Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Triay, Arnaud"'
We consider a Bose gas at density $\rho > 0$, interacting through a repulsive potential $V \in L^2 (\mathbb{R}^3)$ with scattering length $\mathfrak{a} > 0$. We prove an upper bound for the free energy of the system, valid at low temperature $T \less
Externí odkaz:
http://arxiv.org/abs/2405.03378
Autor:
Lampart, Jonas, Triay, Arnaud
We study a dilute system of $N$ interacting bosons coupled to an impurity particle via a pair potential in the Gross--Pitaevskii regime. We derive an expansion of the ground state energy up to order one in the boson number, and show that the differen
Externí odkaz:
http://arxiv.org/abs/2401.14911
We consider a low density Bose gas interacting through a repulsive potential in the thermodynamic limit. We justify, as a rigorous lower bound, a Lee--Huang--Yang type formula for the free energy at suitably low temperatures, where the modified excit
Externí odkaz:
http://arxiv.org/abs/2304.02405
We show that Bogoliubov theory correctly predicts the low-energy spectral properties of Bose gases in the Gross-Pitaevskii regime. We recover recent results from \cite{BBCS,BBCS4}. While our main strategy is similar to the one developed in \cite{BBCS
Externí odkaz:
http://arxiv.org/abs/2203.03440
Publikováno v:
Journal of Mathematical Physics 63 (2022) 061103
We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schr\"odinger equation to describe the ground state energy of a Bose-E
Externí odkaz:
http://arxiv.org/abs/2202.13967
Publikováno v:
Journal of Mathematical Physics 63 (2022) 071903
We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of the intera
Externí odkaz:
http://arxiv.org/abs/2201.13440
Publikováno v:
Prob. Math. Phys. 4 (2023) 91-149
We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the system is a con
Externí odkaz:
http://arxiv.org/abs/2110.08195
Autor:
Nam, Phan Thành, Triay, Arnaud
We consider an inhomogeneous system of $N$ bosons in $\mathbb{R}^3$ confined by an external potential and interacting via a repulsive potential of the form $N^2 V(N(x-y))$. We prove that the low-energy excitation spectrum of the system is determined
Externí odkaz:
http://arxiv.org/abs/2106.11949
Publikováno v:
Analysis & PDE 15 (2022) 1585-1616
We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross-Pitaevskii equation in the large
Externí odkaz:
http://arxiv.org/abs/2001.04364
We give the first derivation of the Scott correction in the large-$Z$ expansion of the energy of an atom in Dirac-Fock theory without projections.
Externí odkaz:
http://arxiv.org/abs/1911.09482