An important theoretical prediction of quantum physics has been confirmed for the first time by an international team of physicists with the participation of the University of Augsburg. The calculations for this are so complex that they have so far been too demanding even for supercomputers. However, researchers have succeeded in greatly simplifying them using methods from the field of machine learning. The research improves understanding of the fundamental principles of the quantum world.it has been published in the journal scientific progress.
The calculation of a single billiards movement is relatively simple. However, predicting the trajectories of the massive gas particles that are constantly colliding, decelerating and deflecting in a container is much more difficult. But what if it wasn’t even clear how fast each particle was moving, so that they would have an infinite number of possible speeds at any given time, just with different probabilities?
The situation in the quantum world is similar: quantum-mechanical particles can even have all possible properties at once. This makes the state space of quantum mechanical systems very large. If your goal is to simulate how quantum particles interact, you have to consider their full state space.
“It’s very complicated,” says Professor Markus Heyl from the Institute of Physics at the University of Augsburg. “The amount of computation grows exponentially with the number of particles. More than 40 particles are already so large that even the fastest supercomputers can’t handle it. This is one of the grand challenges of quantum physics.”
Neural Networks Make Problems Manageable
To simplify the problem, Heyl’s group used an approach from the field of machine learning—artificial neural networks. With these, the quantum mechanical state can be reformulated. “This allows the computer to manage it,” explains Heyl.
Using this approach, the scientists investigated an important theoretical prediction that has so far remained a prominent challenge – the quantum Kibble-Zurek mechanism. It describes the dynamic behavior of physical systems in so-called quantum phase transitions. An example of a phase transition from a macroscopic and more intuitive world is the transition from water to ice. Another example is the demagnetization of magnets at high temperatures.
If you cool the material in reverse, magnets start forming again below a certain critical temperature. However, this does not happen uniformly throughout the material. Instead, many small magnets with differently arranged north and south poles were created at the same time. Thus, the resulting magnet is actually a mosaic of many different, smaller magnets. Physicists also say it contains flaws.
The Kibble-Zurek mechanism predicts how many of these defects are expected (in other words, how many micromagnets the material will ultimately consist of). What is particularly interesting is that the number of these defects is general and thus independent of microscopic details. As a result, many different materials behave exactly the same, even though their microscopic compositions are completely different.
The Kibble-Zurek mechanism and the formation of galaxies after the big bang
The Kibble-Zurek mechanism was originally introduced to explain the formation of the structure of the universe. After the Big Bang, the universe was initially completely homogeneous, meaning that the distribution of host matter was remarkably uniform. It has long been unclear how galaxies, suns or planets form from this homogeneous state.
In this case, the Kibble-Zurek mechanism provides an explanation. As the universe cooled, defects developed in a magnet-like fashion. At the same time, these processes in the macroscopic world are well understood. But there is one type of phase transition for which the validity of the mechanism cannot yet be verified – the quantum phase transition already mentioned. “They only exist at the absolute zero temperature point of -273 degrees Celsius,” explains Heyl. “So the phase transition doesn’t happen during cooling, but through a change in the energy of the interaction — you might consider changing the pressure.”
Scientists have now simulated this quantum phase transition on a supercomputer. Thus, for the first time, they were able to show that the Kibble-Zurek mechanism also works in the quantum world. “It was by no means an obvious conclusion,” said the Augsburg physicist. “Our research allows us to better describe the dynamics of quantum mechanical systems of many particles, and thus to more accurately understand the rules that govern this strange world.”
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Markus Schmitt et al., Quantum Phase Transition Dynamics in a 2D Transverse Field Ising Model, scientific progress (2022). DOI: 10.1126/sciadv.abl6850
Courtesy of the University of Augsburg
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