Physical Review B
Starting from the quantum-mechanical Fano-Anderson Hamiltonian, we derive classical equations of motion for coordinates associated with the discrete and continuum states. The frequency-dependent absorption spectrum associated with this classical system exhibits the same Fano line shape as the quantum-mechanical system when appropriate correspondences between classical and quantum variables are made. In the time domain, the response of this classical Fano oscillator depends upon the asymmetry parameter q that appears in the expression for the Fano line shape. In particular, under the influence of impulsive driving of the system, the discrete oscillator's phase changes by ±π/2 as q increases from zero (maximum asymmetry in the frequency domain) to ∓∞ (minimum asymmetry). Previously published ultrafast-laser-pulse-driven coherent-phonon oscillations in degenerate p-type Si [ K. Kato et al. Jpn. J. Appl. Phys. 48 100205 (2009)] are discussed in light of these theoretical results.
"Classical Fano Oscillator," D. M. Riffe, Phys. Rev. B 84, 064308 (2011) (doi:10.1103/PhysRevB.84.064308).