Researchers from the Faculty of Physics at Warsaw University have made a groundbreaking discovery by proving that the equations of Navier-Stokes can be generalized for quantum systems, specifically for quantum fluids confined to one dimension. Their findings, which were recently published in the journal Physical Review Letters, have been recognized as highly significant by the editor.
The Navier-Stokes equations, which were formulated in the 19th century, serve as the foundation of hydrodynamics, explaining the movement of liquids and gases. These equations have widespread applications in various fields, from meteorology to medicine and the physics of elementary particles. However, adapting them to quantum systems has been a complex challenge.
The research conducted by the scientists from Warsaw University revolves around generalized hydrodynamics, a concept that considers multiple conservation laws unique to integrated quantum systems. Their work examines the impact of interactions that disrupt the system’s integrability, demonstrating that in such cases, the hydrodynamic equations must be supplemented with an additional term resembling the Boltzmann kinetic equation.
In addition to this breakthrough, the researchers also derived formulas for transfer coefficients like viscosity and thermal conductivity. They discovered that these values are comprised of two components: one stemming from integrated interactions and the other from disrupted integrability. This insight helps explain certain disparities between classical kinetic theory and empirical data.
This discovery holds not only theoretical value but also practical implications, particularly for studying ultra-cold quantum gases. Moving forward, the scientists aim to expand their theory to encompass more intricate systems.