Time-dependent Bivariational Principle

New publication by Simen Kvaal, Håkon Richard Fredheim, and Thomas Bondo Pedersen in collaboration with Mads Greisen Højlund at Aarhus University, Denmark. The paper is a study of the time-dependent bivariational principle (TD-BIVP), which is used to derive propagation schemes for many-electron systems, in particular time-dependent coupled-cluster theories. The authors also consider many popular coupled-cluster-based propagation schemes and place them into the context of the new analysis.

Illustration by Simen Kvaal.

By Simen Kvaal, Håkon Richard Fredheim, Mads Greisen Højlund, and Thomas Bondo Pedersen

Published May 7, 2025

Article

Time-dependent Bivariational Principle: Theoretical Foundation for Real-Time Propagation Methods of Coupled-Cluster Type.

Date of publication: 2025, 6th April.

Abstract

The TD-BIVP is studied from an abstract point of view, using symplectic geometry. One interesting finding is the existence of two independent principles that can be used to, in principle, generate complementary time-evolutions from a single ansatz. It is also found that the traditional univariational principles (Dirac-Frenkel, McLachlan, and the time-dependent variational principle) can be recast as special instances of the TD-BIVP.

The paper is published as part of the Trygve Helgaker Festschrift in the Journal of Physical Chemistry A.

https://pubs.acs.org/doi/10.1021/acs.jpca.4c07417

Funding

This work has received funding from the Research Council of Norway (RCN) under Grant No.324944 (QOMBINE), CoE Grant Nos.287906 and 262695 (Hylleraas Centre for Quantum Molecular Sciences), and Independent Research Fund Denmark through Grant No. 1026-00122B.

Tags: Quantum Dynamics, Coupled-Cluster, Mathematical Methods, Bivariational Principle

Published May 7, 2025 4:00 PM - Last modified May 8, 2025 4:28 PM