From field theory to relativistic superfluids

Superfluidity is very general phenomenon which appears in a variety of physical systems. The corresponding critical temperatures of known superfluids extend over 17 orders of magnitude (from about 200 nK for cold atomic gases to up to 1010 K for nuclear and quark matter). On a macroscopic level, superfluidity is usually modeled by a two-fluid hydrodynamic system where the fluid is formally divided into a superfluid and normal fluid part. On a microscopic level, the basic ingredients for superfluidity are - at least in principle - well known: The spontaneous breaking of a continuous symmetry by a Bose-Einstein condensate together with the absence of elementary excitations, which could dissipate energy, allow for frictionless transport of the associated charge. However, the precise translation of microscopic physics into the hydrodynamic description is even today not completely understood. This often leads to misunderstandings between two separate communities (a phenomenological and a microscopic one) which are both equipped with their own terminology. In my past research as a graduate student, I thus pursued the goal to provide for the first time an explicit translation of a microscopic quantum field theory into (non dissipative) superfluid hydrodynamics and to study phenomenological aspects of superfluidity within this approach. In future, I would like to seek cooperation with experts in the field of compact stars physics at the Institute for Nuclear Theory (INT) in Seattle and use the results of my previous studies to investigate a wide range of fascinating astrophysical applications. This will be achieved in two steps: First, the existing derivation of hydrodynamic equations has to be subsequently extended in order to include the physics most relevant to the interior of a compact star. In the second step, I would like to use the framework derived in the first step to describe observable phenomena such as pulsar glitches or the so called r-mode instability of compact stars. In this context, in particular entrainment effects between different fluid components, a proper description of the crust of a compact star and vortices are important. The studies I propose in this application also aim to contribute to a fruitful symbiosis between astrophysics and fundamental interactions: A deeper understanding of dense hadronic matter from first principles allows for a more accurate modeling of compact stars whereas at the same time observations of compact stars can be used as a testing ground for fundamental physics. In both cases, superfluidity acts as an important link.

Neutron stars are formed by the gravitational collapse of the core of giant stars at the end of their life-cycles. Surpassed only by blackholes, they represent the densest stellar objects in the universe, rotate at enormous velocities, and exhibit extremely large magnetic fields. A particularly exciting prospect is the utilization of neutron stars as laboratories to study the properties of matter under extreme conditions. The first direct observation of a neutron star merger by several instruments and detectors on August 17 2017 underlines this prospect in a spectacular fashion. Several properties of neutron stars can be described particularly well using a hydrodynamical model. Hydrodynamics describe the motion of a fluid based on a simple set of equations, which reflect the conservation of mass, energy, and momentum. These equations need to be adapted to the specific system under consideration, taking into account its microscopical composition and properties. The primary goal of this project was to improve on the hydrodynamical description of neutrons stars. Owing to the complex composition of matter in their cores, several fluid components which potentially interact with each other had to be considered. In addition, macroscopic manifestations of quantum phenomena, in particular superfluidity (i.e., the frictionless motion of fluids), had to be taken into account. The obtained results may be used to obtain a better understanding of the spin evolution of neutron stars, to study the oscillation modes of neutron stars and potentially connect them with the emission of gravitational waves, and to improve current simulations of neutron star mergers.