Lattice Study of Dense Matter with Two Colors and Four Flavors

We present results from a simulation of SU(2) lattice gauge theory with N_f=4 flavors of Wilson fermion and non-zero quark chemical potential mu, using the same 12^3x24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study with N_f=2. The string tension for N_f=4 is found to be considerably smaller implying smoother gauge field configurations. Thermodynamic observables and order parameters for superfluidity and color deconfinement are studied, and comparisons drawn between the two theories. Results for quark density and pressure as functions of mu are qualitatively similar for N_f=2 and N_f=4; in both cases there is evidence for a phase in which baryonic matter is simultaneously degenerate and confined. Results for the stress-energy tensor, however, suggest that while N_f=2 has a regime where dilute matter is non-relativistic and weakly-interacting, N_f=4 matter is relativistic and strongly-interacting for all values of mu above onset.Comment: Horizontal axes of several figures rescaled. Version accepted for publicatio

Application of the Maximum Entropy Method to the (2+1)d Four-Fermion Model

We investigate spectral functions extracted using the Maximum Entropy Method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma and massive pseudoscalar meson; our results confirm the Goldstone nature of the pi and permit an estimate of the meson binding energy. We have, however, seen no signal of sigma -> pi pi decay as the chiral limit is approached. In the symmetric phase we observe a resonance of non-zero width in qualitative agreement with analytic expectations; in addition the ultra-violet behaviour of the spectral functions is consistent with the large non-perturbative anomalous dimension for fermion composite operators expected in this model.Comment: 25 pages, 13 figure

Understanding the assembly of Kepler's compact planetary systems

The Kepler mission has recently discovered a number of exoplanetary systems, such as Kepler-11 and Kepler-32, in which ensembles of several planets are found in very closely packed orbits (often within a few percent of an AU of one another). These compact configurations present a challenge for traditional planet formation and migration scenarios. We present a dynamical study of the assembly of these systems, using an N-body method which incorporates a parametrized model of planet migration in a turbulent protoplanetary disc. We explore a wide parameter space, and find that under suitable conditions it is possible to form compact, close-packed planetary systems via traditional disc-driven migration. We find that simultaneous migration of multiple planets is a viable mechanism for the assembly of tightly-packed planetary systems, as long as the disc provides significant eccentricity damping and the level of turbulence in the disc is modest. We discuss the implications of our preferred parameters for the protoplanetary discs in which these systems formed, and comment on the occurrence and significance of mean-motion resonances in our simulations.Comment: 12 pages, 4 figures, 2 tables. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Probability Distribution Function of the Diquark Condensate in Two Colours QCD

We consider diquark condensation in finite density lattice SU(2). We first present an extension of Vafa-Witten result, on spontaneous breaking of vector-like global symmetries, that allows us to formulate a no-go theorem for diquark condensation in a region of the chemical potential-mass parameter space. We then describe a new technique to calculate diquark condensation at any number of flavours directly at zero external source without using any potentially dangerous extrapolation procedure. We apply it to the strong coupling limit and find compelling evidences for a second order phase transition, where a diquark condensate appears, as well as quantitative agreement between lattice results and low-energy effective Lagrangian calculations.Comment: 21 pages, 7 figure

Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical correction

Mesonic Wavefunctions in the three-dimensional Gross-Neveu model

We present results from a numerical study of bound state wavefunctions in the (2+1)-dimensional Gross-Neveu model with staggered lattice fermions at both zero and nonzero temperature. Mesonic channels with varying quantum numbers are identified and analysed. In the strongly coupled chirally broken phase at T=0 the wavefunctions expose effects due to varying the interaction strength more effectively than straightforward spectroscopy. In the weakly coupled chirally restored phase information on fermion - antifermion scattering is recovered. In the hot chirally restored phase we find evidence for a screened interaction. The T=0 chirally symmetric phase is most readily distinguished from the symmetric phase at high T via the fermion dispersion relation.Comment: 18 page

Numerical Portrait of a Relativistic Thin Film BCS Superfluid

We present results of numerical simulations of the 2+1d Nambu - Jona-Lasinio model with a non-zero baryon chemical potential mu including the effects of a diquark source term. Diquark condensates, susceptibilities and masses are measured as functions of source strength j. The results suggest that diquark condensation does not take place in the high density phase mu>mu_c, but rather that the condensate scales non-analytically with j implying a line of critical points and long range phase coherence. Analogies are drawn with the low temperature phase of the 2d XY model. The spectrum of the spin-1/2 sector is also studied yielding the quasiparticle dispersion relation. There is no evidence for a non-zero gap; rather the results are characteristic of a normal Fermi liquid with Fermi velocity less than that of light. We conclude that the high density phase of the model describes a relativistic gapless thin film BCS superfluid.Comment: 37 pages, 16 figure