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Suppose we had two metal plates separated by an Angstrom. Now, apply a voltage $V$ between the two metal plates. There will be a tunneling current $I$ between the metal plates.

Since $P=IV$, does that imply power is being dissipated by the system, even if the tunneling is elastic?

Some additional thoughts: Perhaps this is related to why there is still resistance in ballistic transport.

ChickenGod
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  • if it is quantum mechanical tunneling you are talking about energy should not be lost. have a look at http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html . – anna v Feb 15 '14 at 16:34
  • @annav Yes, I am talking about quantum mechanical tunneling. And yes, if the tunneling is elastic, electrons will tunnel from one state to another of the same energy. However, $P=IV$ indicates that energy will be lost at some point. – ChickenGod Feb 16 '14 at 06:29
  • can you give a link for P=IV ? I suspect it comes from classical considerations. Quantum mechanically there is no energy loss in the tunneling. There may be in the rest of the circuit which has to exist for a current to form and which is adequately described by classical formulae with resistances etc where the power will be lost.. – anna v Feb 16 '14 at 07:13

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