md2011-01-note 9

md2011-01-note 9 - I These are defined as: P = X i p i L =...

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Unformatted text preview: I These are defined as: P = X i p i L = X i r i p i = X i r i m i r i (13) I For a completely isolated system: I P and L are conserved I Hamiltonian H is independent on time , i.e., d H / d t = 0 (total energy is constant). I Further, the equations of motion are reversible in time . I I.e., by changing the signs of all momenta, particles would retrace their trajectories. I A successfull atomistic simulation reproduces all these features! Notes S MD A Notes MD, G C I The natural system to model is the so-called microcanonical ensemble ( NVE ). I This is closest to a real system because its a true solution for the N-body problem, and corresponds to the real atomic motion (but only for a completely isolated system). I Current limit is 10 9 atoms in dynamical calculations for simulation times of a few ns with spatially parallelized codes. I For a N-atomic system, one in principle needs to care about N 2 interactions for each time step t ....
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md2011-01-note 9 - I These are defined as: P = X i p i L =...

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