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8 Quantum Ratchets
Fig. 8.8 Representation of Fig. 8.7 for U(x,t) in 3 dimensions
Fig. 8.9 (a) Poincaré map v
(velocity) vs x, obtained from
Eqs. 8.61, Program8.1b,
under quantum range,
N=2E5, NR=1 γ ν M ,
γ = 0.1, k B T = 1.E − 4,
¯
h = 1., M = 1.,
dt = 1.E − 4,
E 1 = 1.6, E 2 = 2., ω = 1.
θ = π , functions and
parameters are dimensionless.
(b) Idem. with v and x as a
function of time