Jump to main content
Jump to site search

Issue 44, 2016
Previous Article Next Article

Lagrangian descriptors in dissipative systems

Author affiliations


The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory—that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.

Graphical abstract: Lagrangian descriptors in dissipative systems

Back to tab navigation

Publication details

The article was received on 15 Apr 2016, accepted on 08 Jun 2016 and first published on 09 Jun 2016

Article type: Paper
DOI: 10.1039/C6CP02532C
Phys. Chem. Chem. Phys., 2016,18, 30282-30287

  •   Request permissions

    Lagrangian descriptors in dissipative systems

    A. Junginger and R. Hernandez, Phys. Chem. Chem. Phys., 2016, 18, 30282
    DOI: 10.1039/C6CP02532C

Search articles by author