single electron circuits connected to antennas and radiation pattern

[CopperCone]

So if you run an antenna at a very low current, like less then attoamps so you have single charges going through it, does its radiation pattern change? I think the physics term would be single electron circuit (likely made possible with something like CNT or Graphene)

Would there be a difference in isotropic vs directional (horn) antennas?

Since the horn restrictions motion in a particular direction, I expect there to be more chaos (it will be more sensitive to initial conditions due to the restriction of motion). I don't know what the physics word for this is (not familiar with chaos mathematics) but it seems kind of like a intuition I have. The vibration caused by minimum operating temperature would be more focused in the launcher section of a horn then in something like a monopole right?...

Am I wrong?

If you do single charges into a isotropic or horn antenna, is the randomness of emission the same (is it even random in a horn?), could they be used as random number generators if the right receiving antennas are setup far away as not to interact?

How does temperature factor into this?

I'm imaging this from the prospective of a special universe made just to house a perfect generator and some antennas. 

[Nerull]

You never get single electrons flowing through a conductor that isn't atom sized, so I'm not sure that way of thinking of it makes any sense. Electrons flow through a conductor like a giant conga line, a single electron circuit lets you move the line one electron at a time, not send one electron through the whole circuit.

Single electron circuit elements typically need to be operated near absolute zero so your temperature effects will be rather controlled....

[ejeffrey]

So if you run an antenna at a very low current, like less then attoamps so you have single charges going through it, does its radiation pattern change?

Basically no.  Within a metal conductor you don't really see the effect of discrete charges. 

How does temperature factor into this?

Well, if you have very tiny signals, thermal noise may be larger than your signal.

[T3sl4co1l]

The antenna is the boundary condition, and the E&M equations are solving Schrödinger's equation for a massless particle (the photon).

As noted, it is meaningless to speak of antennas (whether made of conductive, permeable or permittable materials) with few electrons, because these are necessarily bulk materials in thermodynamic equilibrium.

You could have a different kind of potential, like a gravitational well (which is agnostic of the material within -- in the extreme case, a black hole's contents are unknowable*), of course the only modes this introduces for photons is scattering or absorption.

*Except that the contents appear on its surface, and are subject to quantum tunneling.  Perhaps using black holes as an example is a bad idea.

A "single-electron antenna" would literally be a hydrogen atom, in which case rather than having a bandwidth defined by boundary conditions, it is determined by quantized energy levels.

This is not an interesting case.

A more interesting case occurs on the boundary of molecular energies, in the submillimeter to infrared band, where conductors stop being conductors as we know it.  Structures can still be made of electron-dense materials, to create useful boundary conditions (antennas, waveguides, semiconductor sources and detectors..), but they are much more difficult to simulate, formulate and fabricate.

Tim

[CopperCone]

So like whats the minimum current flow to connect to something if you say it does not make sense?

Since we can measure attoamps in dc like why does rf have a break down?

I only imagined a low current so your surrounding antennas can get a good idea of which direction which rf photon went. Its to help understand isotropic radiators and radiators in general.

Hydrogen acting as an antenna is a maser i think? I meant like a dipole connected to some kinda funky signal generator. I imagine a normal antenna at some power level just generating so much guff that it looks like a field or density smear.. Or instrad of reducing current we can slow down time.

It wont be the same effect as very low current cuz i think the electrons will interact with eachother but it might help. Like a transient analysis of an antenna.

[TheUnnamedNewbie]

So let us do some math - how narrow a bandwidth would we need to look at to even see that signal?

Let us take a 75 ohm antenna impedance. Now let us assume say 1 fA of current RMS for a sine wave. That would translate to 75 fV RMS, which in turn would be \$75 \cdot 10^{-30}\$ Watts of power. Turn that into say dBm and we get somewhere in the ballpark of -270 dBm.

Thermal noise power can be shown to be equal to \$ -174 \text{dBm} + 10 \log (\text{BW})\$ at room temperature. In order to measure our signal we would need to have a noise floor lower than that, or \$ -174 \text{dBm} + 10 \log (\text{BW}) \leq -270\$. That means that our measurement bandwidth must be narrower than \$10^{-10}\$ Hz.

[AG6QR]

It may be worth reviewing the Feynman Lectures on Quantum Mechanics, especially regarding the dual slit experiment.  One of the things which the experiments proved is that even a single electron will behave as a wave, going through both slits and creating a pattern that interferes with itself, as long as you don't try to observe the single electron and localize it to one slit or the other.  The wave nature of electrons doesn't change based on how many or how few of them are present.

