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Schröder M, Schreiber M, Kleinekathöfer U. Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory. J Chem Phys. 2007;126(11):114102doi: 10.1063/1.2538754.
Schröder, M., Schreiber, M., & Kleinekathöfer, U. (2007). Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory. The Journal of chemical physics, 126(11), 114102. https://doi.org/10.1063/1.2538754
Schröder, Markus, et al. "Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory." The Journal of chemical physics vol. 126,11 (2007): 114102. doi: https://doi.org/10.1063/1.2538754
Schröder M, Schreiber M, Kleinekathöfer U. Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory. J Chem Phys. 2007 Mar 21;126(11):114102. doi: 10.1063/1.2538754. PMID: 17381191.
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J Chem Phys. 2007 Mar 21;126(11):114102. doi: 10.1063/1.2538754.

Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory.

The Journal of chemical physics

Markus Schröder, Michael Schreiber, Ulrich Kleinekathöfer

Affiliations

  1. Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany.

PMID: 17381191 DOI: 10.1063/1.2538754

Abstract

Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.

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