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

#### dRic2

Gold Member
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:

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

Last edited:
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#### dRic2

Gold Member
Yes, this is called Bloch oscillations.
Thanks! Does the electron lose energy due to radiation emission ?

#### fluidistic

Gold Member
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

Gold Member
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

Gold Member
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

Gold Member
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

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

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