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 be composed of). Physicists also say that it contains defects. Thus, the resulting magnet is actually a mosaic of many different, smaller magnets. Instead, many small magnets with differently aligned north and south poles are created at the same time. However, this does not happen evenly across the entire material. If you go the other way round and cool the material, the magnet starts to form again below a certain critical temperature. Another example is the demagnetization of a magnet at high temperatures. An example of a phase transition from the macroscopic and more intuitive world is the transition from water to ice. It describes the dynamical behavior of physical systems at what is called a quantum phase transition. Using this method, the scientists have investigated an important theoretical prediction that has remained an outstanding challenge so far-the quantum Kibble-Zurek mechanism. "This makes it manageable for computers," explains Heyl. With these, the quantum mechanical state can be reformulated. To simplify this problem, Heyl's group used methods from the field of machine learning-artificial neural networks. Neural networks make the problem manageable This is one of the grand challenges of quantum physics." With more than 40 particles, it is already so large that even the fastest supercomputers are unable to cope with it. "The computational effort increases exponentially with the number of particles. Markus Heyl from the Institute of Physics at the University of Augsburg. "And that is extremely complex," says Prof. If you aim to simulate how quantum particles interact with each other, you have to consider their complete state spaces. This makes the state space of quantum mechanical systems extremely large. The situation is similar in the quantum world: Quantum mechanical particles can even have all potentially possible properties simultaneously. But what if it is not even at all clear exactly how fast each particle is moving, so that they would have countless possible velocities at any given time, differing only in their probability? However, predicting the trajectories of a multitude of gas particles in a vessel which are constantly colliding, being slowed down and deflected, is way more difficult. The calculation of the motion of a single billiard ball is relatively simple. It has been published in the journal Science Advances. The study improves the understanding of fundamental principles of the quantum world. However, the researchers succeeded in simplifying them considerably using methods from the field of machine learning. The calculations for this are so complex that they have hitherto proved too demanding even for supercomputers. DOI: 10.1126/sciadv.abl6850Īn 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 healing length ξˆ that determines the size of domains in the Kibble-Zurek (KZ) mechanism is set at the characteristic time ∣∣t∣ GS exceeds the maximal speed of the relevant sound, c, in the system. On the front face, we include the growth of the ferromagnetic correlation range as a function of time t starting from t = −τ Q as the ramp progresses across the critical regime with the critical point located at t = 0. After a slow ramp across a quantum critical point, the system develops a quantum superposition of ferromagnetic domains, which, upon measuring spin configurations along the ordering direction, will yield typically a collapse onto a mosaic of such domains (top). A measurement of the spin configuration in that state along the ordering direction would then typically yield a random pattern of spins pointing up (blue cones) or down (red cones). In the initial paramagnetic state (bottom), spins align with the direction of the transverse magnetic field. Schematic depiction of the dynamics across a phase transition in a two-dimensional spin-1/2 model.
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