Zobrazeno 1 - 10
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pro vyhledávání: '"Hainzl P"'
We study the ground state energy of a gas of spin $1/2$ fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density $\rho$, with the Huang-Yang conjecture. The latter captures the first three terms in an asy
Externí odkaz:
http://arxiv.org/abs/2409.17914
The purpose of this paper is to study the limiting distribution of special {\it additive functionals} on random planar maps, namely the number of occurrences of a given {\it pattern}. The main result is a central limit theorem for these pattern count
Externí odkaz:
http://arxiv.org/abs/2406.05501
Autor:
Hainzl, Eva-Maria, de Panafieu, Élie
It is a classic result in spectral theory that the limit distribution of the spectral measure of random graphs G(n, p) converges to the semicircle law in case np tends to infinity with n. The spectral measure for random graphs G(n, c/n) however is le
Externí odkaz:
http://arxiv.org/abs/2405.08347
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 $T \less
Externí odkaz:
http://arxiv.org/abs/2405.03378
We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in \cite{ChrHaiNam-23b}, our
Externí odkaz:
http://arxiv.org/abs/2405.01386
We consider a low density Bose gas interacting through a repulsive potential in the thermodynamic limit. We justify, as a rigorous lower bound, a Lee--Huang--Yang type formula for the free energy at suitably low temperatures, where the modified excit
Externí odkaz:
http://arxiv.org/abs/2304.02405
Autor:
Drmota, Michael, Hainzl, Eva-Maria
Functional equations with one catalytic appear in several combinatorial applications, most notably in the enumeration of lattice paths and in the enumeration of planar maps. The main purpose of this paper is to show that under certain positivity assu
Externí odkaz:
http://arxiv.org/abs/2212.07741
Publikováno v:
Calculus of Variations and PDE 62, 203 (2023)
We consider the Bardeen-Cooper-Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg-Landau functional. We also provide an asymptotic formula for the BCS critical temperature a
Externí odkaz:
http://arxiv.org/abs/2210.09356
We prove a rigorous upper bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of interaction potentials. Our result covers the Coulomb potential, and in this case we obtain the analogue of the Gell-Mann$-
Externí odkaz:
http://arxiv.org/abs/2208.01581
We present a necessary condition for odd-frequency (odd-f) superconductivity (SC) to occur in a large class of materials described by Eliashberg theory. We use this condition to prove a no-go theorem ruling out the occurrence of odd-f SC in standard
Externí odkaz:
http://arxiv.org/abs/2207.01825