相关论文: Direct and reverse log-Sobolev inequalities in $\m…

We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching…

We consider a Moebius covariant sector, possibly with infinite dimension, of a local conformal net of von Neumann algebras on the circle. If the sector has finite index, it has automatically positive energy. In the infinite index case, we…

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential…

We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is…

Exact finite-energy solutions to the nonlinear governing equations of the Born-Infeld theory of electrodynamics, describing continuous distributions of electric, magnetic, and dyonic charge sources, in both classical and generalized…

The formalism of quantum systems with diagonal singularities is applied to describe scattering processes. Well defined states are obtained for infinite time, which are related to a ''weak form'' of intrinsic irreversibility. Real and…

In quantum information theory, it is widely believed that entanglement concentration for bipartite pure states is asymptotically reversible. In order to examine this, we give a precise formulation of the problem, and show a trade-off…

Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to $N_f$ Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a…

The present paper deals with the parabolic-parabolic Keller-Segel equation in the plane inthe general framework of weak (or "free energy") solutions associated to an initial datum with finite mass $M\textless{} 8\pi$, finite second…

I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst"…

Bukhvostov and Lipatov have shown that weakly interacting instantons and anti-instantons in the $O(3)$ non-linear sigma model in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. We propose an…

We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…

A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in…

We consider the mixed local/nonlocal semilinear equation \begin{equation*} -\epsilon^{2}\Delta u +\epsilon^{2s}(-\Delta)^s u +u=u^p\qquad \text{in } \Omega \end{equation*} with zero Dirichlet datum, where $\epsilon>0$ is a small parameter,…

Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several…

Consider the semigroup of random walk on a complete graph, which we call the Potts semigroup. Diaconis and Saloff-Coste computed the maximum of the ratio of the relative entropy and the Dirichlet form obtaining the constant $\alpha_2$ in…

We consider the stress tensor in the massless Sine--Gordon model in the finite regime $\beta^2 < 4 \pi$ of the theory. We prove convergence of the renormalised perturbative series for the interacting stress tensor defined using the…

We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…

In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an $L^{6}-$norm bound for the difference between general data and…

We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint…