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pro vyhledávání: '"Christiansen, Martin Ravn"'
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in \cite{ChrHaiNam-23b}, our
Externí odkaz:
http://arxiv.org/abs/2405.01386
Autor:
Christiansen, Martin Ravn
Publikováno v:
Commun. Math. Phys. 405, 18 (2024)
We prove that the 2-body operator $\gamma_2^\Psi$ of a fermionic $N$-particle state $\Psi$ obeys $||\gamma_2^\Psi||_{HS} \leq \sqrt{5} N$, which complements the bound of Yang that $||\gamma_2^\Psi||_{op} \leq N$. This estimate furthermore resolves a
Externí odkaz:
http://arxiv.org/abs/2305.00834
Autor:
Christiansen, Martin Ravn
This thesis concerns the correlation structure of interacting Fermi gases on a torus in the mean-field regime. A bosonization method in the spirit of Sawada is developed to analyze the system, and is applied to obtain an upper bound for the correlati
Externí odkaz:
http://arxiv.org/abs/2301.12817
We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann$-
Externí odkaz:
http://arxiv.org/abs/2208.01581
Publikováno v:
Lett. Math. Phys. 112, 114 (2022)
We consider an effective quasi-bosonic Hamiltonian of the electron gas which emerges naturally from the random phase approximation and describes the collective excitations of the gas. By a rigorous argument, we explain how the plasmon modes can be in
Externí odkaz:
http://arxiv.org/abs/2206.13073
We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of $N$ fermions on a torus, interacting via a two-body repulsive potentia
Externí odkaz:
http://arxiv.org/abs/2106.11161
Autor:
Christiansen, Martin Ravn1 christiansen@math.lmu.de, Hainzl, Christian1 hainzl@math.lmu.de, Phan Thành Nam1 nam@math.lmu.de
Publikováno v:
Forum of Mathematics, Pi. 12/22/2023, Vol. 11, p1-131. 131p.
Autor:
Christiansen, Martin Ravn1 (AUTHOR), Hainzl, Christian1 (AUTHOR) hainzl@math.lmu.de, Nam, Phan Thành1 (AUTHOR)
Publikováno v:
Communications in Mathematical Physics. Jul2023, Vol. 401 Issue 2, p1469-1529. 61p.
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