The Naked Scientists

The Naked Scientists Forum

Author Topic: Is there a Lorentz force on a tunneling charge?  (Read 1033 times)

Offline chiralSPO

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 1872
  • Thanked: 143 times
    • View Profile
Is there a Lorentz force on a tunneling charge?
« on: 08/04/2016 16:31:41 »
A question came up during a discussion I had yesterday with some other chemists. None of us being physicists, the question went unanswered...

Imagine a molecule with 6 redox-active fragments arranged in a circle, somewhat like this:

    A
F      B
E      C
    D

The six fragments are not conjugated to each other, so there is no orbital delocalized around the whole cycle (no conduction band), but they are close enough that electrons can hop (tunnel) from one fragment to either nearest neighbor with a fairly short half life (let's say an average of 25 ns between hops).

If an electron tunnels from A to B, then B to C, and so forth around the whole molecule, is there any magnetic field generated?

I know that with a classical description any moving charge generated a magnetic field, but if the electron can be viewed as effectively stationary between hops (tunneling events) how do we ascribe the induced magnetic field? (I am assuming that there will be a magnetic field produced, but if there isn't I would like to know why)

Thanks!
« Last Edit: 11/04/2016 08:59:35 by chris »


 

Offline agyejy

  • Sr. Member
  • ****
  • Posts: 210
  • Thanked: 22 times
    • View Profile
Re: Is there a Lortentz force on a tunneling charge?
« Reply #1 on: 08/04/2016 17:35:48 »
As far as I can discern the dc Josephson current at zero bias which is completely due to tunneling creates a magnetic field. That field actively confines the tunneling current to near the junction itself. Therefore it is likely a current also occurs in your specific case of the electron making a complete circle always moving in one direction. However, as far as I am aware the way in which you described your system suggests that the hopping should be random in direction. Therefore your electron might eventually make it around but I'd wager it would be rather slow going with a one step forward two steps back thing happening. Without knowing precise hopping energies there is no real way to be quantitative about the rates and you'd need a monte carlo simulation to get at the average current (not that I could do any of that math easily even if I had the hopping energies) but I'd wager the current would be small (probably average to zero over long enough time scales) and be little more than fluctuations of the overall magnetic moment of the molecule.
 

Offline chiralSPO

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 1872
  • Thanked: 143 times
    • View Profile
Re: Is there a Lortentz force on a tunneling charge?
« Reply #2 on: 08/04/2016 18:41:11 »
Thanks agyejy!

I was intentionally vague when describing the energies and symmetries involved in the system. One could imagine a system which favors flow in one direction only (but of course would need a source of energy to drive it). If I end up pursuing this line of inquiry with some calculations (DFT models, Monte Carlo simulations and Marcus-Levich-Jortner treatment of electron transfer), I may post some findings here...
 

Offline agyejy

  • Sr. Member
  • ****
  • Posts: 210
  • Thanked: 22 times
    • View Profile
Re: Is there a Lortentz force on a tunneling charge?
« Reply #3 on: 08/04/2016 19:59:18 »
Sounds vaguely like a quantum ratchet:

http://journals.aps.org/pre/pdf/10.1103/PhysRevE.87.022129

They are certainly fun objects to toy around with.
 

Offline Thebox

  • Neilep Level Member
  • ******
  • Posts: 3154
  • Thanked: 44 times
    • View Profile
Re: Is there a Lortentz force on a tunneling charge?
« Reply #4 on: 10/04/2016 08:48:14 »
A question came up during a discussion I had yesterday with some other chemists. None of us being physicists, the question went unanswered...

Imagine a molecule with 6 redox-active fragments arranged in a circle, somewhat like this:

    A
F      B
E      C
    D

The six fragments are not conjugated to each other, so there is no orbital delocalized around the whole cycle (no conduction band), but they are close enough that electrons can hop (tunnel) from one fragment to either nearest neighbor with a fairly short half life (let's say an average of 25 ns between hops).

If an electron tunnels from A to B, then B to C, and so forth around the whole molecule, is there any magnetic field generated?

I know that with a classical description any moving charge generated a magnetic field, but if the electron can be viewed as effectively stationary between hops (tunneling events) how do we ascribe the induced magnetic field? (I am assuming that there will be a magnetic field produced, but if there isn't I would like to know why)

Thanks!


Why would the electron ''hop'' from A-B?   Why not A-F or A-E and why not simultaneous ''hopping'' from all point sources in random directions?

 

Offline chiralSPO

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 1872
  • Thanked: 143 times
    • View Profile
Re: Is there a Lortentz force on a tunneling charge?
« Reply #5 on: 10/04/2016 14:20:09 »

Why would the electron ''hop'' from A-B?   Why not A-F or A-E and why not simultaneous ''hopping'' from all point sources in random directions?

Good question.

To the extent that I have defined the problem here, there is no reason to think that it would favor hopping from A to B over hopping from A to F, but hopping from A to E would be much harder. The probability of hopping is roughly related to ed where d is the distance hopped. There are ways to design the molecule such that A-B tunneling is favored over A-F tunneling (either by changing the energies of the orbitals involved, or by changing the strength of the coupling between the involved orbitals).
 

Offline chiralSPO

  • Global Moderator
  • Neilep Level Member
  • *****
  • Posts: 1872
  • Thanked: 143 times
    • View Profile
Re: Is there a Lortentz force on a tunneling charge?
« Reply #6 on: 10/04/2016 14:24:27 »
Sounds vaguely like a quantum ratchet:

http://journals.aps.org/pre/pdf/10.1103/PhysRevE.87.022129

They are certainly fun objects to toy around with.

Thanks again. That's a very interesting read. I think there is a lot of overlap there with what I was thinking about. I wasn't necessarily planning on trying to capture thermal energy--my initial idea was to pump the molecule with a laser, but unfortunately, this wouldn't be any more than an academic curiosity because the strength of the magnetic field (even at the center of the molecule) would be insignificant compared to the amount of energy input by the light. The sample would probably heat up and decompose before any significant magnetic effects would manifest (at least using the first system I had in mind).
 

Offline Thebox

  • Neilep Level Member
  • ******
  • Posts: 3154
  • Thanked: 44 times
    • View Profile
Re: Is there a Lortentz force on a tunneling charge?
« Reply #7 on: 11/04/2016 07:26:56 »
Sounds vaguely like a quantum ratchet:

http://journals.aps.org/pre/pdf/10.1103/PhysRevE.87.022129

They are certainly fun objects to toy around with.

Thanks again. That's a very interesting read. I think there is a lot of overlap there with what I was thinking about. I wasn't necessarily planning on trying to capture thermal energy--my initial idea was to pump the molecule with a laser, but unfortunately, this wouldn't be any more than an academic curiosity because the strength of the magnetic field (even at the center of the molecule) would be insignificant compared to the amount of energy input by the light. The sample would probably heat up and decompose before any significant magnetic effects would manifest (at least using the first system I had in mind).

So are you saying it jumps to the nearest ''ground''  or the strongest ''ground''?


 

The Naked Scientists Forum

Re: Is there a Lortentz force on a tunneling charge?
« Reply #7 on: 11/04/2016 07:26:56 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums