The Ubiquitous Throat

We attempt to quantify the widely-held belief that large hierarchies induced by strongly-warped geometries are common in the string theory landscape. To this end, we focus on the arguably best-understood subset of vacua -- type IIB Calabi-Yau orientifolds with non-perturbative Kaehler stabilization and a SUSY-breaking uplift (the KKLT setup). Within this framework, vacua with a realistically small cosmological constant are expected to come from Calabi-Yaus with a large number of 3-cycles. For appropriate choices of flux numbers, many of these 3-cycles can, in general, shrink to produce near-conifold geometries. Thus, a simple statistical analysis in the spirit of Denef and Douglas allows us to estimate the expected number and length of Klebanov-Strassler throats in the given set of vacua. We find that throats capable of explaining the electroweak hierarchy are expected to be present in a large fraction of the landscape vacua while shorter throats are essentially unavoidable in a statistical sense.Comment: References added, typos fixed. LaTex, 17 pages, 1 figur

Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [Appl. Math. Model., 46:450-464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work.Comment: 24 pages, 8 figures, accepted version of paper published in Applied Mathematics and Computatio

The Small Observed Baryon Asymmetry from a Large Lepton Asymmetry

Primordial Big-Bang Nucleosynthesis (BBN) tightly constrains the existence of any additional relativistic degrees of freedom at that epoch. However a large asymmetry in electron neutrino number shifts the chemical equilibrium between the neutron and proton at neutron freeze-out and allows such additional particle species. Moreover, the BBN itself may also prefer such an asymmetry to reconcile predicted element abundances and observations. However, such a large asymmetry appears to be in conflict with the observed small baryon asymmetry if they are in sphaleron mediated equilibrium. In this paper we point out the surprising fact that in the Standard Model, if the asymmetries in the electron number and the muon number are equal (and opposite) and of the size required to reconcile BBN theory with observations, a baryon asymmetry of the Universe of the correct magnitude and sign is automatically generated within a factor of two. This small remaining discrepancy is naturally remedied in the supersymmetric Standard Model.Comment: 14 page

Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

We give here the derivation of a Gross-Pitaevskii--type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided.Comment: Phys. Rev. A (accepted

Fast computation of effective diffusivities using a semi-analytical solution of the homogenization boundary value problem for block locally-isotropic heterogeneous media

Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the spatially-varying fine-scale diffusivity with an effective diffusivity calculated from the solution of an appropriate boundary value problem. In this paper, we present a new semi-analytical method for solving this boundary value problem and computing the effective diffusivity for pixellated, locally-isotropic, heterogeneous media. We compare our new solution method to a standard finite volume method and show that equivalent accuracy can be achieved in less computational time for several standard test cases. We also demonstrate how the new solution method can be applied to complex heterogeneous geometries represented by a grid of blocks. These results indicate that our new semi-analytical method has the potential to significantly speed up simulations of diffusion in heterogeneous media.Comment: 29 pages, 4 figures, 5 table

A Unified Theory of Matter Genesis: Asymmetric Freeze-In

We propose a unified theory of dark matter (DM) genesis and baryogenesis. It explains the observed link between the DM density and the baryon density, and is fully testable by a combination of collider experiments and precision tests. Our theory utilises the "thermal freeze-in" mechanism of DM production, generating particle anti-particle asymmetries in decays from visible to hidden sectors. Calculable, linked, asymmetries in baryon number and DM number are produced by the feeble interaction mediating between the two sectors, while the out-of-equilibrium condition necessary for baryogenesis is provided by the different temperatures of the visible and hidden sectors. An illustrative model is presented where the visible sector is the MSSM, with the relevant CP violation arising from phases in the gaugino and Higgsino masses, and both asymmetries are generated at temperatures of order 100 GeV. Experimental signals of this mechanism can be spectacular, including: long-lived metastable states late decaying at the LHC; apparent baryon-number or lepton-number violating signatures associated with these highly displaced vertices; EDM signals correlated with the observed decay lifetimes and within reach of planned experiments; and a prediction for the mass of the dark matter particle that is sensitive to the spectrum of the visible sector and the nature of the electroweak phase transition.Comment: LaTeX, 22 pages, 6 figure

Spacetime as a quantum many-body system

Quantum gravity has become a fertile interface between gravitational physics and quantum many-body physics, with its double goal of identifying the microscopic constituents of the universe and their fundamental dynamics, and of understanding their collective properties and how spacetime and geometry themselves emerge from them at macroscopic scales. In this brief contribution, we outline the problem of quantum gravity from this emergent spacetime perspective, and discuss some examples in which ideas and methods from quantum many-body systems have found a central role in quantum gravity research.Comment: 15 pages; invited contribution to "Many-body approaches at different scales: A tribute to Norman H. March on the occasion of his 90th birthday", edited by G. G. N. Angilella and C. Amovilli (New York, Springer, 2017 - to appear

Tunneling, self-trapping and manipulation of higher modes of a BEC in a double well

We consider an atomic Bose-Einstein condensate trapped in a symmetric one-dimensional double well potential in the four-mode approximation and show that the semiclassical dynamics of the two ground state modes can be strongly influenced by a macroscopic occupation of the two excited modes. In particular, the addition of the two excited modes already unveils features related to the effect of dissipation on the condensate. In general, we find a rich dynamics that includes Rabi oscillations, a mixed Josephson-Rabi regime, self-trapping, chaotic behavior, and the existence of fixed points. We investigate how the dynamics of the atoms in the excited modes can be manipulated by controlling the atomic populations of the ground states.Comment: 12 pages, 5 figure

The key role of off-axis singularities in free-space vortex transmutation

We experimentally demonstrate the generation of off-axis phase singularities in a vortex transmutation process induced by the breaking of rotational symmetry. The process takes place in free space by launching a highly-charged vortex, owning full rotational symmetry, into a linear thin diffractive element presenting discrete rotational symmetry. It is shown that off-axis phase singularities follow straight dark rays bifurcating from the symmetry axis. This phenomenon may provide new routes towards the spatial control of multiple phase singularities for applications in atom trapping and particle manipulation.Comment: 4 pages, 4 figures, to appear in Applied Physics B: Lasers and Optic