Related papers: A rigidity theorem for Kolmogorov-type operators
In this paper, we prove the $W$-entropy formula and the monotonicity and rigidity theorem of the $W$-entropy for the heat flow on RCD$(K, N)$ and RCD$(K, n, N)$ spaces $(X, d, \mu)$, where $K\in \mathbb{R}$, $n\in \mathbb{N}$ is the…
We study $Q$-ball type solitons in arbitrary spatial dimensions in the setting recently described by Kusenko, where the scalar field potential has a flat direction which rises much slower than $\phi^2$. We find that the general formula for…
We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the…
Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective…
We consider the parabolic Anderson model, the Cauchy problem for the heat equation with random potential in $Z^d$. We use i.i.d. potentials $\xi: Z^d \to \R$ in the third universality class, namely the class of almost bounded potentials, in…
The motion of strings on symmetric space target spaces underlies the integrability of the AdS/CFT correspondence. Although these theories, whose excitations are giant magnons, are non-relativistic they are classically equivalent, via the…
Let M be a closed embedded minimal hypersurface in a Euclidean sphere of dimension n+1, we prove that it is strongly rigid. As applications we confirm the conjecture proposed by Choi and Schoen in [3] and the Chern conjecture for n less…
Pure lattice gauge theories in three dimensions are widely expected to confine. A rigorous proof of confinement for three-dimensional $\mathrm{U}(1)$ lattice gauge theory with Villain action was given by G\"opfert and Mack. Beyond the…
We consider a possibly degenerate Kolmogorov-Ornstein-Uhlenbeck operator of the form L = Tr(BD 2) + Az, D , where A, B are N x N matrices, z $\in$ R N , N $\ge$ 1, which satisfy the Kalman condition which is equivalent to the…
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…
A finite set $X \seq \RR^n$ with a weight function $w : X \longrightarrow \RR_{>0}$ is called \emph{Euclidean $t$-design} in $\RR^n$ (supported by $p$ concentric spheres) if the following condition holds: \[ \sum_{i=1}^p…
The Klein-Gordon equation in D-dimensions for a recently proposed Kratzer potential plus ring-shaped potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound-states and the corresponding…
Quantum lattice models describe a wide array of physical systems, and are a canonical way to numerically solve the Schrodinger equation. Here we prove the potential inversion theorem, which says that wavefunction probability in these models…
A differential operator $D$ commuting with an $S^1$-action is said to be rigid if the non-constant Fourier coefficients of $\ker D$ and $\coker D$ are the same. Somewhat surprisingly, the study of rigid differential operators turns out to…
In this paper we prove some rigidity theorems associated to $Q$-curvature analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the analysis of conservation principles within fourth order gravitational theories. A…
The large N limit of SU(N) gauge theories in 3+1 dimensions is investigated on the lattice by extrapolating results obtained for $2 \le N \le 5$. A numerical determination of the masses of the lowest-lying glueball states and of the…
The Lie-Poisson algebra so(N+1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the ND spherical, Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly present a…
Let $(X,d,\mu )$ be a space of homogeneous type in the sense of Coifman and Weiss, i.e. $d$ is a quasi metric on $X$ and $\mu $ is a positive measure satisfying the doubling condition. Suppose that $u$ and $v$ are two locally finite…
We prove the equivalence between the integral central limit theorem and the local central limit theorem for two-body potentials with long-range interactions on the lattice $\mathbb{Z}^d$ for $d\ge 1$. The spin space can be an arbitrary,…
One-loop quantum corrections to the classical vortices in 2+1 dimensional O(3)-models are evaluated. Skyrme and Zeeman potential terms are used to stabilize the size of topological solitons. Contributions from zero modes, bound-states and…