Abstract
Surface hopping (SH) and density matrix evolution (DME) methods which simulate the dynamics of quantum systems embedded in a classical environments are compared with exact quantum-dynamical calculations. These methods are applied to study the inelastic collisions of a classical particle with a five-level quantum harmonic oscillator. One-dimensional, two-state models representing electronic transitions are also treated. In addition, the methods are applied to the dynamics of a proton in a bistable potential bilinearly coupled to the bath of classical harmonic oscillators. Vibrational spectra calculated by both methods compare well with each other. The SH results are, in general, closer to the results of a full quantum treatment than the corresponding DME values. The DME method breaks down in the case of extended coupling with reflection at low energies.
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