TY - JOUR AB - It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit. AU - Henheik, Sven Joscha AU - Lauritsen, Asbjørn Bækgaard AU - Roos, Barbara ID - 14542 JF - Reviews in Mathematical Physics SN - 0129-055X TI - Universality in low-dimensional BCS theory ER - TY - JOUR AB - We consider a class of polaron models, including the Fröhlich model, at zero total momentum, and show that at sufficiently weak coupling there are no excited eigenvalues below the essential spectrum. AU - Seiringer, Robert ID - 14662 IS - 3 JF - Journal of Spectral Theory SN - 1664-039X TI - Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling VL - 13 ER - TY - JOUR AB - Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy. AU - Benedikter, Niels P AU - Porta, Marcello AU - Schlein, Benjamin AU - Seiringer, Robert ID - 13225 IS - 4 JF - Archive for Rational Mechanics and Analysis SN - 0003-9527 TI - Correlation energy of a weakly interacting Fermi gas with large interaction potential VL - 247 ER - TY - JOUR AB - 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 a weak Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in 1/N−−√. For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher-order corrections are given by an Edgeworth-type expansion. AU - Bossmann, Lea AU - Petrat, Sören P ID - 13226 IS - 4 JF - Letters in Mathematical Physics SN - 0377-9017 TI - Weak Edgeworth expansion for the mean-field Bose gas VL - 113 ER - TY - JOUR AB - For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling. AU - Lampart, Jonas AU - Mitrouskas, David Johannes AU - Mysliwy, Krzysztof ID - 14192 IS - 3 JF - Mathematical Physics, Analysis and Geometry KW - Geometry and Topology KW - Mathematical Physics SN - 1385-0172 TI - On the global minimum of the energy–momentum relation for the polaron VL - 26 ER -