While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to the exponential scaling with dimensionality, corresponding classical simulations completely ignore quantum effects. Semiclassical methods are generally more efficient but less accurate than quantum methods, and more accurate but less efficient than classical methods. We find a remarkable exception to this rule by showing that a semiclassical method can be both more accurate and faster than a classical simulation [1]. Specifically, we prove that for the semiclassical dephasing representation [2,3] the number of trajectories needed to simulate quantum fidelity is independent of dimensionality and also that this semiclassical method is even faster than the most efficient corresponding classical algorithm [4]. Analytical results are confirmed with simulations of quantum fidelity in up to 100 dimensions with 21700-dimensional Hilbert space. These results will soon appear in the Physical Review Letters [1].Besides its conceptual value, dephasing representation has important applications in chemical physics, including the evaluation of accuracy of molecular quantum dynamics on an approximate potential energy surface [5,6], evaluation of the nonadiabaticity of molecular quantum dynamics [7,8], and the calculation of the ultrafast time-resolved electronic spectra [9].[1] C. Mollica and J. Vanicek, Phys. Rev. Lett., in press, arXiv:1108.3853v1.[2] J. Vanicek, Rapid Communication, Phys. Rev. E 70  , 055201 (2004).[3] J. Vanicek, Phys. Rev. E 73  , 046204 (2006).[4] C. Mollica, T. Zimmermann, and J. Vanicek, arXiv:1108.0173v1.[5] B. Li, C. Mollica, and J. Vanicek: Communication, J. Chem. Phys. 131  , 041101 (2009).[6] T. Zimmermann, J. Ruppen, B. Li, and J. Vanicek, Int. J. Quant. Chem. 110  , 2426 (2010).[7] T. Zimmermann and J. Vanicek, Communication, J. Chem. Phys. 132  , 241101 (2010).[8] T. Zimmermann and J. Vanicek, submitted to J. Chem. Phys.[9] M. Wehrle, M. Sulc, and J. Vanicek, Chimia 65 , 334 (2011).

Dephasing representation: Beating the efficiency of both quantum and classical simulations with semiclassics

243rd National Meeting (2012)

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