Electric Dipole and Elastic charge eQSNS
literature
Electric field spectroscopy of material defects https://www.nature.com/articles/s41534-019-0224-1
https://web.physics.ucsb.edu/~martinisgroup/papers/Shalibo2010.pdf
https://en.wikipedia.org/wiki/Rayleigh_scattering#Of_sound_in_amorphous_solids
large variation of coupling constant - Caruzzo-Yu
QED-dipole moment
αQED=e2ℏc=d2QEDa2Bℏc
this is the definition of fine dipole moment depending on the length a between charges e.
The lengtha can be taken either as aB https://en.wikipedia.org/wiki/Bohr_radius or https://en.wikipedia.org/wiki/Classical_electron_radius
The dimensionality of dipole squared is d2=erg∗cm3
effective-QSNS charge is about the same as electric charge!!!!! .. or even numerically/definition-wise larger?
QED charge is e2=αQEDℏc, numerically e2∼25∗10−20erg∗cm
QSNS charge is e2QSNS=αQSNSρc2tξ4, because e2QSNSξ2=Pγ2ξ6=αQSNSρc2tξ6 (see below for dimensionality argument). The dipole moment and effective charge eQSNS are defined d2QSNS=e2QSNSξ2=[erg∗cm3]
Numerically, QSNS charge is e2QSNS=10−32(g/cm3)(4∗105cm/s)2(3∗10−7cm)4∼25∗10−19erg∗cm, where ξ∼30A=3∗10−7cm
- therefore e2QSNS∼10∗e2
imagine that there are no free charges, but only dipole interactions
- let us compare with fine coupling in low-T glasses
αQSNS=Pγ2ρc2t
where P=1erg∗cm3, γ=erg, and ρc2=erg/cm3
To write down explicit dipole moment, we need to introduce length ξ
ℏcξ=γ2ρc2t1ξ3, therefore ξ=γ√1ℏρc3t
ξ∼50A∼10∗aB
Dimensionally d2QSNS=erg∗cm3, the energy density P=[1erg∗cm3], and γ=erg, Therefore d2QSNS=Pγ2ξ6
compare d2QSNS and d2QED
this ratio d2QSNS/d2QED implicitly depends on the ratio aB/ξ
for QSNSs, for electric dipole and elastic dipole moments compare
e2a2B→Pγ2ξ6=αQSNSρc2tξ6
e2a2B∼(5∗10−10esu∗0.5∗10−8cm)2∼6∗10−36erg∗cm3
versus
αQSNSρc2tξ6∼4∗10−4(4∗105cm/s)2(5∗10−7cm)6∼800∗125∗10−36erg∗cm3∼105∗10−36erg∗cm3
- BIGGER d2QSNS!!!!! ... it feels strange
d2QSNS/d2QED∼104
do the same for electric dipole moment of LEEs
- electric and elastic energy per volume - just for intuition - comparable!!!
e2a4B→αQSNSρc2t
(5∗10−10esu)2(5∗10−8cm)4∼4∗1010erg/cm3 versus αQSNSρc2t∼0.6∗108erg/cm3
elastic energy is about 10−3 smaller than electric-charge-hydrogen-smoothered energy
analogies
a2Bℏc→ρc2tξ6
speculatively on the dimensionality basis ℏ→ρctξ4
ℏ=10−27erg∗s
ρctξ4→1(g/cm3)∗4∗105(cm/s)∗(5∗10−7)4∼25∗10−21erg∗s
just compare dimensionally ℏ→ρca4B
- ℏQSNS→ρctξ4∼10−20erg∗s
2∗4∗105∗(3∗10−7cm)4∼0.6∗10−20erg∗s