[CopperCone]

Ok that calculation rules out practical application as a noisesource i think. You would need something that is not know to exist currently to make some kind of measurement (and curent physics laws make it hard to imagine)

I need to review single electrom partical wave duality i never studied or did that experiment.

I guess the wave nature does not change. But what governs which direction the wave will come out of? Theoretically unmeasued. Minor surface impedance variations due to temperature?

[ejeffrey]

So like whats the minimum current flow to connect to something if you say it does not make sense?

There is no minimum current.  Electrons in a metal behave basically like a continuous medium almost all the time, even at very low currents, such that for example each "cycle" represents less than 1 electron charge movement. 

Rather than an antenna, just think of a capacitor.  You can have a net charge of .1 electron on a capacitor plate.  This is possible because the metal plates as well as the wires leading up to them and everything else is filled with ~10^23 electrons balancing 10^23 protons, and the electrons are all moving around randomly.  The "charging" of the plate is just a slight redistribution of those electrons so the net effect looks like a slight average net negative charge on one plate and a slight positive charge on the other.

Think of the difference between a dripping faucet and water flowing in a tiny tube.  Each drip has to have an integer number of water molecules, but the average number in section of the tube is not constrained.

With very low currents you will sometimes run into shot noise.  Shot noise is the fluctuations of the number of charge carriers around the average.  If the charge carriers move indepedently, they have Poisson statistics.  That means that if you have an average of 100 electrons/s, and you measure for 1 second you might see 90 or you might see 110.  The standard deviation of the Poisson distribution is sqrt(N).  If you have an average current of .1 electron/s then most of the time you will measure 0 and sometimes you will measure 1.

The key thing about shot noise is that it is only correct for non-interacting electrons.  This means it applies to electrons moving across a junction in a diode or BJT where the carrier density is low (due to being a semiconductor) and the junction length is very short, so the electrons don't have time to interact while crossing the barrier.  They behave more like water droplets.  In a metal wire, resistor, or to some extent a FET channel, shot noise is suppressed because the electrons are scattering off of each other a lot, and they behave more like a fluid. 

[CopperCone]

 :box:It might be a bad analogy but can the emission direction of a photon from an antenna be thought of like lightning or an arc that you kinda cant predict exactly how it will branch out (i.e. discharging many kv into an acrylic block produces a shape predictable but dimensionally random fractal? Kind like an antenna has some predictable radiation pattern but you cant predict where each photon will go? Then again with plasma arc the impedance is constantly changing.

Im having a really hard time likening water to rf


I know of shot noise but i never considered the explaination or visualization of why it happens. I need to think about that.

Are there like animations that can help me understand?  Is it because the holes are scattered far away from each other so its kind of like particles in space vs a gas? And if it was long rather then short the random dispersion of holes in the semicodncutor medium makes it more likely that tbere will be electron interaction?

So semiconductors chosen for low shot noise have a non uniform distribution of holes where the electrons can interact with each other? Can you think about it like a funnel filled with ling pong balls being shot at it, i.e. if its clogged you don't have the posibility of a ping pong ball flying right through the middle and it will instead strike the other balls slowly going through the holes because of vibrational lubrication (since gravity does not apply) and general folward momentum?

Do low shot noise devices have slower electron flow? If my choke point / crossing pathes idea is correct then wont high shot noise devices have higher resistance then low shot noise devices and so les dissipation in the semiconductor?

It makes me think of turbulance and laminar flow. That the electrons are experiancing turbulance that causes them to lose folward momentum colliding into each other

Do soliton waves factor into this some how?

[CopperCone]

And with proven developed antennas lobes can be considered probability distribution function location of photon emission? To simplify my question maybe. And according to what you guys say the large signal power will match up prefectly with very low signal power distribution funcction?.

[ejeffrey]

:box:It might be a bad analogy but can the emission direction of a photon from an antenna be thought of like lightning or an arc that you kinda cant predict exactly how it will branch out (i.e. discharging many kv into an acrylic block produces a shape predictable but dimensionally random fractal? Kind like an antenna has some predictable radiation pattern but you cant predict where each photon will go? Then again with
plasma arc the impedance is constantly changing.

