Probability of Slowroll Inflation in the Multiverse

Slowroll after tunneling is a crucial step in one popular framework of the multiverse---false vacuum eternal inflation (FVEI). In a landscape with a large number of fields, we provide a heuristic estimation for its probability. We find that the chance to slowroll is exponentially suppressed, where the exponent comes from the number of fields. However, the relative probability to have more e-foldings is only mildly suppressed as $N_e^{-\alpha}$ with $\alpha\sim3$. Base on these two properties, we show that the FVEI picture is still self-consistent and may have a strong preference between different slowroll models.Comment: version 3, 21 pages, resubmit to PRD recommanded by refere

The Strong Multifield Slowroll Condition and Spiral Inflation

We point out the existing confusions about the slowroll parameters and conditions for multifield inflation. If one requires the fields to roll down the gradient flow, we find that only articles adopting the Hubble slowroll expansion are on the right track, and a correct condition can be found in a recent book by Liddle and Lyth. We further analyze this condition and show that the gradient flow requirement is stronger than just asking for a slowly changing, quasi-de Sitter solution. Therefore it is possible to have a multifield slowroll model that does not follow the gradient flow. Consequently, it no longer requires the gradient to be small. It even bypasses the first slowroll condition and some related no-go theorems from string theory. We provide the "spiral inflation" as a generic blueprint of such inflation model and show that it relies on a monodromy locus---a common structure in string theory effective potentials.Comment: 12 pages, version 4, cosmetic changes recommended by referee, resubmitting to PR

Solitary Waves Bifurcated from Bloch Band Edges in Two-dimensional Periodic Media

Solitary waves bifurcated from edges of Bloch bands in two-dimensional periodic media are determined both analytically and numerically in the context of a two-dimensional nonlinear Schr\"odinger equation with a periodic potential. Using multi-scale perturbation methods, envelope equations of solitary waves near Bloch bands are analytically derived. These envelope equations reveal that solitary waves can bifurcate from edges of Bloch bands under either focusing or defocusing nonlinearity, depending on the signs of second-order dispersion coefficients at the edge points. Interestingly, at edge points with two linearly independent Bloch modes, the envelope equations lead to a host of solitary wave structures including reduced-symmetry solitons, dipole-array solitons, vortex-cell solitons, and so on -- many of which have never been reported before. It is also shown analytically that the centers of envelope solutions can only be positioned at four possible locations at or between potential peaks. Numerically, families of these solitary waves are directly computed both near and far away from band edges. Near the band edges, the numerical solutions spread over many lattice sites, and they fully agree with the analytical solutions obtained from envelope equations. Far away from the band edges, solitary waves are strongly localized with intensity and phase profiles characteristic of individual families.Comment: 23 pages, 15 figures. To appear in Phys. Rev.

Many-particle theory of nuclear systems with application to neutron star matter

The energy-density relation was calculated for pure neutron matter in the density range relevant for neutron stars, using four different hard-core potentials. Calculations are also presented of the properties of the superfluid state of the neutron component, along with the superconducting state of the proton component and the effects of polarization in neutron star matter

Adaptive primal-dual genetic algorithms in dynamic environments

This article is placed here with permission of IEEE - Copyright @ 2010 IEEERecently, there has been an increasing interest in applying genetic algorithms (GAs) in dynamic environments. Inspired by the complementary and dominance mechanisms in nature, a primal-dual GA (PDGA) has been proposed for dynamic optimization problems (DOPs). In this paper, an important operator in PDGA, i.e., the primal-dual mapping (PDM) scheme, is further investigated to improve the robustness and adaptability of PDGA in dynamic environments. In the improved scheme, two different probability-based PDM operators, where the mapping probability of each allele in the chromosome string is calculated through the statistical information of the distribution of alleles in the corresponding gene locus over the population, are effectively combined according to an adaptive Lamarckian learning mechanism. In addition, an adaptive dominant replacement scheme, which can probabilistically accept inferior chromosomes, is also introduced into the proposed algorithm to enhance the diversity level of the population. Experimental results on a series of dynamic problems generated from several stationary benchmark problems show that the proposed algorithm is a good optimizer for DOPs.This work was supported in part by the National Nature Science Foundation of China (NSFC) under Grant 70431003 and Grant 70671020, by the National Innovation Research Community Science Foundation of China under Grant 60521003, by the National Support Plan of China under Grant 2006BAH02A09, by the Engineering and Physical Sciences Research Council (EPSRC) of U.K. under Grant EP/E060722/1, and by the Hong Kong Polytechnic University Research Grants under Grant G-YH60