I Periodic electron motion in a perfect conductor using a semiclassical model

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dRic2

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Summary
Imagine to have a perfect conductor, i.e. no impurities and no thermal motion (0K)
According to the semiclassical approximation, in response to a constant electric field I would get a periodic motion of the electron, like this:
Schermata 2019-09-02 alle 17.28.01.png

The sinusoidal type function is the velocity, while the function that goes to infinity is the effective mass. Thus I was wondering, since ##v## also gets negative values, does it means that an electron oscillates back and forth ?

Thanks,
Ric
 
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fluidistic

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Thanks! Does the electron lose energy due to radiation emission ?
Good question. I think not, because radiation is a surface phenomenon while we are considering a perfect crystal (and at 0 K), i.e. a bulk. But then it's very strange, because we have a time varying current (AC), but no radiation. I'm not sure what's going on.
 

dRic2

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Good question. I think not, because radiation is a surface phenomenon while we are considering a perfect crystal (and at 0 K), i.e. a bulk. But then it's very strange, because we have a time varying current (AC), but no radiation. I'm not sure what's going on.
That's reasonable. At least it is the only think I can think of... I am dumber than usual when it comes to radiation, but assuming that there is a continuous exchange of radiation between electrons in the bulk, wouldn't you expect a more complicated motion instead of simple oscillations ?
 

fluidistic

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That's reasonable. At least it is the only think I can think of... I am dumber than usual when it comes to radiation, but assuming that there is a continuous exchange of radiation between electrons in the bulk, wouldn't you expect a more complicated motion instead of simple oscillations ?
Yeah for sure. For one, Bloch oscillations are derived from the idependant electrons assumption.
 

dRic2

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Yeah for sure. For one, Bloch oscillations are derived from the idependant electrons assumption.
Then I find very surprising that they have been detected experimentally 😯😯
 

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