Results 271 to 280 of about 773,321 (331)

Analysis of density matrix embedding theory around the non‐interacting limit

open access: yesCommunications on Pure and Applied Mathematics, EarlyView.
Abstract This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground‐state density matrix is a fixed‐point of the DMET map for non‐interacting systems, (ii) there exists a unique physical solution in the weakly‐interacting regime, and (iii ...
Eric Cancès   +4 more
wiley   +1 more source

First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet

open access: yesCommunications on Pure and Applied Mathematics, EarlyView.
Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley   +1 more source

The porous medium equation: Large deviations and gradient flow with degenerate and unbounded diffusion

open access: yesCommunications on Pure and Applied Mathematics, EarlyView.
Abstract The problem of deriving a gradient flow structure for the porous medium equation which is thermodynamic, in that it arises from the large deviations of some microscopic particle system is studied. To this end, a rescaled zero‐range process with jump rate g(k)=kα,α>1$g(k)=k^\alpha, \alpha >1$ is considered, and its hydrodynamic limit and ...
Benjamin Gess, Daniel Heydecker
wiley   +1 more source

Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature

open access: yesCommunications on Pure and Applied Mathematics, EarlyView.
Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli   +2 more
wiley   +1 more source

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