Thinking about the emission from an antenna as photons is probably not helpful.  This is that whole "wave particle duality" thing -- in the case of an antenna, the EM field acts like a classical wave in essentially all ways, even at arbitrarily low signal power.  It is actually quite hard to show the particle nature of light/EM waves in an ironclad way, and it requires more than simply using very low signal powers.

[CopperCone]

This video puts something on the tip of my tongue (about masers) at like 9:40. That video got me thinking about this issue. It talks abit about dipoles but is hard to relate

I just think of low signal powers again because it slows everything down and isolates the electrons from eachother so you can visualize one or two in a certain wide area rather then some kind of 'thermodynamics' type visualization with a bunch of smeared guff and gradients

It also makes me think of how electrons leave some kind of a thermal 'wake' behind them that can effect other electrons, like if you send one through, then another one, the first one is going to heat the material oh so slightly and shift the vibrations right, so the other one will be effected, but at some absurd time constant (so I am not sure if they even effect each other),.

 if you ever drove a speed boat you will know what I mean, once you start going fast another boat can turn fast in front of you and literary ruin your ass as you crash off a wave and feel like you just jumped on concrete with your butt. You feel each and every surface disturbance and it effects steering and more noticeably comfort. But if the boats are far enough away or speed is slow then you wont notice, it depends on the wave disturbance and your velocity. I think you basically go airborne jumping off waves sometimes.

I don't know if your heading is actually changed though, if you fixed the steering wheel, it would be interesting to find out. I can't remember if its a psychological thing where you jerk the wheel after experiencing an impact. It certainly felt like your heading is changed but I guess you would need to fix the steering wheel and find out.

Like 30 MPH+ on a lake for instance, I never tried oceans or sea. Kind of fun but I vomit after words. Highly recommend scopolamine if you take out a faster motor boat.

[David Hess]

It may be worth reviewing the Feynman Lectures on Quantum Mechanics, especially regarding the dual slit experiment.  One of the things which the experiments proved is that even a single electron will behave as a wave, going through both slits and creating a pattern that interferes with itself, as long as you don't try to observe the single electron and localize it to one slit or the other.  The wave nature of electrons doesn't change based on how many or how few of them are present.

Exactly, the probability distribution for the single photon emitted from the antenna follows the radiation pattern.  At low power all you get is more shot noise.

Note that you can make *gain* antennas based on the double slit experiment.  Long long ago Radio Electronics had an article about building a satellite TV antenna using plywood with circular slots cut into it so the front of the antenna was flat.  The diffraction pattern focuses the incoming microwave photons on the antenna located behind the flat plywood "lens".  And just like in the double slit experiment, if just one photon came in, then it interferes with itself because it takes every path like Feynman discussed and gets bent to hit the focus point.  A transmitting antenna works the same way so a single outgoing photon interferes with itself producing the radiation pattern.

[T3sl4co1l]

Again, note that, anywhere you have a conductor, you have moving electrons in thermodynamic equilibrium.  Even at absolute zero.  Indeed, especially at absolute zero, it seems; about half the periodic table becomes superconducting down there, meaning not only do electrons continue to move at absolute zero, but they often do so with zero friction!

And, anywhere you have an insulator (ε > 1), you likewise have electrons in thermal equilibrium, in bound states.  It is the electron density that gives rise to dielectric constant, not the signal strength or frequency/energy, not the number of excess particles, just the tiny, incremental response of a statistical ensemble of particles.

It is fundamentally, deeply impossible to speak of an antenna, not made of these materials.  Your only remaining option would seem to be free space itself, but that's only a propagation medium, with no way to shape the radiation pattern.  And anyway, indeed, vacuum itself has ε and µ > 0, that is to say, it's not an empty vacuum at all, but (as it happens) a quantum foam shimmering with virtual particles.

QM doesn't magically drop statistical mechanics just when it's dealing with single particles!  Rather, SM arises out of QM applied to large systems, and QM is simplified by using the results from SM back in the original problem.

Tim

[rfeecs]

Trying to think of a single electron circuit...

Maybe a shielded electron gun that shots single electrons out in a vacuum, one at a time.
Say the electron passes through a static magnetic field and starts traveling in a circle (or spiral) and radiates at a frequency related to the rotation frequency.

Now crank up the electron gun so there are lots of electrons present all around the circle?  Is this equivalent to a DC current passing through a static magnetic field, so no radiation?

