Semiclassical initial value methods for dissipative quantum systems
Final Report Abstract
In the two projects we have extended and used time-dependent semiclassical methodology with the aim to describe the complex interplay between a quantum system of interest and its environment. The quantum-classical transition has been in the focus of interest, as well as thermalization due to coupling to a bath of a well-defined temperature. Fully quantum mechanically, this endeavor is impossible, due to the exponential increase of the numerical effort with the number of degrees of freedom. We have followed two different, complementary strategies in the course of the projects. Firstly, the non-Markovian dynamics that ensues in a reduced description was tackled by a combined sampling strategy of the semiclassical phase space integral as well as the noise averaging due to the non-Markovian dynamics. Secondly, a large enough subset of the bath degrees of freedom was treated explicitly, albeit on a different level of accuracy, compared to the dynamics of the system of interest. This way, we have studied harmonic as well as anharmonic oscillators in different environments. Converged dynamics of such coupled systems has been reported until thermalization was reached. Furthermore, theoretically predicted blue shifts of the system’s frequency as well as transition to classicality were reproduced in numerical simulations of the reduced density matrix of the system of interest. A system of special experimental relevance that was studied is the Iodine molecule in a rare gas matrix (the “bath”). We could show that non-Gaussian distortions in the bath’s density matrix appear as a function of time, which is an indication of the non-classicality of the bath dynamics.
Publications
- Non-Markovian dissipative semiclassical dynamics, Physical Review Letters 100, 230402 (2008)
W. Koch, F. Großmann, J. T. Stockburger, and J. Ankerhold
- Decoherence and dissipation in a molecular system coupled to an environment: An application of semiclassical hybrid dynamics, Journal of Chemical Physics 130, 244107 (2009)
C.-M. Goletz and F. Großmann
- Investigating quantum transport with an initial value representation of the semiclassical propagator, Physical Review E 80, 031101 (2009); Erratum: Phys. Rev. E 82, 019902 (2010)
C.-M. Goletz, F. Großmann, and S. Tomsovic
- Semiclassical dynamics of open quantum systems: Comparing the finite with the infinite perspective, Chemical Physics 375, 227 (2010)
C.-M. Goletz, W. Koch, and F. Großmann
- Trajectory based non-Markovian dissipative tunneling. Physical Review Letters, 105, 230405 (2010)
W. Koch, F. Großmann, and D. J. Tannor
- Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator . Journal of Physics A, 44, 445309 (2011)
F. Großmann, and T. Kramer
- Dominant interaction Hamiltonians for high harmonic generation in laserassisted collisions. Physical Review A 85, 041401(R) (2012)
C. Zagoya, C.-M. Goletz, F. Großmann, and J.-M. Rost
(See online at https://doi.org/10.1103/PhysRevA.85.041401) - Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I2 Kr17 Cluster. Journal of Physical Chemistry A 116, 11199 (2012)
M. Buchholz, C.-M. Goletz, F. Großmann, B. Schmidt J. Heyda, and P. Jungwirth
(See online at https://doi.org/10.1021/jp305084f) - nterference nature of quantum breather oscillation. Journal of Physics A 47, 165102 (2014)
C. Zagoya, L. S. Schulman, and F. Großmann
(See online at https://doi.org/10.1088/1751-8113/47/16/165102) - Spin effects and the Pauli principle in semiclassical electron dynamics. Physical Review A 89, 032104 (2014)
F. Großmann, M. Buchholz, E. Pollak, and M. Nest
(See online at https://doi.org/10.1103/PhysRevA.89.032104) - A semiclassical hybrid approach to linear response functions for infrared spectroscopy. 2015
F. Großmann
- Mixed Semiclassical Initial Value Representation Time-Averaging Propagator for Spectroscopic Calculations. 2015
M. Buchholz, F. Großmann, and M. Ceotto
