TY - JOUR
AB - We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.
AU - Henheik, Sven Joscha
ID - 10623
IS - 1
JF - Mathematical Physics, Analysis and Geometry
KW - geometry and topology
KW - mathematical physics
SN - 1385-0172
TI - The BCS critical temperature at high density
VL - 25
ER -
TY - JOUR
AB - We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.
AU - Henheik, Sven Joscha
AU - Teufel, Stefan
ID - 10643
JF - Forum of Mathematics, Sigma
KW - computational mathematics
KW - discrete mathematics and combinatorics
KW - geometry and topology
KW - mathematical physics
KW - statistics and probability
KW - algebra and number theory
KW - theoretical computer science
KW - analysis
TI - Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk
VL - 10
ER -
TY - JOUR
AB - We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We nd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.
AU - Ivanov, Grigory
AU - Tsiutsiurupa, Igor
ID - 10856
IS - 1
JF - Analysis and Geometry in Metric Spaces
KW - Applied Mathematics
KW - Geometry and Topology
KW - Analysis
SN - 2299-3274
TI - On the volume of sections of the cube
VL - 9
ER -
TY - JOUR
AB - We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.
AU - Boissonnat, Jean-Daniel
AU - Kachanovich, Siargey
AU - Wintraecken, Mathijs
ID - 8940
IS - 1
JF - Discrete & Computational Geometry
KW - Theoretical Computer Science
KW - Computational Theory and Mathematics
KW - Geometry and Topology
KW - Discrete Mathematics and Combinatorics
SN - 0179-5376
TI - Triangulating submanifolds: An elementary and quantified version of Whitney’s method
VL - 66
ER -
TY - JOUR
AB - The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of an ellipse of small eccentricity which preserves integrability near the boundary, is itself an ellipse. This extends the result in Avila et al. (Ann Math 184:527–558, ADK16), where integrability was assumed on a larger set. In particular, it shows that (local) integrability near the boundary implies global integrability. One of the crucial ideas in the proof consists in analyzing Taylor expansion of the corresponding action-angle coordinates with respect to the eccentricity parameter, deriving and studying higher order conditions for the preservation of integrable rational caustics.
AU - Huang, Guan
AU - Kaloshin, Vadim
AU - Sorrentino, Alfonso
ID - 8422
IS - 2
JF - Geometric and Functional Analysis
KW - Geometry and Topology
KW - Analysis
SN - 1016-443X
TI - Nearly circular domains which are integrable close to the boundary are ellipses
VL - 28
ER -