We report on the observation of spontaneously drifting coupled spin and quadrupolar density waves in the ground state of laser driven Rubidium atoms. These laser-cooled atomic ensembles exhibit ...spontaneous magnetism via light mediated interactions when submitted to optical feedback by a retroreflecting mirror. Drift direction and chirality of the waves arise from spontaneous symmetry breaking. The observations demonstrate a novel transport process in out-of-equilibrium magnetic systems.
We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal ...contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$-insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D. Specializing to
$(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E. Specializing further to $S={\mathbb P}^2$, we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve. Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$, we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. ...As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.
Alday & Maldacena conjectured an equivalence between string amplitudes in AdS$_5 \times S^5$ fixed by null polygonal boundaries in Minkowski-space with both amplitudes and Wilson loops in planar ...$\mathcal{N}=4$ super-Yang-Mills (SYM). At strong coupling this leads to an identification of SYM amplitudes with areas of minimal surfaces in AdS. Together with Gaiotto, Sever & Vieira, they introduced a `Y-system' for computing this area. We first establish a correspondence between Y-systems and twistor spaces that will apply more generally, and which, in the cases considered here determine a geometry on the space of kinematic data. In the case of minimal surfaces in AdS$_3$ with boundaries on null polygons with $4k+2$ edges, we show that the geometry in question is a split signature pseudo-hyperkähler structures and that the remainder function for the amplitude is a Plebanski scalar that generates the geometry. This geometry leads to explicit overdetermined completely integrable systems of differential equations for the area, and we also give its Lax system.
The heat transport by rapidly rotating Rayleigh-Bénard convection is of fundamental importance to many geophysical flows. Laboratory measurements are impeded by robust wall modes that develop along ...vertical walls, significantly perturbing the heat flux. We show that narrow horizontal fins along the vertical walls efficiently suppress wall modes ensuring that their contribution to the global heat flux is negligible compared with bulk convection in the geostrophic regime, thereby paving the way for new experimental studies of geophysically relevant regimes of rotating convection.
For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of ...a ground state of the Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.
This paper provides a comprehensive study of the dimer model on infinite minimal graphs with Fock's elliptic weights Foc15. Specific instances of such models were studied in BdTR17, BdTR18, dT17; we ...now handle the general genus 1 case, thus proving a non-trivial extension of the genus 0 results of Ken02, KO06 on isora-dial critical models. We give an explicit local expression for a two-parameter family of inverses of the Kasteleyn operator with no periodicity assumption on the underlying graph. When the minimal graph satisfies a natural condition, we construct a family of dimer Gibbs measures from these inverses, and describe the phase diagram of the model by deriving asymptotics of correlations in each phase. In the Z 2-periodic case, this gives an alternative description of the full set of ergodic Gibbs measures constructed in KOS06. We also establish a correspondence between elliptic dimer models on periodic minimal graphs and Harnack curves of genus 1. Finally, we show that a bipartite dimer model is invariant under the shrinking/expanding of 2-valent vertices and spider moves if and only if the associated Kasteleyn coefficients are antisymmetric and satisfy Fay's trisecant identity.
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