Research project Deformed or disordered quantum liquids in and out of equilibrium
A project in mathematical physics to understand equilibrium and non-equilibrium properties of deformed or disordered quantum many-body systems.
Non-equilibrium physics opens the door to study exotic and counter-intuitive phenomena. Examples include stabilizing an inverted pendulum or suspending a liquid in air by vertical vibrations, even allowing one to float toy boats upside down in the otherwise non-existent bottom surface.
For quantum systems, related phenomena are actively studied, such as new quantum states of matter like Floquet topological insulators and time crystals. This is in large parts thanks to recent experimental advances on trapped ultra-cold atoms, which are experiments where atoms at very low temperatures are placed on an optical lattice created by lasers and used to simulate or even engineer quantum many-body systems. One reason why such experiments are important is their use for understanding collective properties of the large number of interacting particles that make up the simulated many-body system.
On the theoretical side, understanding these collective properties is a difficult task, often since the particles are too many to be studied numerically. This means that other approaches, which can capture the physics of these systems, are important to develop, for instance by reducing the full systems to the relevant degrees of freedom, length scales, sets of observables, or spatial dimensionality.
Two frameworks to address such questions within the scope of this project are quantum field theory and hydrodynamics, and particular importance is placed on exact analytical results to understand the resulting effective models in those frameworks.
Project description
The project centers on two topics: (i) Inhomogeneous quantum liquids, which concerns effective descriptions of a large class of quantum many-body systems with deformations or disorder, opening up a path to discover new collective properties and combines tools from quantum field theory, partial differential equations, and wave propagation in random media. (ii) Transport and emergent hydrodynamics, which concerns the study of energy or particle flows in quantum many-body systems and the difficult task of deriving effective hydrodynamic descriptions for them, which is an important outstanding problem in theoretical and mathematical physics. Being theoretical in nature, the aims of both topics are to address questions for quantum many-body systems in theoretical physics and mathematics, while connecting with experimental research on such systems.
