Zobrazeno 1 - 10
of 44
pro vyhledávání: '"Boßmann, Lea"'
We consider a system of $N$ bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form $N^{3\beta-1} v (N^\beta x)$ for $\beta \in (0,1)$. We prove the next order correction to Bogoliubov theory
Externí odkaz:
http://arxiv.org/abs/2309.12233
We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose-Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic exp
Externí odkaz:
http://arxiv.org/abs/2307.13115
We consider the dynamics of a 2D Bose gas with an interaction potential of the form $N^{2\beta-1}w(N^\beta\cdot)$ for $\beta\in (0,3/2)$. The interaction may be chosen to be negative and large, leading to the instability regime where the correspondin
Externí odkaz:
http://arxiv.org/abs/2307.00956
We consider a gas of N bosons with interactions in the mean-field scaling regime. We review a recent proof of the asymptotic expansion of its spectrum and eigenstates and two applications of this result, namely the derivation of an Edgeworth expansio
Externí odkaz:
http://arxiv.org/abs/2304.12910
Autor:
Boßmann, Lea, Petrat, Sören
We consider the ground state and the low-energy excited states of a system of $N$ identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive an Edgeworth expansion for the fluctuations of bounded one-body ope
Externí odkaz:
http://arxiv.org/abs/2208.00199
Autor:
Boßmann, Lea
We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/
Externí odkaz:
http://arxiv.org/abs/2203.00730
Publikováno v:
Forum Math. Sigma 9, e28 (2021)
We consider a system of $N$ bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides
Externí odkaz:
http://arxiv.org/abs/2006.09825
Publikováno v:
Pure Appl. Analysis 3 (2021) 677-726
We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in te
Externí odkaz:
http://arxiv.org/abs/1912.11004
Autor:
Boßmann, Lea
Publikováno v:
Arch. Ration. Mech. Anal. 238(2) (2020)
We study the dynamics of a system of $N$ interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to a region of order $\varepsilon$. The interaction is non-negative and sc
Externí odkaz:
http://arxiv.org/abs/1907.04547
Publikováno v:
J. Stat. Phys. 178(6) (2020)
In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of $N$ $d$-dimensional bosons for large $N$. The bosons ini
Externí odkaz:
http://arxiv.org/abs/1905.06164