Fluctuating hydrodynamics theory could describe chaotic many-body systems, study finds

Although systems composed of many small interacting particles can be extremely complex and chaotic, some can still be described using simple theories. Does this also apply to the world of quantum physics?

A research team led by Professor Monika Aidelsburger and Professor Immanuel Bloch from the Faculty of Physics at LMU investigated this question regarding quantum many-body systems and found indications that they can be described macroscopically by simple diffusion equations with random noise. The study was recently published in the journal Physics of nature.

“If you want to describe the behavior of water flow, you don’t have to start with the physics of water molecules. Instead, you can formulate flow equations and analyze the problem on a purely macroscopic basis,” says Julian Wienand, a doctoral student in Immanuel Bloch’s research team and lead author of the new study.

This approach is known as hydrodynamics. However, when we observe the movement of small particles in water, we find that they are not only carried along by the current, but also perform small erratic movements called Brownian motions. These fluctuations are a direct consequence of the particles’ random collisions with individual water molecules.

“Because these erratic motions are random, we can describe them as white noise, and the hydrodynamics becomes fluctuating hydrodynamics (FHD),” Wienand explains. “It is remarkable that this FHD theory tells us that under certain circumstances the entire behavior of a system can be determined by a single quantity: the diffusion constant, even though the physics is very complex and chaotic at the microscopic level.” This greatly simplifies the macroscopic description of such systems and avoids having to tackle a description of the microscopic interactions of particles.

Does this also apply to quantum systems?

It is assumed that chaotic systems could be described in general by FHD. But the question of whether and to what extent this is also true for chaotic quantum systems remains largely open. The laws of physics that determine how quantum particles interact are fundamentally different from those governing classical particles and are characterized by phenomena such as “uncertainty” and “entanglement”, which defy everyday intuition. At the same time, quantum systems are even more difficult to calculate and could therefore particularly benefit from an FHD description.

The research team pursued this question by studying the behavior of chaotic many-body quantum systems under a microscope. To observe the dynamics, the team prepared a quantum system of ultracold cesium atoms in optical lattices in an initial nonequilibrium state and then allowed it to evolve freely.

“The high resolution of our imaging system allows us to measure not only the average density of particles in the lattice sites, but also their fluctuations,” Wienand explains. “We were thus able to measure the growth of density fluctuations and correlations over time and conclude that FHD describes our system both qualitatively and quantitatively.” The researchers consider this an important indication that chaotic quantum systems, despite their microscopic complexity, can be described simply as a macroscopic diffusion process, similar to Brownian motion.