What are theorists most proud of? My answer: Universality What are theorists most proud of? My answer: Universality

Creep: v» v0 exp{-(E0/E) }

(D-2+2e)/(2-e) universal,

Equlibrium exponents (Bragg glass: e=0)

v0, E0.. non-universal

Depinning:

T! 0 v» (E-Ec) T>0 : v» T /

» (E-Ec) trel» z

(z-)=1/(2-)=

Non-equilibrium exponents universal =0

Ec, size of critical region non-universalHigh v corrections follow from this

Works for domain walls,FLL, dislocation lines, CDW?

Example: Example: Creep of Magnetic Domain WallCreep of Magnetic Domain Wall

D=1, =2/3 (exact), =D-2+2= 1/3

=/(2-)=1/4

Lemerle et al. 1998

Other examples: Dislocation in solids Flux lines insuperconductors

What are the assumptions?What are the assumptions?

1. (x)=0(1+Q-1r )+1cos(Qx+(x)) 1>0 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! c||k||2+c?k?

2+cdip(k?/a0)2/(1+k22) changes critical dimension to D=3, 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 >> LLarkin» n-1/(4-d), not always true in all directions, L<LLarkin no depinning transition

7. Overdamped equation of motion (no inertia, will die out, but cross-over effects? Generation of friction constant on intermediate scales ) / t = - H/ + f +(x,t) homogeneous driving force f» E

8. Statistical tilt symmetry, valid on small scales only for v(x)» v (x)

Problem: too many details ! parameters any theory works. (Fitting an experiment is not a proof that the theory is correct).