Aspects of Parity Breaking in Classical and Quantum Fluids
Parity-breaking is ubiquitous across many scales of physics, from the rotation of galaxies at the largest of scales, to the cyclotron orbits of electrons at the microscopic scale. In describing the collective dynamics of many particle systems, parity breaking effects typically originate from some form of chirality, such as angular momentum, at the level of the constituent particles. External forces can also induce chiral motion, with the primary examples being the Lorentz and Coriolis forces. The effects of parity breaking are perhaps most strikingly seen in active matter, systems of complex particles that tend to convert energy into some directed mechanical motion. Within a fluid description additional transport coefficients arise, beyond shear viscosity, which capture the parity broken nature of the flow. In 2D this is encapsulated by odd viscosity, a unique and well studied transport coefficient which is neither dissipative nor invariant under parity symmetry. On the other hand, parity breaking in 3D is described by a much larger class of viscosity coefficients, and is still a very active area of research. Notably, while parity breaking effects in 2D tend to be localized to system boundaries, 3D parity broken flows display novel effects even in the bulk. In a similar fashion, quantum system with internal or external parity breaking will generate observable signatures, such as point vortices in the bulk, and chiral modes that propagate along a boundary. When recast as a hydrodynamic problem these effects are readily studied by use of the familiar fluid boundary conditions, which can always be formulated as a no-penetration condition and either no-slip or no-stress conditions. Within a hydrodynamic framework, the properties of the bulk matter fields naturally flow into the properties of the edge. Additionally, quantum fluids always contain an additional constraint on the fluid vorticity, quite unique from their classical counterparts. In this thesis we investigate some classical and quantum systems that display features of parity breaking, in particular the modification to bulk flows in 3D, and the boundary effects in 2D. We begin with a general overview of fluid dynamics. Within a first order gradient expansion, we outline the different types of transport coefficients allowed by symmetry. With classical fluids, we start with a review of active matter, emphasizing the aspects that apply to general parity broken flows. We then detail our work on experimental probes of parity breaking effects, namely the Hele-Shaw cell. We also explore how these effects may manifest in a ferrofluid. In the second half of this thesis we move to quantum systems, beginning with the fractional quantum Hall effect. Starting with a microscopic theory of electrons in an external magnetic field, we demonstrate how a hydrodynamic description naturally arises. We then give a general review of how hydrodynamic equations arise in other quantum systems. We finish by seeing how this plays out in driven-dissipative polariton fluids and rotating Bose Einstein condensates.
Condensed Matter Physics, Fluid Dynamics
City University of New York - Graduate Center
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