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The atomistic to continuum interface for quasicontinuum energies
exhibits nonzero forces under uniform strain that have been
called ghost forces.
In this paper,
we prove for a linearization of a one-dimensional quasicontinuum energy
around a uniform strain
that the effect of the ghost forces on the displacement
nearly cancels and has a small effect on the error away from the interface.
We give optimal order error estimates
that show that the quasicontinuum displacement
converges to the atomistic...
The entropy of an ideal gas, both in the case of classical and quantum particles, is maximised when the number particle density, linear momentum and energy are fixed. The dispersion law energy to momentum is chosen as linear or quadratic, corresponding to non-relativistic or relativistic behaviour.
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 of the time-dependent...
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