Researchers answer a fundamental question in quantum physics

Researchers answer a fundamental question in quantum physics

Q as the ramp progresses 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 (KZ) mechanism is fixed at the characteristic time ∣∣t ∣GS exceeds the maximum speed of relevant sound, c, in the system. Credit: Scientists progress (2022). DOI: 10.1126/sciadv.abl6850″ width=”800″ height=”530″/>
Schematic representation 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 spin configuration in this state along the control direction would then typically yield a random pattern of spins 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, when measuring spin configurations along the order direction, will typically produce a collapse on a mosaic of such domains (at the top). On the front panel, we include the growth of the ferromagnetic correlation range as a function of time t from t = −τQ as the ramp progresses 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 (KZ) mechanism is fixed at the characteristic time ∣∣t ∣GS exceeds the maximum speed of relevant sound, c, in the system. Credit: Scientists progress (2022). DOI: 10.1126/sciadv.abl6850

An international team of physicists, with the participation of 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 proven to be too demanding, even for supercomputers. However, the researchers succeeded in simplifying them considerably by using methods from the field of machine learning. The study improves the understanding of the fundamental principles of the quantum world. It was published in the journal Scientists progress.

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

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

“And it’s extremely complex,” says Professor Dr. Markus Heyl of 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 big that even the fastest supercomputers are unable to cope with it. It 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. “That makes it manageable for computers,” says Heyl.

Using this method, scientists investigated 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 during what is called a quantum phase transition. An example of a macroscopic and more intuitive phase transition of the world is the transition from water to ice. Another example is the demagnetization of a high temperature magnet.

If you go the other way and cool the material, the magnet starts forming again below a certain critical temperature. However, this does not occur uniformly throughout the material. Instead, many small magnets with differently aligned 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 flaws.

The Kibble-Zurek mechanism predicts how many of these defects are expected (in other words, how many mini-magnets the material will eventually be composed of). 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 in exactly the same way, even though 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 structure in the universe. After the Big Bang, the universe was initially completely homogeneous, which means that the hosted matter was perfectly distributed. For a long time it was not known how galaxies, suns or planets were able to form from such a homogeneous state.

In this context, the Kibble-Zurek mechanism provides an explanation. As the universe cooled, flaws developed much like 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 – maybe you could think 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 to the quantum world. “It was by no means an obvious conclusion,” says the physicist from Augsburg. “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, Scientists progress (2022). DOI: 10.1126/sciadv.abl6850

Provided by the University of Augsburg

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