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Unformatted text preview: I Above, μ is a fictitious mass assigned to the orbital degrees of freedom. I Looking back at the Lagrangian (eq. 22), the nuclei evolve in time at a certain physical temperature ∝ ∑ I M I ˙ R 2 I , whereas a “fictitious temperature” ∝ ∑ i μ D ˙ φ i ˙ φ i E can be associated with the electronic degrees of freedom. I Using this terminology, “low electronic temperature” or “cold electrons” mean that the electronic subsystem is close to its instantaneous minimum energy (i.e., the exact Born-Oppenheimer surface). I Thereby, a low fictitious temperature assures that the electronic subsystem remains close to the ground state. I The question is how to keep the fast electronic subsystem cold for long times while it still follows the motion of the nuclei. The nuclei must be kept at much higher temperatures. Notes I This is only possible if the energy transfer from the “hot nuclei” to the “cold electrons” remains practically impossible at the relevant time scales.impossible at the relevant time scales....
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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.
- Winter '12