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Keywords = vortex, fractional quantization

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35 pages, 534 KB  
Article
Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance
by Lorenzo Gavassino, Marco Antonelli and Brynmor Haskell
Universe 2021, 7(2), 28; https://doi.org/10.3390/universe7020028 - 29 Jan 2021
Cited by 15 | Viewed by 3477
Abstract
We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact [...] Read more.
We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons is locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system. Full article
(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)
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15 pages, 306 KB  
Article
Zero-Energy Modes, Fractional Fermion Numbers and The Index Theorem in a Vortex-Dirac Fermion System
by Takashi Yanagisawa
Symmetry 2020, 12(3), 373; https://doi.org/10.3390/sym12030373 - 2 Mar 2020
Cited by 3 | Viewed by 4104
Abstract
Physics of topological materials has attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological superconductors. A zero-energy mode exists when Dirac fermions couple to objects [...] Read more.
Physics of topological materials has attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological superconductors. A zero-energy mode exists when Dirac fermions couple to objects with soliton-like structure such as kinks, vortices, monopoles, strings, and branes. We discuss a system of Dirac fermions interacting with a vortex and a kink. This kind of systems will be realized on the surface of topological insulators where Dirac fermions exist. The fermion number is fractionalized and this is related to the presence of fermion zero-energy excitation modes. A zero-energy mode can be regarded as a Majorana fermion mode when the chemical potential vanishes. Our discussion includes the case where there is a half-flux quantum vortex associated with a kink in a magnetic field in a bilayer superconductor. A normalizable wave function of fermion zero-energy mode does not exist in the core of the half-flux quantum vortex. The index of Dirac operator and the fermion number have additional contributions when a soliton scalar field has a singularity. Full article
(This article belongs to the Special Issue Vortex, Topology and Singularity in Quantum Systems)
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