Various variational approximations of quantum dynamics

• URL: http://arxiv.org/abs/2103.11783v2
• Date: Wed, 13 Oct 2021 07:10:09 GMT
• Title: Various variational approximations of quantum dynamics
• Authors: Caroline Lasser and Chunmei Su
• Abstract summary: We investigate variational principles for the approximation of quantum dynamics that apply to approximations that do not have complex linear tangent spaces. We characterize both principles in terms of metric and a symplecticity conditions, consider their conservation properties, and derive an elementary a-posteriori error estimate.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan (1964) minimizes the residuum of the time-dependent Schr\"odinger equation, while the second one, originating from the lecture notes of Kramer--Saraceno (1981), imposes the stationarity of an action functional. We characterize both principles in terms of metric and a symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a-posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets.

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