Zobrazeno 1 - 10
of 70
pro vyhledávání: '"Ammari, Zied"'
In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schr\"odinger and Hartree equations on the d-dimensional torus when d=1,2,3. Due to the focusing nature of the nonlinearity in these PDEs, Gibbs measures
Externí odkaz:
http://arxiv.org/abs/2412.05354
We consider the many-body quantum Gibbs state for the Bose-Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a mean-field limit where the temperature is of the order of th
Externí odkaz:
http://arxiv.org/abs/2405.04055
This article is concerned with the almost sure existence of global solutions for initial value problems of the form $\dot{\gamma}(t)= v(t,\gamma(t))$ on separable dual Banach spaces. We prove a general result stating that whenever there exists $(\mu_
Externí odkaz:
http://arxiv.org/abs/2305.17789
The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr's correspondence principle of quantum mecha
Externí odkaz:
http://arxiv.org/abs/2202.05015
In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics, in the semiclassical regime $\hslash\to 0$, with an interaction subject to an ultraviolet cutoff. We show that the transition amplitudes between fi
Externí odkaz:
http://arxiv.org/abs/2111.03352
Publikováno v:
In Advances in Mathematics September 2024 453
Autor:
Ammari, Zied, Sohinger, Vedran
The classical Kubo-Martin-Schwinger (KMS) condition is a fundamental property of statistical mechanics characterizing the equilibrium of infinite classical mechanical systems. It was introduced in the seventies by G. Gallavotti and E. Verboven as an
Externí odkaz:
http://arxiv.org/abs/2102.12202
Gross-Pitaevskii and Hartree hierarchies are infinite systems of coupled PDEs emerging naturally from the mean field theory of Bose gases. Their solutions are known to be related to an initial value problem, respectively the Gross-Pitaevskii and Hart
Externí odkaz:
http://arxiv.org/abs/1802.09041
Publikováno v:
Tunisian J. Math. 1 (2019) 221-272
We study, via multiscale analysis, some defect of compactness phenomena which occur in bosonic and fermionic quantum mean-field problems. The approach relies on a combination of mean-field asymptotics and second microlocalized semiclassical measures.
Externí odkaz:
http://arxiv.org/abs/1701.06423
Autor:
Ammari, Zied, Liard, Quentin
In this paper, we give a uniqueness result to a transport equation fulfilled by probability measure on a infinite dimensional Hilbert space. Main arguments are based on projective aspects and a probabilistic representation of the solutions. It extend
Externí odkaz:
http://arxiv.org/abs/1602.06716