Quantum Systems Keep a Permanent 'Birthmark' of Their Starting State, Even in Chaos
Physicists at Tampere, Harvard and TU Dresden show a quantum particle in a chaotic space stays at least twice as likely to be found in its original state as in any comparable one, a rule that classical chaos forbids.
In the everyday world, chaos wipes the slate clean. Stir cream into coffee, or let a billiard ball bounce around a table long enough, and the starting conditions stop mattering. A new theory paper shows that a quantum particle does not play by that rule: no matter how chaotic its surroundings, it keeps a lasting imprint of where it began.
The work was published October 5 in Physical Review X (DOI 10.1103/dhzb-28rb) by researchers at Tampere University in Finland, Harvard University and TU Dresden. The lead author is Joonas Keski-Rahkonen of Tampere's Quantum Control and Dynamics group. The team calls the effect a "quantum birthmark."
The test case is a standard one in the field, the stadium billiard, a table shaped like a stadium with straight sides and semicircular ends. A classical ball bounced around a stadium behaves chaotically, so tiny differences in its starting position grow into wildly different paths, and over a long time it is equally likely to be anywhere. A quantum particle is described by a wave packet that spreads over the same table. The researchers found that if you average over a long enough time, the wave packet is at least twice as likely to be found back in its original condition as in any other comparable one. The memory does not fade as time passes.
"In the everyday world, chaos wipes the slate clean," Keski-Rahkonen said. "What we found is that quantum systems can't hide their origin, even in the middle of chaos."
The result builds on a famous effect called quantum scarring. In 1984 Eric Heller, now at Harvard, showed that some quantum states in chaotic systems pile up along the paths a classical particle would repeat, leaving sharp ghostly traces. For decades scarring looked like a curiosity tied to special repeating orbits. The new paper argues it is only one special case of a broader rule that applies to every quantum system, whether or not it has such orbits.
The stadium billiard is a long-standing proving ground for this kind of question. Its shape was shown in the 1970s to be chaotic in the classical sense, which makes it a clean test of what survives when a classical ball would have forgotten everything. Quantum mechanics describes the particle as a wave, and a wave in a closed space interferes with itself, which is where the leftover memory comes from.
There are practical stakes. Quantum simulators and nanoscale electronic devices operate in the regime where these memory effects are large enough to show up in measurements. If a device's behavior depends on how it was prepared even after a long time, designers need to account for it, and in some cases may be able to use it.
