Distribution Of Field Values Research Articles

Chaotic solitons in driven sine-Gordon model

Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially different if the respective mechanical motions are chaotic. This happens in multifield models and models with spatially dependent potential. We illustrate our findings using one-field sine-Gordon model in external Dirac comb potential. First, we show that the number of different "chaotic" solitons grows exponentially with their length, and the growth rate is related to the topological entropy of the mechanical system. Second, the field values of stable solitons form a fractal; we compute its box-counting dimension. Third, we demonstrate that the distribution of field values in the fractal is related to the metric entropy of the analogous mechanical system.

Statistics of inflating regions in eternal inflation

We compute the distribution of sizes of inflating and non-inflating regions in an eternally inflating Universe. As a first illustrative problem, we study a simple scenario of an eternally inflating Universe in the presence of a massless scalar field $\varphi$ whose field values lie within some finite domain $\varphi\in(-\varphi_{cr},\varphi_{cr})$, with $\pm\varphi_{cr}$ marking the onset of thermalization/crunching. We compute many important quantities, including the fractal dimension, distribution of field values among inflating regions, and the number of inflating and non-inflating Hubble regions. With the aid of simulations in 1 spatial dimension, we show this eternally inflating Universe reaches a steady state in which average sizes of inflating regions grow only as a power law in the field's crunch value $\sim \varphi_{cr}^2$ (extension to higher dimensions is $\sim\varphi^{2/D}$), contrary to a naive expectation of an exponential dependence. Furthermore, the distribution in sizes exhibits an exponential fall off for large distances (with an initial power law for inflating regions). We leave other interesting cases of more realistic potentials and time varying Hubble parameter for future work, with a possible application to the SM Higgs in the early Universe.

μSR studies of the vortex lattice in high-T c and other superconductors

We review some of the assumptions made in the use of muon spin rotation in superconductors: i.e. that the muons are implanted at random positions in the flux lattice, remain static after implantation and do not appreciably affect the properties of the surrounding superconductor; also that the flux lines are straight and static, and that the observed muon rotation frequency spectrum reflects the microscopic distribution of field values. We shall show how evidence for and against the truth of these assumptions in particular cases may be obtained from the μSR results themselves or by comparison with other measurements, and how this in turn may lead to deeper understanding of flux line structure and motion in superconductors.