Zobrazeno 1 - 10
of 88
pro vyhledávání: '"Sohinger, Vedran"'
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
Autor:
Rout, Andrew, Sohinger, Vedran
In this work, we obtain a microscopic derivation of Gibbs measures for the focusing quintic nonlinear Schr\"{o}dinger equation (NLS) on $\mathbb{T}$ from many-body quantum Gibbs states. On the quantum many-body level, the quintic nonlinearity corresp
Externí odkaz:
http://arxiv.org/abs/2308.06569
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
Autor:
Rout, Andrew, Sohinger, Vedran
Publikováno v:
Communications in Partial Differential Equations 48 (2023), no. 7-8, 1008-1055
In this paper, we give a microscopic derivation of Gibbs measures for the focusing cubic nonlinear Schr\"odinger equation on the one-dimensional torus from many-body quantum Gibbs states. Since we are not making any positivity assumptions on the inte
Externí odkaz:
http://arxiv.org/abs/2206.03392
We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the interaction be
Externí odkaz:
http://arxiv.org/abs/2201.07632
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
We study interacting Bose gases in thermal equilibrium on a lattice. We establish convergence of the grand canonical Gibbs states of such gases to their mean-field (classical field) and large-mass (classical particle) limits. The former is a classica
Externí odkaz:
http://arxiv.org/abs/2012.05110
We review some recent results on interacting Bose gases in thermal equilibrium. In particular, we study the convergence of the grand-canonical equilibrium states of such gases to their mean-field limits, which are given by the Gibbs measures of class
Externí odkaz:
http://arxiv.org/abs/2001.11714
We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schr\"odinger equation in the mean-field limit, where the density of the gas becomes large and the interaction strength is
Externí odkaz:
http://arxiv.org/abs/2001.01546