I work on the hydrodynamics of non-linear Luttinger liquids. In one dimension, the low energy properties of a system have long been known to be described by the Luttinger liquid, a quantum mechanical state comprising of non-interacting, non-dispersing density waves. In recent years it has been realised that this description falls short in resolving quantities such as the density-density response function at fixed momentum, which is necessarily a delta-function peak if the density waves cannot decay. Calculating perturbatively in the ratio of interaction to dispersion, we can zoom in on the response function in the vicinity of the classical solutions to the hydrodynamic theory. We are currently interested in whether this non-linear dynamics may be found at the quantum Hall edge, and whether there is a connection to the bulk "odd viscosity" transport coefficient.
In Plain English
My research concentrates on the properties of one dimensional quantum fluids. Here, "one dimensional" means that to a good approximation, the fluid is only free to move in one direction. "Quantum" means that the temperature of the fluid is so low that quantum-mechanical phenomena become important for a description of the fluid. Such systems are particularly interesting to theorists, as many more tricks are available to solve problems that would be intractable in higher dimensions.
As well as being of intrinsic interest to the theorist, essentially one-dimensional systems can be found in highly anisotropic crystals, quantum wires, and on the edge of the incompressible two-dimensional electron gas trapped between two semiconductors that forms the mysterious quantum Hall state.
- The Fine Structure of the Phonon in One Dimension from Quantum Hydrodynamics