The fundamental laws of physics insist that no patterns can permanently survive natureās steady course towards disorder ā or can they? A new proof offers a peculiar counterexample to the once-settled notion that all collections of particles must eventually succumb to entropy.
āOur result might seem quite surprising,ā says at the University of Colorado Boulder. But his teamās finding is actually the most recent entry in a decades-long debate over whether quantum particles can maintain certain properties forever.
Since the 1800s, physicists have agreed that it is nearly impossible for a system of many warm particles to spontaneously assume a state that is more ordered than disordered ā the system canāt become less scrambled over time. As an analogy, picture a crate of mixed red and green apples. If you leave them on a kitchen counter, they will never spontaneously sort themselves by colour.
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In fact, the second law of thermodynamics dictates that any ordered system is destined to grow increasingly disordered until it becomes perfectly even and featureless, a process called thermalisation. That crate of apples, for instance, will eventually rot into a relatively smooth-looking mush, a state that has more entropy than the original solid fruit. In the 1950s, however, at Bell Laboratories started to think up scenarios where particles could cheat thermalisation.
Anderson worked in the quantum realm, where particles have wave-like properties and thermalisation turns each into a single, very evenly extended wave. He identified conditions under which a particle wouldnāt undergo this elongation process, but rather stay in one place as a very narrow wave that never changes.
As it turns out, a single particle isnāt the only system that can defy thermalisation. In 2016, at the University of Virginia that it is similarly possible for a collection of many quantum particles to assume a quantum state that resists thermalisation forever. This phenomenon is now known as many-body localisation (MBL).
However, Imbrieās proof contained an assumption about the energies of those particles, which has become the basis for debate about the possibility of MBL. Experiments and mathematical studies performed since then have failed to fully resolve the issue.
There is some consensus among theorists that MBL is allowed by the laws of physics, but there are also still dissenters, says at Princeton University. He says that some of the difficulty lies in how rigorous the mathematical arguments must be. Another problem is that even when systems look like they have achieved MBL, proving this is difficult ā unless you can wait thousands of years to see whether thermalisation eventually destroys them.
Lucas and his colleagues have added to the debate using a novel mathematical approach inspired by computer science. It is common to study MBL by starting with physics equations for infinitely many interacting particles that are arranged in a line, but instead they used the mathematical language of graphs. In their set-up, a localised quantum state looks like a graph error that canāt be removed. The researchers used mathematics to rigorously prove that such states do exist and can remain unchanged indefinitely. In other words, they confirmed the existence of MBL.
āWe leveraged results from computer science to come up with a relatively short and understandable proof of the infinite timescale. The good thing about it is that it doesnāt rely on any unproven assumptions,ā says proof co-author , also at the University of Colorado Boulder. But there is one ābad thingā, he says: the proof only works for systems that have infinitely many dimensions.
Nevertheless, Lucas is optimistic that this work can advance physicistsā understanding of MBL.
āIt is a new approach, and it does kind of put a lamppost in the ground, saying āthis is something that we now know for sureā,ā he says. āNow you can make assumptions or guesses while having this ironclad thing that you have to make sure you donāt contradict.ā
āThis [new] proof sort of came out of left field, but I am very supportive of it,ā says Imbrie. He says that, while it centres a somewhat unconventional type of MBL, he still sees it as being concordant with his past work.
Huse says the new proof also requires the system that can achieve MBL to be colder than in past studies, so it is an intriguing entry, but not a full resolution of the long-standing debate about thermalisation. While infinite dimensions may seem abstract, it is possible that some of these ideas from the proof could be connected to practical applications, such as establishing best practices for making future programs for quantum computers, he says.
The researchers are now hoping to leverage their mathematical success to study more realistic systems. And the stakes for doing so are higher than settling a squabble among physicists ā if thermalisation can be broadly defeated, that would shake up the theoretical scaffolding of all thermal and statistical physics, says Nandkishore.
Physical Review Letters
