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We numerically simulate the motion of a black hole as it plunges radially through an ultralight dark matter soliton. We investigate the timescale in which dynamical friction reduces the kinetic energy of the black hole to a minimum, and consider the sensitivity of this timescale to changes in the ULDM particle mass, the total soliton mass, and the mass of the black hole. We contrast our numerical results with a semi-analytic treatment of dynamical friction, and find that the latter is poorly suited to this scenario. In particular, we find that the back-reaction of the soliton to the presence of the black hole is significant, resulting in oscillations in the coefficient of dynamical friction which cannot be described in the simple semi-analytical framework. Furthermore, we observe a late-time reheating effect, in which a significant amount of kinetic energy is transferred back to the black hole after an initial damping phase. This complicates the discussion of ULDM dynamical friction on the scales relevant to the final parsec problem., Comment: 15 pages

Ultralight dark matter (ULDM) is an interesting alternative to the cold dark matter (CDM) paradigm. Due to the extremely low mass of the constituent particle ($\sim 10^{-22}$ eV), ULDM can exhibit quantum effects up to kiloparsec scales. In particular, runaway collapse in the centres of ULDM halos is prevented by quantum pressure, providing a possible resolution to the 'core-cusp problem' of CDM. However, the the detailed relationship between the ULDM core mass and that of the overall halo is poorly understood. We simulate the collapse of both spherical and aspherical isolated ULDM overdensities using AxioNyx, finding that the central cores of collapsed halos undergo sustained oscillatory behaviour which affects both their peak density and overall morphology. The variability in core morphology increases with the asphericity of the initial overdensity and remnants of initial asphericity persist long after collapse. Furthermore, the peak central densities are higher in spherical configurations. Consequently, astrophysically realistic halos may exhibit substantial departures from theoretical core-halo profiles and we would expect a significant variance of the properties of halos with the same mass., Comment: 11 pages, 11 figures

In this Working Paper we analyse computational strategies for using aggregated spatio-temporal population data acquired from telecommunications networks to infer travel and movement patterns between geographical regions. Specifically, we focus on hour-by-hour cellphone counts for the SA-2 geographical regions covering the whole of New Zealand. This Working Paper describes the implementation of the inference algorithms, their ability to produce models of travel patterns during the day, and lays out opportunities for future development., Comment: Submitted to Covid-19 Modelling Aotearoa

Ultralight dark matter (ULDM) is usually taken to be a single scalar field. Here we explore the possibility that ULDM consists of $N$ light scalar fields with only gravitational interactions. This configuration is more consistent with the underlying particle physics motivations for these scenarios than a single ultralight field. ULDM halos have a characteristic granular structure that increases stellar velocity dispersion and can be used as observational constraints on ULDM models. In multifield simulations, we find that inside a halo the amplitude of the total density fluctuations decreases as $1/\sqrt{N}$ and that the fields do not become significantly correlated over cosmological timescales. Smoother halos heat stellar orbits less efficiently, reducing the velocity dispersion relative to the single field case and thus weakening the observational constraints on the field mass. Analytically, we show that for $N$ equal-mass fields with mass $m$ the ULDM contribution to the stellar velocity dispersion scales as $1/(N m^3)$. Lighter fields heat the most efficiently and if the smallest mass $m_L$ is significantly below the other field masses the dispersion scales as $1/(N^2 m_L^3)$., Comment: 11 pages, 7 figures, to be submitted to PRD

UltraLight Dark Matter (ULDM) is an axion-like dark matter candidate with an extremely small particle mass. ULDM halos consist of a spherically symmetric solitonic core and an NFW-like skirt. We simulate halo creation via soliton mergers and use these results to explore the core-halo mass relation. We calculate the eigenstates of the merged halos and use these to isolate the solitonic core and calculate its relative contribution to the halo mass. We compare this approach to using a fitting function to isolate the core and find a difference in masses up to 30%. We analyze three families of simulations: equal-mass mergers, unequal-mass mergers, and halos with a two-step merger history. Setting the halo mass to the initial mass in the simulation does not yield a consistent core-halo relationship. Excluding material "ejected" by the collision yields a core-halo relationship with a slope of 1/3 for simultaneous mergers and roughly 0.4 for two-step mergers. Our findings suggest there is no universal core-halo mass relationship for ULDM and shed light on the differing results for the core-halo relationship previously reported in the literature., Comment: 10 pages, 8 figures; published in PRD, updated with referee changes

