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Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation

Bernard Ducomet (2010)

Applications of Mathematics

We consider an effective model of nuclear matter including spin and isospin degrees of freedom, described by an N -body Hamiltonian with suitably renormalized two-body and three-body interaction potentials. We show that the corresponding mean-field theory (the time-dependent Hartree-Fock approximation) is “exact” as N tends to infinity.

Weyl sums and atomic energy oscillations.

Antonio Córdoba, Charles L. Fefferman, Luis A. Seco (1995)

Revista Matemática Iberoamericana

We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.

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