Classical and Quantum Creep in Disordered Solids

1
What are theorists most proud of? My answer
Universality
Depinning T! 0 v (E-Ec) ?, Tgt0 v T
?/? ? (E-Ec)? trel ?z ?/(z-?)1/(2-?)?
Non-equilibrium exponents universal ?0 Ec,
size of critical region non-universal High v
corrections follow from this
Creep v v0 exp-(E0/E) ?
?(D-22?e)/(2-?e) universal, Equlibrium
exponents (Bragg glass ?e0) v0,
E0.. non-universal
Works for domain walls, FLL, dislocation lines,
CDW?
2
Example Creep of Magnetic Domain Wall
D1, ?2/3 (exact), ?D-22?
1/3 ??/(2-?)1/4 Lemerle et al. 1998
Other examples Dislocation in solids
Flux lines insuperconductors
3
What are the assumptions?

• 1. ?(x)?0(1Q-1r ?)?1cos(Qx?(x))
  ?1gt0 everywhere ! Keep only ?1 term
• 
  ?
  single valued, no dislocations
• 2. H s dDx p2/2m c(r ?)2 ?i v(x-Ri)?(x)
  v(x) short ranged
• 3. If Coulomb interaction and anisotropy
  important
• 
  ck2! ck2c?k?2cdip(k??/a0)2/(1k2?2)
• changes critical dimension to D3, exponents
  trivial apart from logarithmic corrections
• 4. neglect quantum fluctuations, probably OK
• 5. Weak pinning (but also strong pinning shows
  asymptotically the same scaling behavior)
• Ideal, random distribution of pinning
  centers (no correlations!)
• Strong pinning changes parameter dependence
  of Ec,
• 6. L gtgt LLarkin n-1/(4-d), not always true
  in all directions, LltLLarkin no depinning
  transition
• 7. Overdamped equation of motion (no inertia,
  will die out, but cross-over effects?
• Generation of friction constant ? on
  intermediate scales )