相关论文: Relative entropy and modulated free energy without…
We consider mean-field limits for overdamped Langevin dynamics of $N$ particles with possibly singular interactions. It has been shown that a modulated free energy method can be used to prove the mean-field convergence or propagation of…
We prove by means of a renormalization group method that in weakly interacting many-electron systems at half-filling on a periodic hyper-cubic lattice, the free energy density uniformly converges to an analytic function of the coupling…
We derive the quantitative propagation of chaos in the sense of relative entropy for the first time for the 2D Log gas or the weakly interacting particle systems with 2D Coulomb interactions on the whole space. We resolve this problem by…
We derive quantitative propagation of chaos in the sense of relative entropy for the 2D viscous vortex model with general circulations, approximating the vorticity formulation of the 2D Navier-Stokes equation on the whole Euclidean space.…
We consider the mean-field limit of systems of particles with singular interactions of the type $-\log|x|$ or $|x|^{-s}$, with $0< s<d-2$, and with an additive noise in dimensions $d \geq 3$. We use a modulated-energy approach to prove a…
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method…
We consider conservative and gradient flows for $N$-particle Riesz energies with mean-field scaling on the torus $\mathbb{T}^d$, for $d\geq 1$, and with thermal noise of McKean-Vlasov type. We prove global well-posedness and relaxation to…
Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy…
The degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation…
This article shows how to combine the relative entropy method by D. Bresch, P.-E. Jabin, and Z. Wang in arXiv:1706.09564, arXiv:1906.04093 and the regularized $L^2(\mathbb{R}^d)$-estimate by Oelschl\"ager (Probability theory and related…
We develop a unified relative entropy framework for macroscopic limits of kinetic equations with Riesz-type interactions and Fokker-Planck relaxation. Our analysis covers three prototypical singular regimes: the diffusive limit leading to a…
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit \beta/a<<1 of a massive field theory in 3-dimensional spherical spaces M_3 with constant curvature 6/a^2. For…
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a…
Utilizing the Tomita-Takesaki modular theory, we derive a closed-form analytic expression for the Araki-Uhlmann relative entropy between a single-mode squeezed state and the vacuum state in a free relativistic massive scalar Quantum Field…
We derive a formula which applies to conformal field theories on a spatial torus and gives the asymptotic density of states solely in terms of the vacuum energy on a parallel plate geometry. The formula follows immediately from global scale…
We show that the energy of a perturbed system can be fully recovered from the unperturbed system's electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule and…
We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy between…
We develop a quantum relative entropy method for the mean-field limit of quantum many-body systems. For closed systems governed by the von Neumann equation, we prove a quantitative stability estimate between the $N$-body density matrix and…
This paper is an attempt to introduce methods and concepts of the Riemann-Cartan geometry largely used in such physical theories as general relativity, gauge theories, solid dynamics, etc. to fluid dynamics in general and to studying and…
We construct local minimizers to the Ginzburg-Landau functional of superconductivity whose number of vortices N is prescribed and blows up as the parameter epsilon, inverse of the Ginzburg-Landau parameter kappa, tends to zero. We treat the…