Researchers answer fundamental question of quantum physics

Forscher beantworten grundlegende Frage der Quantenphysik

Schematic representation of the dynamics across 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 spin configuration in this state along the ordering direction would then typically yield a random pattern of spins pointing up (blue cones) or down (red cones). After a slow ramp over a quantum critical point, the system develops a quantum superposition of ferromagnetic domains, which typically leads to a collapse to a mosaic of such domains when measuring spin configurations along the ordering direction (top). On the front we plot the growth of the ferromagnetic correlation range as a function of time t from t = −τQ when the ramp progresses above the critical regime, where the critical point is at t=0. The healing length ξˆ, which determines the size of the domains in the Kibble-Zurek (KZ) mechanism, is set to the characteristic time ∣∣t∣GS exceeds the maximum speed of the relevant noise c in the system. Recognition: scientific advances (2022). DOI: 10.1126/sciadv.abl6850

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

Calculating the movement of a single billiard ball is relatively easy. However, it is far more difficult to predict the trajectories of a large number of gas particles in a ship, which are constantly colliding, decelerated and deflected. But what if it is not even clear exactly how fast each particle is moving, so that at any point in time they would have innumerable possible velocities that only differ in their probability?

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

“And that is extremely complex,” says Prof. Dr. Markus Heyl from the Institute of Physics at the University of Augsburg. “The computational effort increases exponentially with the number of particles. With more than 40 particles, it is already so large that even the fastest supercomputers can no longer cope with it. That 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. This allows the quantum mechanical state to be reformulated. “That makes it manageable for computers,” explains Heyl.

Using this method, the scientists have investigated an important theoretical prediction that has so far posed a major challenge – the quantum Kibble Zurek mechanism. It describes the dynamic behavior of physical systems during a so-called 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 the opposite is done and the material cools down, the magnet begins to form again below a certain critical temperature. However, this does not happen evenly across the entire material. Instead, many small magnets with differently oriented north and south poles are created at the same time. So the resulting magnet is actually a mosaic of many different, smaller magnets. Physicists also say it contains defects.

The Kibble-Zurek mechanism predicts how many of these defects to expect (in other words, how many mini-magnets the material will eventually consist of). What is particularly interesting is that the number of these defects is universal and thus independent of microscopic details. Accordingly, many different materials behave absolutely 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 structure formation in the universe. After the Big Bang, the universe was initially completely homogeneous, which means that the matter in it was distributed completely evenly. For a long time it was unclear 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, defects developed similar to those found in magnets. These processes are now well understood in the macroscopic world. But there is one type of phase transition for which the validity of the mechanism has not yet been verified – namely the quantum phase transitions already mentioned. “They only exist at absolute zero temperature of -273 degrees Celsius,” explains Heyl. “So the phase transition does not take place during cooling, but through changes in the interaction energy – one might think of varying the pressure.”

The 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. “That was by no means an obvious conclusion,” says the Augsburg physicist. “Our study enables us to better describe the dynamics of quantum mechanical systems of many particles and thus to better understand the rules of this exotic world.”

New fur for the quantum cat: Entanglement of many atoms discovered for the first time

More information:
Markus Schmitt et al, Quantum phase transition dynamics in the two-dimensional transverse field Ising model, scientific advances (2022). DOI: 10.1126/sciadv.abl6850

Provided by the University of Augsburg

Citation: Researchers answer fundamental question of quantum physics (2022, September 22), retrieved September 22, 2022 from

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