In a recent Letter [Chem. Phys. Lett. 221, 482 (1994)], we demonstrated that the dynamics of reduced density matrices for systems in contact with dissipative harmonic environments can be obtained in an iterative fashion by multiplication of a propagator tensor. The feasibility of iterative procedures in reduced dimension spaces arises from intrinsic features of the dissipative influence functional in Feynman’s path integral formulation of quantum dynamics. Specifically, the continuum of frequencies characteristic of broad condensed phase spectra disrupts phase coherence to a large extent, such that the dynamics of an augmented reduced density tensor becomes Markovian. In a preceding article [J. Chem. Phys. 102, 4600 (1995)] we examined in detail the formal properties of the tensor propagator. In the present paper we show that the tensor propagator can be further decomposed into a product of small rank tensors, resulting in an extremely simple and efficient numerical scheme that scales almost linearly with the dimension of the augmented reduced density tensor. Numerical application to a model electron transfer reaction is presented.
Skip Nav Destination
Article navigation
15 March 1995
Research Article|
March 15 1995
Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology
Nancy Makri;
Nancy Makri
School of Chemical Sciences, University of Illinois, 505 S. Mathews Avenue, Urbana, Illinois 61801
Search for other works by this author on:
Dmitrii E. Makarov
Dmitrii E. Makarov
School of Chemical Sciences, University of Illinois, 505 S. Mathews Avenue, Urbana, Illinois 61801
Search for other works by this author on:
J. Chem. Phys. 102, 4611–4618 (1995)
Article history
Received:
September 08 1994
Accepted:
December 01 1994
Citation
Nancy Makri, Dmitrii E. Makarov; Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology. J. Chem. Phys. 15 March 1995; 102 (11): 4611–4618. https://doi.org/10.1063/1.469509
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
DeePMD-kit v2: A software package for deep potential models
Jinzhe Zeng, Duo Zhang, et al.
CREST—A program for the exploration of low-energy molecular chemical space
Philipp Pracht, Stefan Grimme, et al.
Dielectric profile at the Pt(111)/water interface
Jia-Xin Zhu, Jun Cheng, et al.
Related Content
Influence functionals with semiclassical propagators in combined forward–backward time
J. Chem. Phys. (January 1999)
Efficient memory equation algorithm for reduced dynamics in spin-boson models
J. Chem. Phys. (January 1999)
Resolvent approach for the evaluation of the reduced density-matrix functional of correlated electron systems
AIP Conference Proceedings (August 2013)
Iterative path integral formulation of equilibrium correlation functions for quantum dissipative systems
J. Chem. Phys. (January 2002)
Sum rules for the tunneling effect in superconductors
Sov. J. Low Temp. Phys. (May 1979)