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- Courant Institute of Mathematical SciencesUS36 papers
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4 papers · 1 filter
Grassmann Integral Representation for Spanning Hyperforests
Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Spe…
Universality in Random Matrix Theory for orthogonal and symplectic ensembles
Percy Deift, Dimitri Gioev
We give a proof of the Universality Conjecture for orthogonal and symplectic ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a p…
Accuracy of the time-dependent Hartree-Fock approximation
Claude Bardos, Francois Golse, Alex D. Gottlieb +1
This article examines the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find the TDHF approximation to be accu…
Derivation of the Euler equations from many-body quantum mechanics
Bruno Nachtergaele, Horng-Tzer Yau
The Heisenberg dynamics of the energy, momentum, and particle densities for fermions with short-range pair interactions is shown to converge to the compressible Euler equations in…