Exploring Quantum Systems That Don’t Find Equilibrium

Some physical systems, particularly in the quantum world, do not reach stable equilibrium, even after long. An ETH researcher has now discovered a sophisticated description of this phenomenon.

If a bottle of beer is placed in a huge bathtub loaded with icy water, it will not be long before you can enjoy a chilly beer. Physicists uncovered how this works over a hundred years ago. Heat exchange happens through the glass container until equilibrium is reached.

However, other systems, specifically quantum systems, that do not reach an equilibrium exist. They resemble a theoretical beer bottle in a bath of ice-cold water that does not constantly and undoubtedly cool to the temperature of the bathwater; however, it instead gets to different states depending on its initial temperature. Previously, such systems have befuddled physicists.

A farther influence

Specifically, we speak about systems in which the individual building blocks impact their immediate neighbors and faraway objects. One instance would be a galaxy: the gravitational forces of the specific stars and planetary systems act not only on the bordering celestial bodies yet far past that– albeit ever more weakly — on the other constituents of the galaxy.

Defenu’s approach starts by simplifying the problem to a world with a single dimension. Inside, there is a solitary quantum particle that can reside just in really specific locations along a line. This world looks like a board game like Ludo, where a little token hops from square to square. Imagine there is a game die whose sides are all marked ‘one’ or ‘minus one, and presume the player rolls the die over and over again consecutively. The token will jump to an adjacent square, and from there, it will either hop back otherwise on to the next square. And so on.

The concern is, What happens if the player rolls the die an infinite number of times? If there are just a few squares in the game, the token will undoubtedly go back to its starting point from time to time. Nonetheless, it is impossible to predict precisely where it will go at any given time since the tosses of the die are unknown.

Back to square one

It is a similar circumstance with particles that are subject to the legislation of quantum mechanics: there is no way to recognize precisely where they go at any time. However, it is feasible to determine their whereabouts using probability distributions. Each distribution arises from a different superposition of the probabilities for the individual locations and corresponds to the particle’s particular energy state. It turns out that the amount of stable energy states coincides with the number of levels of freedom of the system and thus matches precisely to the number of permitted locations. The crucial point is that all the stable probability distributions are non-zero at the starting point. Therefore, at some point, the token returns to its starting square.

It will return to its initial location more rarely the more squares there are; finally, it won’t ever return with an unlimited number of possible squares. This means that there are an endless number of distributions that may be made using the probabilities of the different positions for the quantum particle. As a result, it can no longer occupy only particular discrete energy states; instead, the entire range of potential states is present.

This is not new knowledge. However, there are variants of the game or physical systems where the die can also have numbers over one and smaller than minus one, i.e., the steps permitted per move can be larger-to be precise, even infinitely large. This essentially changes the situation, as Defenu has shown: in these systems, the energy spectrum always stays discrete, even when there are infinite squares. This implies that the particle will undoubtedly return to its starting point from time to time.

Strange phenomena

This new theory clarifies what researchers have observed various times in experiments: systems in which long-range interactions happen do not get to a steady equilibrium, but rather a meta-stable state in which they always go back to their initial placement. When it comes to galaxies, this is one reason they develop spiral arms rather than being uniform clouds.

Ions, composed of atoms with charges bound in fields of electricity, are one type of quantum system that can be explained by Defenu’s theory. The construction of classical computer systems using such ion traps is one of the largest scientific initiatives going on right now in the world. However, a significant number of simultaneously trapped ions will be necessary for these computers to produce a step modification in terms of computational capacity; this is precisely the point at which the new hypothesis turns intriguing. “During systems with 100 or even more particles, you would see peculiar effects that we can presently explain,” claims Defenu, a member of the research team led by ETH Professor Gian Michele Graf. His experimental physics colleagues are making daily progress toward their goal of being able to realize such forms. Additionally, it might be worthwhile for them to enjoy a cold drink with Defenu as soon as they arrive.

Read the original article on PHYS.

Reference: Nicolò Defenu, Metastability and discrete spectrum of long-range systems, Proceedings of the National Academy of Sciences (2021). DOI: 10.1073/pnas.2101785118