Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Leopold, Nikolai"'
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
Autor:
Leopold, Nikolai, Saffirio, Chiara
We consider the Maxwell-Schr\"odinger equations in the Coulomb gauge describing the interaction of extended fermions with their self-generated electromagnetic field. They heuristically emerge as mean-field equations from non-relativistic quantum elec
Externí odkaz:
http://arxiv.org/abs/2308.16074
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 time evolution of the renormalized Nelson model, which describes $N$ bosons linearly coupled to a quantized scalar field, in the mean-field limit of many particles $N\gg 1$ with coupling constant proportional to $N^{-1/2}$. First, we
Externí odkaz:
http://arxiv.org/abs/2305.06722
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:
Leopold, Nikolai
We study the time evolution of the Fr\"ohlich Hamiltonian in a mean-field limit in which many particles weakly couple to the quantized phonon field. Assuming that the particles are initially in a Bose-Einstein condensate and that the excitations of t
Externí odkaz:
http://arxiv.org/abs/2207.01598
Autor:
Falconi, Marco, Leopold, Nikolai
We slightly extend prior results about the derivation of the Maxwell-Schr\"odinger equations from the bosonic Pauli-Fierz Hamiltonian. More concretely, we show that the findings from [SIAM J. Math. Anal. 52(5), 4900-4936 (2020)] about the coherence o
Externí odkaz:
http://arxiv.org/abs/2203.16368
Autor:
Leopold, Nikolai, Saffirio, Chiara
Publikováno v:
SIAM J. Math. Anal. 55(3), 1676-1706 (2023)
We investigate the semiclassical limit from the semi-relativistic Hartree-Fock equation describing the time evolution of a system of fermions in the mean-field regime with a relativistic dispersion law and interacting through a singular potential of
Externí odkaz:
http://arxiv.org/abs/2203.03031
We study the time evolution of the Nelson model in a mean-field limit in which N non-relativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov
Externí odkaz:
http://arxiv.org/abs/2110.00458
Autor:
Leopold, Nikolai, Mitrouskas, David, Rademacher, Simone, Schlein, Benjamin, Seiringer, Robert
Publikováno v:
Pure Appl. Analysis 3 (2021) 653-676
We consider the Fr\"ohlich Hamiltonian with large coupling constant $\alpha$. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolutio
Externí odkaz:
http://arxiv.org/abs/2005.02098