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pro vyhledávání: '"Carlen, Eric"'
The Lane-Emden inequality controls $\iint_{\mathbb{R}^{2d}}\rho(x)\rho(y)|x-y|^{-\lambda}\,dx\,dy$ in terms of the $L^1$ and $L^p$ norms of $\rho$. We provide a remainder estimate for this inequality in terms of a suitable distance of $\rho$ to the m
Externí odkaz:
http://arxiv.org/abs/2410.20113
We study finite-dimensional open quantum systems whose density matrix evolves via a Lindbladian, $\dot{\rho}=-i[H,\rho]+{\mathcal D}\rho$. Here $H$ is the Hamiltonian of the isolated system and ${\mathcal D}$ is the dissipator. We consider the case w
Externí odkaz:
http://arxiv.org/abs/2408.06887
Autor:
Carlen, Eric A., Loss, Michael P.
We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the non Neumann entropy.
Comment: This version corrects several typos, includes a short discussion of cases of equality, and corrects a small
Comment: This version corrects several typos, includes a short discussion of cases of equality, and corrects a small
Externí odkaz:
http://arxiv.org/abs/2402.15920
In modeling phase transitions, it is useful to be able to connect diffuse interface descriptions of the dynamics with corresponding limiting sharp interface motions. In the case of the deep quench obstacle problem (DQOP) and surface diffusion (SD), w
Externí odkaz:
http://arxiv.org/abs/2312.11098
Autor:
Carlen, Eric A.
We apply a duality method to prove an optimal stability theorem for the logarithmic Hardy-Littlewood-Sobolev inequality, and we apply it to the estimation of the rate of approach to equilibrium for the critical mass Keller-Segel system.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2312.00614
Autor:
Carlen, Eric
This document presents the contents of three lectures delivered by the author at the Erd\H{o}s Center School ``Optimal Transport on Quantum Structures'', Septemer 19-23, 2022 in Budapest, Hungary. It presents a fairly self contained account of an act
Externí odkaz:
http://arxiv.org/abs/2306.10903
Autor:
Carlen, Eric A., Zhang, Haonan
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter sa
Externí odkaz:
http://arxiv.org/abs/2205.02342
Autor:
Carlen, Eric A., Loss, Michael P.
We compute the spectrum for a class of quantum Markov semigroups describing systems of $N$ particle interacting through a binary collision mechanism. These quantum Markov semgroups are associated to a novel kind of quantum random walk on graphs, with
Externí odkaz:
http://arxiv.org/abs/2204.07860
Autor:
Carlen, Eric A., Lieb, Elliott H.
The Golden-Thompson trace inequality which states that $Tr\, e^{H+K} \leq Tr\, e^H e^K$ has proved to be very useful in quantum statistical mechanics. Golden used it to show that the classical free energy is less than the quantum one. Here we make th
Externí odkaz:
http://arxiv.org/abs/2203.06136
Let $\phi$ be a linear map from the $n\times n$ matrices ${\mathcal M}_n$ to the $m\times m$ matrices ${\mathcal M}_m$. It is known that $\phi$ is $2$-positive if and only if for all $K\in {\mathcal M}_n$ and all strictly positive $X\in {\mathcal M}_
Externí odkaz:
http://arxiv.org/abs/2203.03433