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

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

Multi-scaling mix and non-universality between population and facility density

The distribution of facilities is closely related to our social economic activities. Recent studies have reported a scaling relation between population and facility density with the exponent depending on the type of facility. In this paper, we show that generally this exponent is not universal for a specific type of facility. Instead by using Chinese data we find that it increases with Per Capital GDP. Thus our observed scaling law is actually a mixture of some multi-scaling relations. This result indicates that facilities may change their public or commercial attributes according to the outside environment. We argue that this phenomenon results from the unbalanced regional economic level and suggest a modification for previous model by introducing consuming capacity. The modified model reproduces most of our observed properties.Comment: 6 pages, 5 figure

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

Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet

In this article we discuss the ground state of a parabolically confined quantum dots in the limit of very strong magnetic fields where the electron system is completely spin-polarized and all electrons are in the lowest Landau level. Without electron-electron interactions the ground state is a single Slater determinant corresponding to a droplet centered on the minimum of the confinement potential and occupying the minimum area allowed by the Pauli exclusion principle. Electron-electron interactions favor droplets of larger area. We derive exact criteria for the stability of the maximum density droplet against edge excitations and against the introduction of holes in the interior of the droplet. The possibility of obtaining exact results in the strong magnetic field is related to important simplifications associated with broken time-reversal symmetry in a strong magnetic field.Comment: 17 pages, 5 figures (not included), RevTeX 3.0. (UCF-CM-93-002