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Generalized quantum cumulant dynamics

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journal contribution
posted on 07.01.2020, 13:09 by Joe Bowen, Mark EverittMark Everitt, Iain PhillipsIain Phillips, Vincent Dwyer
A means of unifying some semiclassical models of computational chemistry is presented; these include quantized Hamiltonian dynamics, quantal cumulant dynamics, and semiclassical Moyal dynamics (SMD). A general method for creating the infinite hierarchy of operator dynamics in the Heisenberg picture is derived together with a general method for truncation (or closure) of that series, and in addition, we provide a simple link to the phase space methods of SMD. Operator equations of arbitrary order may be created readily, avoiding the tedious algebra identified previously. Truncation is based on a simple recurrence formula which is related to, but avoids the more complex contractions of, Wick's theorem. This generalized method is validated against a number of trial problems considered using the previous methods. We also touch on some of the limitations involved using such methods, noting, in particular, that any truncation will lead to a state which is in some sense unphysical. Finally, we briefly introduce our quantum algebra package QuantAL which provides an automated method for the generation of the required equation set, the initial conditions for all variables from any start, and all the higher order approximations necessary for truncation of the series, at essentially arbitrary order.

History

School

  • Science
  • Mechanical, Electrical and Manufacturing Engineering

Department

  • Computer Science
  • Physics

Published in

The Journal of Chemical Physics

Volume

151

Issue

24

Publisher

AIP Publishing

Version

AM (Accepted Manuscript)

Rights holder

© Authors

Publisher statement

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Bowen et al., J. Chem. Phys. 151, 244107 (2019); doi: 10.1063/1.5130754 and may be found at https://doi.org/10.1063/1.5130754.

Acceptance date

07/12/2019

Publication date

2019-12-24

Copyright date

2019

ISSN

0021-9606

eISSN

1089-7690

Language

en

Depositor

Dr Vincent Dwyer. Deposit date: 4 January 2020

Article number

244107

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