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Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function.

ABSTRACT: In an adiabatic mixed quantum-classical simulation, the avoided crossing of weakly coupled eigenstates can lead to unphysical discontinuities in wave function dynamics, otherwise known as the trivial crossing problem. A standard solution to the trivial crossing problem eliminates spatial discontinuities in wave function dynamics by imposing changes to the eigenstate of the wave function. In this paper, we show that this solution has the side effect of introducing transient discontinuities in the nodal symmetry of the wave function. We present an alternative solution to the trivial crossing problem that preserves both the spatial and nodal structure of the adiabatic wave function. By considering a model of exciton dynamics on conjugated polymer systems, we show that failure to preserve wave function symmetry yields exciton dynamics that depends unphysically on polymer system size. We demonstrate that our symmetry-preserving solution to the trivial crossing problem yields more realistic dynamics and can thus improve the accuracy of simulations of larger systems that are prone to the trivial crossing problem.

SUBMITTER: Lee EMY

PROVIDER: S-EPMC6750758 | biostudies-literature | 2019 Aug

REPOSITORIES: biostudies-literature

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Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function.

Lee Elizabeth M Y EMY Willard Adam P AP

Journal of chemical theory and computation 20190729 8

In an adiabatic mixed quantum-classical simulation, the avoided crossing of weakly coupled eigenstates can lead to unphysical discontinuities in wave function dynamics, otherwise known as the trivial crossing problem. A standard solution to the trivial crossing problem eliminates spatial discontinuities in wave function dynamics by imposing changes to the eigenstate of the wave function. In this paper, we show that this solution has the side effect of introducing transient discontinuities in the ...[more]

PMID: 31305997

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Project description:In this paper we argue that a synthesis of findings across the various sub-areas of research in complex problem solving and consequently progress in theory building is hampered by an insufficient differentiation of complexity and difficulty. In the proposed framework of person, task, and situation (PTS), complexity is conceptualized as a quality that is determined by the cognitive demands that the characteristics of the task and the situation impose. Difficulty represents the quantifiable level of a person's success in dealing with such demands. We use the well-documented "semantic effect" as an exemplar for testing some of the conceptual assumptions derived from the PTS framework. We demonstrate how a differentiation between complexity and difficulty can help take beyond a potentially too narrowly defined psychometric perspective and subsequently gain a better understanding of the cognitive mechanisms behind this effect. In an empirical study a total of 240 university students were randomly allocated to one of four conditions. The four conditions resulted from contrasting the semanticity level of the variable labels used in the CPS system (high vs. low) and two instruction conditions for how to explore the CPS system's causal structure (starting with the assumption that all relationships between variables existed vs. starting with the assumption that none of the relationships existed). The variation in the instruction aimed at inducing knowledge acquisition processes of either (1) systematic elimination of presumptions, or (2) systematic compilation of a mental representation of the causal structure underpinning the system. Results indicate that (a) it is more complex to adopt a "blank slate" perspective under high semanticity as it requires processes of inhibiting prior assumptions, and (b) it seems more difficult to employ a systematic heuristic when testing against presumptions. In combination, situational characteristics, such as the semanticity of variable labels, have the potential to trigger qualitatively different tasks. Failing to differentiate between 'task' and 'situation' as independent sources of complexity and treating complexity and difficulty synonymously threaten the validity of performance scores obtained in CPS research.

Dataset Information

Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function.

Publications

Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function.

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