Nonlinear and geometric effects in quantum condensed matter systems

NONTECHNICAL SUMMARY

This award supports theoretical research and education using hydrodynamics and geometric methods to describe unusual collective behavior of quantum electronic systems and active matter. Active matter consists of assemblies of self-driven particles and the PI focuses on the coordinated behavior of their constituents or their collective behavior. This project is also focused on the coordinated or collective behavior of electrons that can result from their strong interactions in diverse materials or devices.

The matter we observe around us consists of vast numbers of microscopic particles, atoms, molecules, ions, and electrons. Understanding the properties of the collections of a huge number of particles is crucial for technological progress. There are well-developed techniques of computing the properties of such systems when the constituent particles do not interact or interact only very weakly with each other.

In this case, the properties of the system can be obtained by summing over one-particle motions. Examples include the properties of gases or electrons in good metals.

When constituent particles interact strongly, the computation of collective properties of matter from microscopic properties of its constituent particles is much more challenging. For some kinds of matter, one of the powerful methods known is fluid dynamics. In fluid dynamics, the collective state of matter is characterized by fluid density, velocity, and temperature as they vary with time.

Instead of considering microscopic particles, physicists can more easily solve equations describing their collective behavior. The equations include viscosity, compressibility, thermal conductivity, and other fluid properties as parameters. The challenge is to derive those properties from microscopic properties and expand the range of validity and the scope of fluid dynamics applications.

The PI plans to apply fluid dynamics methods to quantum mechanical and classical systems with unusual characteristics such as the fluid of electrons in two dimensions in high magnetic field that gives rise to the quantum Hall effects, chiral materials, and chiral active matter. For these materials, the mirror image cannot be perfectly superimposed on the material or state of matter.

Chiral active fluids, for example, are composed of self-spinning rotors that continuously inject energy and angular momentum at the microscopic scale. The collective fluid dynamics of these materials are qualitatively different from the descriptions of conventional hydrodynamics.

Another part of the research involves the description of the limit shape phenomenon - the appearance of a most probable macroscopic state in random systems. This state is usually characterized by a well-defined boundary separating frozen and liquid spatial regions.

Teaching the basics of math and physics and communicating the values of cutting-edge research in modern physics to high school students is an essential part of the project. PI will continue to participate in the enrichment program for children in Stony Brook, in the science sleepaway camp for students 13-16-years old in Stony Brook, and the summer camp for gifted high school students in Russia.

TECHNICAL SUMMARY

This award supports theoretical research and education using hydrodynamic and geometric methods to study quantum and classical collective phenomena with a focus on electronic fluids and active matter. Recent decades brought a renewed interest in applications of topological and geometric methods in physics research. The overall trend of “geometrization of condensed matter physics” is characterized by the essential use of symmetries and effective descriptions of condensed matter systems.

Those descriptions often have geometric meanings facilitating the use of the existent and development of new mathematics. The broad field of topological phases of matter, studies of collective behavior of active systems, research in chaotic and out-of-equilibrium systems are just a few fields strongly affected by this approach.

The proposed research is in the field of theoretical condensed matter physics. It is unified using hydrodynamic and geometric methods in studies of quantum and classical collective phenomena. This project includes studies of anomalous fluids and odd transport coefficients, the interplay between topological degrees of freedom and effective boundary fluid dynamics, aspects of melting in Coulomb plasma in two dimensions, geometrical aspects of large fluctuations in low dimensional quantum fluids, and instanton effects on integrability breaking and chaotic behavior in one-dimensional quantum spin chains. It is expected that geometric ideas will be especially useful in understanding the above systems.

The character of the proposed research provides an excellent environment for the comprehensive training of graduate students. The tools developed in the described projects can be used in very different fields of physics: quantum many-body theory, integrable models, nonlinear dynamics, classical integrability, fluid dynamics, nuclear physics, cosmology, etc.

Part of the excitement of the proposed line of studies is due to the ability to apply findings across barriers, sometimes separating different areas of research. The obtained results can be verified by numerical simulations of correspondent systems and, ultimately, by comparison with experiments.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.