Causal Fermions in Discrete Spacetime

In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete spacetime can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete spacetime that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete spacetime can be efficiently simulated on a quantum computer.Comment: 16 pages, 1 figur

Discrete Spacetime and Relativistic Quantum Particles

We study a single quantum particle in discrete spacetime evolving in a causal way. We see that in the continuum limit any massless particle with a two dimensional internal degree of freedom obeys the Weyl equation, provided that we perform a simple relabeling of the coordinate axes or demand rotational symmetry in the continuum limit. It is surprising that this occurs regardless of the specific details of the evolution: it would be natural to assume that discrete evolutions giving rise to relativistic dynamics in the continuum limit would be very special cases. We also see that the same is not true for particles with larger internal degrees of freedom, by looking at an example with a three dimensional internal degree of freedom that is not relativistic in the continuum limit. In the process we give a formula for the Hamiltonian arising from the continuum limit of massless and massive particles in discrete spacetime.Comment: 6 page

NLTE 1.5D Modeling of Red Giant Stars

Spectra for 2D stars in the 1.5D approximation are created from synthetic spectra of 1D non-local thermodynamic equilibrium (NLTE) spherical model atmospheres produced by the PHOENIX code. The 1.5D stars have the spatially averaged Rayleigh-Jeans flux of a K3-4 III star, while varying the temperature difference between the two 1D component models ($\Delta T_{\mathrm{1.5D}}$), and the relative surface area covered. Synthetic observable quantities from the 1.5D stars are fitted with quantities from NLTE and local thermodynamic equilibrium (LTE) 1D models to assess the errors in inferred $T_{\mathrm{eff}}$ values from assuming horizontal homogeneity and LTE. Five different quantities are fit to determine the $T_{\mathrm{eff}}$ of the 1.5D stars: UBVRI photometric colors, absolute surface flux SEDs, relative SEDs, continuum normalized spectra, and TiO band profiles. In all cases except the TiO band profiles, the inferred $T_{\mathrm{eff}}$ value increases with increasing $\Delta T_{\mathrm{1.5D}}$. In all cases, the inferred $T_{\mathrm{eff}}$ value from fitting 1D LTE quantities is higher than from fitting 1D NLTE quantities and is approximately constant as a function of $\Delta T_{\mathrm{1.5D}}$ within each case. The difference between LTE and NLTE for the TiO bands is caused indirectly by the NLTE temperature structure of the upper atmosphere, as the bands are computed in LTE. We conclude that the difference between $T_{\mathrm{eff}}$ values derived from NLTE and LTE modelling is relatively insensitive to the degree of the horizontal inhomogeneity of the star being modeled, and largely depends on the observable quantity being fit.Comment: 46 pages, 14 figures, 7 tables, accepted for publication in ApJ on April 5, 201

Combining Semi-Analytic Models of Galaxy Formation with Simulations of Galaxy Clusters: the Need for AGN Heating

We present hydrodynamical N-body simulations of clusters of galaxies with feedback taken from semi-analytic models of galaxy formation. The advantage of this technique is that the source of feedback in our simulations is a population of galaxies that closely resembles that found in the real universe. We demonstrate that, to achieve the high entropy levels found in clusters, active galactic nuclei must inject a large fraction of their energy into the intergalactic/intracluster media throughout the growth period of the central black hole. These simulations reinforce the argument of Bower et al. (2008), who arrived at the same conclusion on the basis of purely semi-analytic reasoning.Comment: 4 pages, 1 figure. To appear in the proceedings of "The Monster's Fiery Breath", Eds. Sebastian Heinz and Eric Wilcots (AIP conference series