In this work, we investigate the parameters governing the rate at which a quantum channel arises at the onset of an interaction between two systems, $A$ and $B$. In particular, when system $A$ is pre-entangled with an ancilla, $\tilde{A}$, we quantify the early-time transmission of pre-existing entanglement by calculating the leading order change in coherent information of the complementary channel ($A\rightarrow B'$). We show that, when $A$ and $B$ are initially unentangled and $B$ is pure, there is no change in coherent information to first order, while the leading (second) order change is divergent. However, this divergence may be regulated by embedding the conventional notion of coherent information into what we call the family of $n$-coherent informations, defined using $n$-R\'enyi entropies. We find that the rate of change of the $n$-coherent information at the onset of the interaction is governed by a quantity, which we call the $n$-exposure, which captures the extent to which the initial coherent information of $A$ with $\tilde{A}$ is exposed to or `seen by' the interaction Hamiltonian between $A$ and $B$. We give examples in qubit systems and in the light-matter interaction., Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretical

In this work we present an algorithm with which any arbitrary cubic planar map may be constructed through successive edge insertion while simultaneously constructing a set of proper edge labels and Hamiltonian cycles for each configuration. We present a publicly available Python implementation of this algorithm, and discuss both theoretical and numerical support for its validity, with reference to the well-known Four Colour Theorem.

At the onset of an interaction between two initially independent systems, each system tends to experience an increase in its n-Renyi entropies, such as its von Neumann entropy (n = 1) and its mixedness (n = 2). We here ask which properties of a system determine how quickly its Renyi entropies increase and, therefore, how sensitive the system is to becoming entangled. We find that the rate at which the n-Renyi entropy increases in an interaction is determined by a quantity which we term the n-fragility of the system. The 2-fragility is closely related to the notion of 2-norm coherence, in that it too quantifies the extent to which a density matrix is off-diagonal with respect to the eigenbasis of a reference operator. Nevertheless, the 2-fragility is not a coherence monotone in the resource theoretic sense since it depends also on the eigenvalues of the reference operator. It is this additional sensitivity to the eigenvalues of the reference operator, here the interaction Hamiltonian, which enables the 2-fragility to quantify the rate of entropy production in interactions. We give an example using the light-matter interaction and we anticipate applications to the study of the rates at which two systems exchange classical and quantum information when starting to interact., Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretical

The core-cusp problem is a widely cited motivation for the exploration of dark matter models beyond standard CDM. One such alternative is ULDM; extremely light scalar particles exhibiting wavelike properties on kiloparsec scales. Astrophysically realistic ULDM halos are expected to consist of inner solitonic cores embedded in NFW-like outer halos. The presence of the solitonic core suggests that ULDM may resolve the core-cusp discrepancy associated with pure NFW halos without recourse to baryonic physics. However, it has been demonstrated that the density of ULDM halos can exceed those of comparable NFW configurations at some radii and halo masses, apparently exacerbating the problem rather than solving it. This situation arises because, although solitonic cores are flat at their centres, they obey an inverse mass-radius scaling relationship. Meanwhile, the mass of the inner soliton increases with the total halo mass, and therefore the inner core becomes more peaked at large halo masses. We describe a parameterisation of the radial density profiles of ULDM halos that allows for environmental variability of the core-halo mass relation in order to investigate this issue in more detail. For halos up to 10^12 solar masses we find feasible ULDM profiles for which the central density is lower than their NFW counterparts at astrophysically accessible radii. However, comparisons to observed profiles do not strongly favour either option; both give reasonable fits to subsets of the data for some parameter choices. Consequently, we find that robust tests of the core-cusp problem in ULDM will require more comprehensive observational data and simulations that include baryonic feedback., Comment: 15 pages, accepted for publication in PASA

PyUltraLight simulates the dynamics of ultralight dark matter in a non-expanding background. PyUltraLight can describe the evolution of several interacting ultralight dark matter halos or one or more halos orbiting a central, fixed Newtonian potential, the latter scenario corresponding to dwarf galaxies orbiting a massive central galaxy. We verify PyUltraLight by showing that it reproduces qualitative dynamical features of previously published simulations and demonstrate that it has excellent energy-conservation properties. PyUltraLight is implemented in a Python-based Jupyter notebook, solving the Schrodinger-Poisson equation governing ultralight scalar field dark matter dynamics in the non-relativistic regime using a symmetrised split-step pseudospectral algorithm. The notebook interface makes it simple to specify simulation parameters and visualise the resulting output but performance-critical routines are managed via calls to computationally efficient compiled libraries. PyUltraLight runs on standard desktop hardware with support for shared memory mutlithreading and is available on GitHub., Comment: available at: https://github.com/auckland-cosmo/PyUltraLight