[ejeffrey]

Now crank up the electron gun so there are lots of electrons present all around the circle?  Is this equivalent to a DC current passing through a static magnetic field, so no radiation?

Nope.  The electron beam in a magnetic field will radiate just like a single electron. 

The reason electrons in a wire don't radiate is that the wire holds them in place and keeps them from spiraling inward.  In the DC current in a magnetic field, there will be a force on the wire trying to push it inward (or outward).  If you let the wire move, then it will radiate energy due to the (slightly) moving current but if you hold it stationary it will not.

[CopperCone]

But what about my idea of the thermal wake left behind an electron path? Doesent the vibrational energy distribution of the atoms of the change if heated by the electron?

So then the path of the electron behind the path finding electron changes since it gets disturbed by the motions of atoms?

Or do you guys see it kind of like a sponge where the pathway between atoms is large enought and uneffected enough by the low heating of an electron that it basically is limited to deflections that are subangstrom so you basically tend to stay in the same lane, maybe jittering a bit? And still take the same offramp basically(emission vector)?

But i think statistically even if you use this lane explaination it would be possible but unlikely to see chaotic behavior resulting from electron trains passing through matter.

Can some physicist quantify the elevels of energy and positional variations to an order of magnitude or two? Or am i still not getting something?

[T3sl4co1l]

An electron in relative motion, leaves a wake as such, which is precisely the electric and magnetic field of that particle.

An electron in unaccelerated motion, leaves a wake which superimposes on itself and cancels out, giving off no radiation -- but interacting (in QED terms, via virtual photons, but the overall effect is simply classical) in terms of E and M as usual.

It is only when acceleration occurs, that the "wake" is unbalanced and radiation is given off.  This is synchrotron radiation (at least, when relativistic, it is).

Tim

[AG6QR]

For emphasis, it may be worth pointing out what's obvious to many.  Electrons and photons both obey quantum mechanics, and have the dual particle/wave nature.  But the things which are emitted and received by antennas are photons, not electrons.

The quantized nature of electrons is important for understanding what's really going on inside transistors and other semiconductor devices.  The quantized nature of photons comes into play when explaining the photoelectric effect and the behavior of LEDs.

But in practice, you can do a lot of engineering without dealing with quantum mechanics much.  In particular, I've never heard of a radio antenna which was designed using anything other than the wave model of EM radiation.  Maxwell's equations describe waves, not quantum-mechanical particle/wave entities.  The wave model keeps working even when talking about a single photon per second.  But the background EM radiation at RF in the most well-shielded environments is many orders of magnitude higher than that.

[rfeecs]

Now crank up the electron gun so there are lots of electrons present all around the circle?  Is this equivalent to a DC current passing through a static magnetic field, so no radiation?

Nope.  The electron beam in a magnetic field will radiate just like a single electron. 

The reason electrons in a wire don't radiate is that the wire holds them in place and keeps them from spiraling inward.  In the DC current in a magnetic field, there will be a force on the wire trying to push it inward (or outward).  If you let the wire move, then it will radiate energy due to the (slightly) moving current but if you hold it stationary it will not.

Hmm.  I'm not buying that explanation.
It's obvious that the wire doesn't radiate from Maxwell's equations:  no time varying fields, so no radiation.
Spiraling inward is not particularly relevant.  You can neglect the spiraling.  If the electron is moving in a circle, it is accelerating and it will radiate.

My point was trying to address the original question of if you had an "antenna" with only one charge moving through it, would the radiation pattern be different.  I'm saying in this case, although it is not really an antenna, then yes:  as you add more electrons, the radiated fields from each electron will start to interfere with each other, and you will get a different pattern depending on how many electrons you have.

I suspect as you add more and more electrons, the summed up fields from each electron will start to cancel entirely, and you will be left with a situation like the wire where you have effectively a continuous current density that results in no time varying field.

If you have an hour to kill, this lecture takes the formula for the far field of an accelerating charge and calculates the example of an oscillating charge.  In the last 10 minutes, he applies it to a charge moving in a circle:
https://youtu.be/wF8vLZ9ceb0

I think that formula is derived in this lecture, but I'm not fanatical enough to watch it:
https://youtu.be/QpGBs307qYs

[CopperCone]

anyone else black out after watching that youtube video? 

the second video actually has fire in it, he had to burn something to keep the class awake 

[timelessbeing]

reminds me of this video