Results 211 to 220 of about 1,685,804 (365)

The Huang–Yang Formula for the Low‐Density Fermi Gas: Upper Bound

open access: yesCommunications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We study the ground state energy of a gas of spin 1/2$1/2$ fermions with repulsive short‐range interactions. We derive an upper bound that agrees, at low density ϱ$\varrho$, with the Huang–Yang conjecture. The latter captures the first three terms in an asymptotic low‐density expansion, and in particular the Huang–Yang correction term of order
Emanuela L. Giacomelli   +3 more
wiley   +1 more source

Self‐Similar Blowup for the Cubic Schrödinger Equation

open access: yesCommunications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

open access: yesCommunications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

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