Related papers: Sharp decay estimates for critical Dirac equations

In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.

We study the behavior of the spectrum of the Dirac operator on degenerating families of compact Riemannian surfaces, when the length $t$ of a simple closed geodesic shrinks to zero, under the hypothesis that the spin structure along the…

It is shown how to embed a critical point in a smooth background equation of state so as to yield the critical exponents and critical amplitude ratios expected of a transition in the same universality class as the liquid-gas phase…

We study positive solutions to the heat equation on graphs. We prove variants of the Li-Yau gradient estimate and the differential Harnack inequality. For some graphs, we can show the estimates to be sharp. We establish new computation…

We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single point blow-up property for this equation and determine its final blow-up profile. We also give a sharper…

We revisit the Dicke superradiance problem, where an ensemble of N identical two-level systems undergoes collective spontaneous decay. While an exact analytical solution has been known since 1977, its algebraic complexity has hindered…

We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in $n=3$ dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping…

The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…

In this paper we prove global well-posedness and scattering for the defocusing, intercritical nonlinear wave equation in dimensions $d \geq 4$ with radial initial data. We prove this for sharp initial data.

We investigate the asymptotic stability of a tropical climate model posed on $\bR^2$, with temperature-dependent diffusion in the barotropic mode $u$ and linear damping in the first baroclinic mode $v$. We consider two distinct cases for…

The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…

We prove pointwise-in-time dispersive decay for solutions to the energy-critical nonlinear Schr\"odinger equation in spatial dimensions $d = 3,4$ for both the initial-value and final-state problems.

Using analysis for 2-admissible functions in weighted Sobolev spaces and stochastic calculus for possibly degenerate symmetric elliptic forms, we construct weak solutions to a wide class of stochastic differential equations starting from an…

In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…

We consider decays of the lowest-lying radially excited baryons. Assuming a single-quark decay approximation, and negligible configuration mixing, we make model-independent predictions for the partial decay widths to final states with a…

We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke…

We prove the first classification of blow-up rates of the critical norm for solutions of the energy supercritical nonlinear heat equation, without any assumptions such as radial symmetry or sign conditions. Moreover, the blow-up rates we…

We prove global weighted Strichartz estimates for radial solutions of linear Schr\"odinger equation on a class of rotationally symmetric noncompact manifolds, generalizing the known results on hyperbolic and Damek-Ricci spaces. This yields…

We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our derivation, the TAP equations are a simple consequence of the…

Binder-cumulant analysis of the critical point in the heavy-quark region of QCD is performed by Monte-Carlo simulations with the hopping-parameter expansion at $N_t=6$. We extend our previous analysis at $N_t=4$ to finer lattices and…