Who needs doors, when I can tunnel?

Tunneling is one of the mysterious features of quantum mechanics, but there is a very nice way to visualize it. There is a simulation method in order to obtain the ground state of quantum systems, called path integral Monte Carlo. It is based, as its name suggests, on Feynman’s path integral approach to quantum mechanics, but I will not go deeper in that… The idea is the following: a particle becomes a set of many, many copies, beads or replicas. Which one is the real particle? All of them, and none. Then, link them all, each one to the next, with a spring whose natural length is zero, and with a spring constant which increases with the mass. Now, put all the system in a “fake temperature”, which depends on \hbar… and that’s all! Simulate that, just using Monte Carlo, and the equilibrium distribution that you obtain is the ground state of the quantum system.

In the simulation, the potential is represented with the background colors: blue is low, orange is high. So, you see the potential consists of many minima, the central one is deeper. In fact, the energy of the particle is not enough to jump over the barriers… but it does not matter now. The “ring polymer” can jump, even if a classical particle can’t. The height of the barrier is not a huge problem if it is thin, because in that case the “spring” can stretch, and make one of the beads jump over it! That’s the tunneling, indeed.

So, what you’re observing in that video is the quantum cloud. In fact, each ring polymer represents a possible history for the particle, returning to the initial point.  Each bead corresponds to the position of the particle at a certain instant, and the energy in the springs corresponds to… the kinetic energy, which will not be zero because of the uncertainty principle.

If you need more explanations (I would!), read qfluct


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