Complex microscopic many-body processes are often interpreted in terms of so-called “reaction coordinates,” i.e., in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of such observables is to use projection operator techniques, which split the dynamics of the observables into a main contribution and a marginal one. The basis of any derivation in this framework is the classical Heisenberg equation for an observable. If the Hamiltonian of the underlying microscopic dynamics and the observable under study do not explicitly depend on time, this equation is obtained by a straightforward derivation. However, the problem is more complicated if one considers Hamiltonians which depend on time explicitly as, e.g., in systems under external driving, or if the observable of interest has an explicit dependence on time. We use an analogy to fluid dynamics to derive the classical Heisenberg picture and then apply a projection operator formalism to derive the nonstationary generalized Langevin equation for a coarse-grained variable. We show, in particular, that the results presented for time-independent Hamiltonians and observables in the study by Meyer, Voigtmann, and Schilling, J. Chem. Phys. 147, 214110 (2017) can be generalized to the time-dependent case.
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Research Article| May 07 2019
On the dynamics of reaction coordinates in classical, time-dependent, many-body processes
Hugues Meyer ;
Hugues Meyer a)
Physikalisches Institut, Albert-Ludwigs-Universität, 79104 Freiburg,
Research Unit in Engineering Science, Université du Luxembourg, L-4364 Esch-sur-Alzette,
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Thomas Voigtmann ;
Hugues Meyer, Thomas Voigtmann, Tanja Schilling; On the dynamics of reaction coordinates in classical, time-dependent, many-body processes. J. Chem. Phys. 7 May 2019; 150 (17): 174118. https://doi.org/10.1063/1.5090450
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