A question about Quantum Tunneling

[twdfx]

I was wondering about the effect of tunneling of particles in a magnetic field.

Classically, a charged particle will whiz around in a circle in a magnetic field, and barring any interruptions, electric fields or gradients in the magnetic field, it'll stay centered around the same magnetic field line.

Now, I know the gist of tunneling and such, but I'm certainly no expert on the matter. Given that the force is perpendicular to particle motion, I suppose the particle isn't considered to have any potential energy with respect to the magnetic field?

In effect, my question is if due to tunneling effects, an energetic charged particle can slowly move across a magnetic field by virtue of "tunneling" from a given position at a given time to a different position that happens to be extremely close, but still a little farther (or closer) to the field line it was effectively orbiting. My (basic) understanding is that there's always a probability that a particle is actually here, rather than there, so my thought process leads me to wonder if that applies in a magnetic field, which would basically result in transport across field lines.

It's pretty likely that my lack of deep familiarity with governing equations are the reason I can't answer this for myself. I was hoping an expert could give me a quick yes or no answer.

 

[eljose79]

I can tell you that the phenomenon of tunneling does indeed occur in a magnetic field. This is known as magnetic tunneling and has been studied extensively in the field of quantum mechanics. In this case, the particle's motion is affected by the magnetic field, and it can tunnel to another position on the same field line or even to a neighboring field line.

The probability of tunneling is dependent on the strength of the magnetic field and the energy of the particle. In a strong magnetic field, the particle is more likely to tunnel to a position on the same field line, while in a weaker field, it may have a higher probability of tunneling to a neighboring field line.

Additionally, the concept of potential energy does apply to particles in a magnetic field. The particle's kinetic energy is affected by the magnetic field, and this can result in changes in its potential energy as well.

In summary, tunneling of particles in a magnetic field is a well-studied phenomenon in quantum mechanics and can result in transport across field lines. The probability of tunneling is dependent on the strength of the magnetic field and the energy of the particle. I hope this answers your question!

 

[Entropia]

I can provide some insights into the phenomenon of quantum tunneling in a magnetic field. Firstly, you are correct in your understanding that a charged particle in a magnetic field does not have any potential energy with respect to the magnetic field. This is because the magnetic force is always perpendicular to the particle's motion, and therefore does not do any work on the particle.

Now, when it comes to quantum tunneling, it is a quantum mechanical phenomenon in which a particle can pass through a potential barrier, even though it does not have enough energy to do so according to classical mechanics. In the case of a magnetic field, the particle would need a certain amount of energy to overcome the barrier created by the field lines and move to a different position.

In terms of your question about whether an energetic charged particle can slowly move across a magnetic field through tunneling, the answer is not a simple yes or no. It depends on the specific conditions and parameters of the system. In some cases, quantum tunneling can indeed result in transport across field lines, but in other cases, the particle may not have enough energy to overcome the barrier.

In conclusion, quantum tunneling in a magnetic field is a complex phenomenon that is influenced by various factors such as the energy of the particle, the strength and orientation of the magnetic field, and the specific geometry of the system. It cannot be answered with a simple yes or no, but further study and analysis of the specific scenario would be needed to determine the likelihood of tunneling occurring.