A quantum system consisting of only 51 charged atoms can assume more than two quadrillion different states. Calculating the system's behavior is a piece of cake for a quantum simulator. Yet even with today's supercomputers it is almost impossible to verify the result. A research team from the University of Innsbruck and the Technical University of Munich (TUM) has now shown how these systems can be described using equations from the 18th century.
At first glance, a system consisting of 51 ions may appear simple. But even if these charged atoms can only assume two different states, there will be more than two quadrillion (1015) different configurations which the system can realize.
The behavior of such a system can therefore hardly be calculated with conventional computers. Especially since once an excitation has been introduced into the system, it can propagate in leaps and bounds. It follows a statistic known as Lévy flight.
A characteristic of the movement of such a quantum particle is that, in addition to the smaller jumps, also significantly larger jumps occur. This phenomenon can also be observed in the flight of bees and in unusual fierce movements in the stock market.
Simulating quantum dynamics: A classically hard problem
While simulating the dynamics of a complex quantum system is a very hard problem even for today's super computers, the task is a piece of cake for quantum simulators. But how are you supposed to check the results of a quantum simulator when you cannot recalculate them?
Theoretical predictions suggested that it might be possible to represent at least the long-term behavior of such systems with equations as those developed by the Bernoulli brothers in the 18th century to describe the behavior of fluids.
To test this hypothesis, the research team used a quantum system that simulates the dynamics of quantum magnets. With this they were able to show that after an initial regime in which quantum-mechanical effects dominate, the system can be described by equations known from fluid dynamics.
Furthermore, they showed that the very same Lévy flight statistics which describes the search strategies of bees also describes the fluid-dynamics in this quantum system.
Publications:
Observing emergent hydrodynamics in a long-range quantum magnet
M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, C. F. Roos
Science, 13.05.2022 - DOI: 10.1126/science.abk2400
