Displaying similar documents to “Over the evolution of fundamental ideas of fracture mechanics.”

Mean-field evolution of fermionic systems

Marcello Porta (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

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We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution...

A characterization of evolution operators

Naoki Tanaka (2001)

Studia Mathematica

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A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.