Two-dimensional spin 1/2 model. In the initial paramagnetic state (bottom), the spin is aligned with the direction of the transverse magnetic field. Then, measuring the spin configuration in this state along the sorting direction will usually produce a random spin pattern pointing upwards (blue cone) or downwards (red cone). After the quantum critical point slowly rises, the system develops quantum superposition for ferromagnetic domain . When measuring spin configurations in an ordered direction, collapse (top) will usually occur on the mosaic of such domains. On the front, we take the growth of the ferromagnetic correlation range as a function of time t starting from t = −τ Q When the slope passes through the critical state, the critical point is at t = 0. The healing length that determines the domain size in the Kipur-Zulek (KZ) mechanism is the maximum speed at which the ∣∣t∣GS set at feature time exceeds the relevant sound c in the system. Credits: Scientific Advances (2022).DOI: 10.1126/sciadv.abl6850
With the participation of Augsburg University , an international team of physicists confirmed for the first time an important theoretical prediction in quantum physics . The calculations for this are so complex that so far they have been too demanding even for supercomputers. However, the researchers successfully used the machine learning method to greatly simplify them. This study improves understanding of the fundamentals of the quantum world. It has been published in the journal Science Advances" .
The calculation of a single billiards is relatively simple. However, it is difficult to predict the trajectory of a large number of gas particles in the container, which are constantly colliding, slowed down and deflected, which is much more difficult. But what if it is not even clear at all how fast each particle moves so that they have countless possible speeds at any given time that only differ in probability? The situation in the quantum world of
is similar: quantum mechanics particles can even have all potential possibilities at the same time. This makes the state space of quantum mechanics 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," said Dr. Markus Heyl, PhD, from the Institute of Physics, Augsburg University. “The computational workload grows exponentially with the increase in the number of particles. It has more than 40 particles, and it is already so large that even the fastest supercomputers can’t handle it. This is one of the major challenges in quantum physics.
Neural Network makes the problem easy to manage
To simplify this problem, Heyl’s team used the approach in the field of machine learning— Artificial Neural Network . With these, quantum mechanic states can be re-formed. “This makes it manageable for computers,” Heyl explains.
Using this approach, scientists studied an important theoretical prediction, which so far remains an open challenge – Quantum Kibble-Zurek mechanism. It describes the dynamic behavior of physical systems under so-called quantum phase transitions. An example of a phase transition from macroscopic and more intuitive world is the transition from water to ice. Another example is the demagnetization of magnets at high temperatures.
If you in turn cool the material, the magnet starts to form again when it is below a certain critical temperature. However, this does not happen uniformly throughout the material. Instead, many small magnets with different arrangements of the North and South Poles are produced simultaneously The resulting magnet is therefore actually a mosaic of many different, smaller magnets. Physicists also say it contains defects. The
Kibble-Zurek mechanism predicts how many of these defects are expected (in other words, how many micro magnets the material will eventually consist of). It is particularly interesting that the number of these defects is universal and therefore not related to microscopic details. Therefore, many different materials behave exactly the same, even if their microscopic composition is completely different.
Kipur-Zulek mechanism and the formation of galaxies after the Big Bang
Kipur-Zulek mechanism was originally introduced to explain the formation of structures in the universe. After the Big Bang, the universe was initially completely uniform, meaning that the host matter was completely uniformly distributed. For a long time, it has been unclear how galaxies, the sun, or planets form from this uniform state.
In this case, the Kipur-Zulek mechanism provides an explanation. As the universe cools, defects develop in a way similar to magnets. At the same time, these processes in the macro world are well known. But there is one type of phase transition that cannot yet verify the effectiveness of this mechanism - i.e., the quantum phase transition mentioned above. "They only exist at an absolute zero temperature point at -273 degrees Celsius," Heyl explained. "So the phase transition does not occur during cooling, but through changes in the interaction energy - you might think, maybe, change the pressure.
scientists have now simulated this quantum phase transition on supercomputers. So, they were able to prove for the first time that the Kible-Zulek mechanism also applies to the quantum world. "This is by no means an obvious conclusion," said the Augsburg physicist. "Our research allows us to better describe the dynamics of quantum mechanics systems of many particles, thus more accurately understanding the rules that control this strange world.
More information: Markus Schmitt et al., Quantum phase change dynamics in the two-dimensional transverse field Isin model, Scientific progress (2022). DOI: 10.1126/sciadv.abl6850
Journal information: Scientific progress
