Quantum-classical transition in the electron dynamics of thin metal films
Résumé
The quantum electrons dynamics in a thin metal film is studied numerically using the self-consistent Wigner-Poisson equations. The initial equilibrium is computed from the Kohn-Sham equations at finite temperature, and then mapped into the phase-space Wigner function. The time-dependent results are compared systematically with those obtained previously with a classical approach (Vlasov-Poisson equations). It is found that, for large excitations, the quantum and classical dynamics display the same low-frequency oscillations due to ballistic electrons bouncing back and forth on the film surfaces. However, below a certain excitation energy (roughly corresponding to one quantum of plasmon energy \hbar\omega_{{\rm p}} ), the quantum and classical results diverge, and the ballistic oscillations are no longer observed. These results provide an example of a quantum-classical transition that may be observed with current pump-probe experiments on thin metal films.
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