134
8 Quantum Ratchets
Fig. 8.6 (a)λ vs k B T , γ = 0.1, ¯
h = 1.; (b) λ vs γ, k B T = 1.E − 4, ¯
h = 1. The
functions and parameters dimensionless
where ν M = k B T / ¯
h is the first Matsmubara freqüency.
8.1.4.2 Classical Smoluchowski Range
ω 0 ¯
h
k B T
1. and k B T ¯
hγ
(8.52)
where ω 2
0 =
U (q 0 )
M , from the Brownian motion in the harmonic potential U(q) =
1
2 Mω 2
0 (q − q 0 ) 2
8.1.4.3 Quantum Range
γ ν M
(8.53)
8 Quantum Ratchets
Fig. 8.6 (a)λ vs k B T , γ = 0.1, ¯
h = 1.; (b) λ vs γ, k B T = 1.E − 4, ¯
h = 1. The
functions and parameters dimensionless
where ν M = k B T / ¯
h is the first Matsmubara freqüency.
8.1.4.2 Classical Smoluchowski Range
ω 0 ¯
h
k B T
1. and k B T ¯
hγ
(8.52)
where ω 2
0 =
U (q 0 )
M , from the Brownian motion in the harmonic potential U(q) =
1
2 Mω 2
0 (q − q 0 ) 2
8.1.4.3 Quantum Range
γ ν M
(8.53)