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Basic lengths in SNSs

length scales

  • inter-atomic distance is ainteratomic2.4A

The nearest neighbor distance is 0.235 nm which is about 5x of Bohr radius. And the diameter of a silicon atom is 2.35A (lattice size of Si is 5.4A)

  • medium-range order is ξ=Λ(c3sρ)1/21.6101012erg(131010)1/244 ˙A,

where Λ=10eV=1.61011erg

by matching energy scales of phonon and dipole interaction energy csξΛ2c2sρξ3

  • fundamental glasson length agl=2Λ2mgl2ρc2t

by matching energy scales of localised kinetic energy and dipole interaction energy 22mglξ2Λ2c2sρξ3

taking mgl=51026g, we get

agl2(1.61011erg)251026g(1026ergs)2(2g/cm3)(4105)280˙A

we get the mass scale mgl=51026g without any particular model