8.1 The Quantum Langevin Equation
131
Fig. 8.2 Contributions to Eq. 8.44 for ˜
F load
=
0. and ˜
λ=0.146, U(x)
=
U 0
2π
−sin
2π
L x
+
1
4 cos
4π
L x
, tilted slightly to the left
d ˜
v
d ˜
t
= − ˜
γ ˜
v − U ( ˜
x) − 0.5 ˜
λ
U ( ˜
x) +
F +
˜
x, ˜
t
(8.48)
We observe in Fig. 8.6a λ increases as k B T tends to zero (temperature), which means
quantum effects increase.
We usually use the following ratchet, lightly tilded to the right.
131
Fig. 8.2 Contributions to Eq. 8.44 for ˜
F load
=
0. and ˜
λ=0.146, U(x)
=
U 0
2π
−sin
2π
L x
+
1
4 cos
4π
L x
, tilted slightly to the left
d ˜
v
d ˜
t
= − ˜
γ ˜
v − U ( ˜
x) − 0.5 ˜
λ
U ( ˜
x) +
F +
˜
x, ˜
t
(8.48)
We observe in Fig. 8.6a λ increases as k B T tends to zero (temperature), which means
quantum effects increase.
We usually use the following ratchet, lightly tilded to the right.