Researchers answer the fundamental question of quantum physics

Q as the ramp advances through the critical regime with the critical point located at t = 0. The healing length ξˆ which determines the size of the domains in the Kibble-Zurek mechanism (KZ) is set to the characteristic time ∣∣t∣GS exceeds the maximum speed of sound in question, c, in the system. Credit: Scientific advances (2022). DOI: 10.1126 / sciaadv.abl6850 “width =” 800 “height =” 530 “/>

Schematic description of the dynamics through a phase transition in a two-dimensional spin-1/2 model. In the initial paramagnetic state (bottom), the spins align with the direction of the transverse magnetic field. A measurement of the rotation pattern in that state along the sort direction would then typically produce a random pattern of rotations pointing up (blue cones) or down (red cones). After a slow ramp through a quantum critical point, the system develops a quantum superposition of ferromagnetic domains, which, by measuring spin configurations along the ordering direction, will typically collapse on a mosaic of those domains (top). On the front face we include the growth of the ferromagnetic correlation interval as a function of time t starting from t = −τQ as the ramp advances through the critical regime with the critical point located at t = 0. The healing length ξˆ which determines the size of the domains in the Kibble-Zurek mechanism (KZ) is set to the characteristic time ∣∣t∣GS exceeds the maximum speed of its sound, c, in the system. Credit: Science advances (2022). DOI: 10.1126 / sciaadv.abl6850

An international team of physicists, with the participation of the University of Augusta, has for the first time confirmed an important theoretical prediction in quantum physics. The calculations for this are so complex that so far they have proved too challenging even for supercomputers. However, the researchers managed to simplify them considerably by using methods from the field of machine learning. The study improves understanding of the fundamental principles of the quantum world. It was published in the magazine Science advances.

Calculating the motion of a single billiard ball is relatively simple. However, it is much more difficult to predict the trajectories of a multitude of gas particles in a ship that are constantly colliding, slowing and deflecting. But what if it’s not even entirely clear exactly how fast each particle is moving, so that they would have countless speeds at any given time, differing only in their probability?

The situation is similar in the quantum world: quantum mechanical particles can also have all potentially possible properties simultaneously. This makes the state space of quantum mechanical systems extremely large. If you aim to simulate how quantum particles interact with each other, you need to consider their complete state spaces.

“And this is extremely complex”, says prof. dr. Markus Heyl of the Physics Institute of the University of Augusta. “The computational effort increases exponentially with the number of particles. With more than 40 particles, it is already so great that even the fastest supercomputers are unable to make it. This is one of the great challenges of quantum physics.”

Neural networks make the problem manageable

To simplify this problem, Heyl’s group used methods from the field of machine learning: artificial neural networks. With these, the state of quantum mechanics can be reformulated. “This makes it manageable for computers,” says Heyl.

Using this method, the scientists studied an important theoretical prediction that has remained an exceptional challenge so far: the Kibble-Zurek quantum mechanism. It describes the dynamic behavior of physical systems in what is called the quantum phase transition. An example of a phase transition from the macroscopic and more intuitive world is the transition from water to ice. Another example is the demagnetization of a magnet at high temperatures.

If you do the opposite and cool the material, the magnet starts forming again below a certain critical temperature. However, this does not happen evenly across the entire material. Instead, many small magnets with differently aligned north and south poles are created at the same time. Therefore, the resulting magnet is actually a mosaic of many different and smaller magnets. Physicists also say it contains flaws.

The Kibble-Zurek mechanism predicts how many of these defects are to be expected (in other words, how many mini-magnets the material will eventually make up). What is particularly interesting is that the number of these defects is universal and therefore independent of microscopic details. As a result, many different materials behave exactly identically, even if their microscopic composition is 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 in the universe. After the Big Bang, the universe was initially completely homogeneous, which means that the hosted matter was distributed perfectly evenly. For a long time it was not clear how galaxies, suns or planets could have formed from such a homogeneous state.

In this context, the Kibble-Zurek mechanism provides an explanation. As the universe cooled, the defects developed similar to magnets. Meanwhile, these processes in the macroscopic world are well understood. But there is a type of phase transition for which it has not yet been possible to verify the validity of the mechanism, namely the quantum phase transitions already mentioned above. “They only exist at the absolute zero temperature point of -273 degrees Celsius,” says Heyl. “So the phase transition doesn’t happen during cooling, but through changes in the interaction energy – you might think, perhaps, of varying the pressure.”

Scientists have now simulated such a quantum phase transition on a supercomputer. They were thus able to show for the first time that the Kibble-Zurek mechanism also applies in the quantum world. “It wasn’t an obvious conclusion at all,” says the Augusta physicist. “Our study allows us to better describe the dynamics of quantum mechanical systems of many particles and thus to understand more precisely the rules that govern this exotic world.”


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More information:
Markus Schmitt et al, Quantum Phase Transition Dynamics in the Two-Dimensional Transverse Field Ising Model, Science advances (2022). DOI: 10.1126 / sciaadv.abl6850

Provided by the University of Augusta

Citation: Researchers answer the fundamental question of quantum physics (2022, September 22) retrieved on September 22, 2022 from https://phys.org/news/2022-09-fundamental-quantum-physics.html

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