Current Ratcheting

Figure 1-6 Unrestrained Current Ratcheting, and Ways to Prevent It...

However, in many cases the fluctuating systems of interest are far from thermal equilibrium. Examples include optical bistable devices [45], lasers [23,46], pattern forming systems [47], trapped electrons that display bistability and switching in a strong periodic field [48-50], and spatially periodic systems (ratchets) that display a unidirectional current when driven away from thermal equilibrium [51-56]. 

A not-trivial ratchet effect can be observed when the injected charge density is voltage-independent, EL/R = Ep eV/2. Symmetry considerations require an asymmetric U (x) for a non-vanishing ratchet current in this case. Also an electron interaction must be present. Indeed, for free particles the reflection coefficient R(E) is independent of the electron propagation direction [14] and hence I(V) = —/(—V). 

Now we can substitute the renormalized potential U = U + W for U in Eq. (2). The Fourier component W2kF is different for the opposite voltage signs. Hence, we obtain the asymmetric part of the I — V characteristics /r eU3 eV i9 2/(hEp). The ratchet effect is strongest for g —> 0 when the ratchet current grows as the voltage decreases. 

The above Hartree-Fock argument provides a qualitatively correct picture at small g but underestimates fluctuations in Luttinger liquids. As shown below, the ratchet current growth at small voltages differs from our estimate ... 

We use the bosonization technique [17] to calculate the ratchet current. After an appropriate rescaling of the time variable, the system can be described by the action [13]... 

If all ak = 0 then the ratchet current is zero. Indeed, at ak = 0 the action (3) is invariant under the transformation —> — —V while the current operator (4) changes its sign. As discussed above, for an asymmetric potential we expect a2 0. Then a ratchet current Ir emerges in the order U2k r. Before the calculation of Ir let us determine its voltage... 

This expression becomes 0 at g = 1/2. We also get a zero ratchet current for non-interacting electrons, g = 1, because the Hamiltonian (1) is quadratic in Fermi-operators in the non-interacting case and hence no operators which backscatter more than one electron can appear, = 0. 

At small g the ratchet current (8) is proportional to a negative power of the voltage. This means an unusual behavior the dc response to an ac voltage grows as the ac voltage decreases. 

For g > 1/3 and V > V the contribution (9) always exceeds (8). At g < 1/3 the current (9) is greater than (8) above a threshold voltage that depends on U and g. As we already discussed, Ir (8) is comparable with the total current I(V) e2V/h at small g near the border of the perturbatively accessible region UV9 l/E9F < 1. On the other hand, Eq. (9) provides only a small correction to the total current for any g. Still a repulsive interaction of any strength enhances the ratchet effect as seen from the comparison of the current (9) for g < 1 and for the non-interacting case g = 1. 

In conclusion, we have found the ratchet current for strong and weak asymmetric potentials. It exhibits a set of universal power dependencies on the voltage and can grow as the voltage decreases. In Ref. [25] our analysis was extended to include the electron spin. This leads to a complicated phase diagram with several qualitatively different transport regimes for different interaction strengths. 

The applied voltage renormalizes other terms in the action too (for example, the Luttinger parameter g). Power counting shows that some of them could also give rise to ratchet current contributions of the order of U2V29 lns V, s = const. 

Currently the evidence does not strongly favor either possibility for hybrid fitness selection on pyramided traits such as alkaloids, or Muller s ratchet. It seems likely that both of these forces may be operative separately in some circumstances, and together in others. 

The problem was solved (2, 7) by splitting a straight horizontal platinum electrode into a vertical array with each member attached to a diode and then onto a common bus (hence named diode isolated electrodes). A diode can be thought of as an electrical ratchet because it confines electrical current to unidirectional flow. This new electrode design permits more than one electrode pair to coexist simultaneously in the same conductive media without any appreciable interaction. 

From the analyses of these tests a modification of the ratcheting laws in die case of very low primary stress loadings was proposed. Furthemore a method based on elastic calculation was also proposed. This method is currently being validated on complex structrures and loadings. 

Traditionally, efficiency of molecular motors has been studied within ratchet models where the motor undergoes a continuous motion in a periodic potential that depends on the current chemical. Dissipation then involves both the continuous degree of freedom and the discrete switching of the potential. 

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