Conductance quantum

In a 1D wire, connecting two reservoirs of potential u_1 and u_2 adiabatically: The density of states is \frac{\mathrm{d}n}{\mathrm{d} \epsilon} = \frac{2}{hv} , where the factor 2 comes from electron spin degeneracy, h is the Planck constant, and v is the electron velocity. The voltage is: V = -\frac{(\mu_1 - \mu_2)}{e} , where e is the electron charge. The 1D current going across is the current density: j = -ev(\mu_1-\mu_2) \frac{\mathrm{d}n}{\mathrm{d} \epsilon} . This results in a quantized conductance: G_0 = \frac{I}{V} = \frac{j}{V} = \frac{2e^2}{h} . == Occurrence ==

Quantized conductance occurs in wires that are ballistic conductors, when the elastic mean free path is much larger than the length of the wire: l_{\rm el} \gg L . B. J. van Wees et al. first observed the effect in a point contact in 1988. Carbon nanotubes have quantized conductance independent of diameter. The quantum hall effect can be used to precisely measure the conductance quantum value. It also occurs in electrochemistry reactions and in association with the quantum capacitance defines the rate with which electrons are transferred between quantum chemical states as described by the quantum rate theory. == See also ==