Elementary excitations and avalanches in the Coulomb ... - PhysioNet

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$J. Phys. A: Math. Gen., Vol. 9. No. 9,1976. Printed in Great Britain ...$

# of unstable long hops created (3D):M u =∫ Lr 04πr 2 dr∫ 1/r20g(ɛ)dɛ ∝ O(1)O(L)rdrGalton-Watson branching processS = tree size = λλ =1 p(S) ∼ S −3/2λ < 1 p(S) ∼ S −3/2 e −S/S c
Long hops explain why cutoff S c ∝ LS c ∼ number of successive events created bya hop that reaches the boundaryHence in 2D we expect S c ∼ log LAvalanche size distribution in 2D:p(S) in 2D10 0 0.60.4p(0) ∼ exp(−g0.20 log L)~ 1 / [ C log(L) ]030 60 100240LL= 30601202400 5 10 15 20 2510 -110 -210 -310 -410 -5Scharge insertionsqrt(2 π) λ (1-exp(-λ)) Y c3/2 p(Y)10 1 ( Y/Y c ) -3/2 exp(- Y/Y c )10 0Dipole-triggered avalanches in 2DL= 3060120240110 -110 -210 -310 -410 -5Y / Y cdipole insertionwith Y c = log(L/3)
Page 1 and 2: Elementary excitations andavalanche
Page 3 and 4: Classical electron glass model (Efr
Page 5 and 6: One-particle energy:ɛɛ i = ∑ j
Page 7 and 8: Dipole excitations:ω ij = ɛ j −
Page 9: Charge avalanches1. Find a local mi
Page 12 and 13: Infinite-range spin glass3D Coulomb
Page 14 and 15: Avalanches and nonlinear screeningB
Page 16 and 17: Avalanche size distribution for dip
Page 20: Infinite-range spin glass3D Coulomb
Page 23 and 24: Equilibrium finite temperature 1-DO
Page 25 and 26: Zero temperature 1-DOSL = 100L = 10
Page 27: conclusionsyessaturatedquadratic ga

Elementary excitations and avalanches in the Coulomb ... - PhysioNet

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