0.
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Equations (2) and (5) imply that distances are scaled by αx = p¯h/M ωx, time by 1/ωx and energies, including Vb above, by ¯hωx, where M is the atomic mass, and ωx/2π is the harmonic frequency.
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I (0)) ˆ̺b,ph is the correlation function; τcorr is its typical scale.
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