複雑な量子系における「カオス」から「秩序」を選別する理論(Theory can sort order from chaos in complex quantum systems)

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計算機、電気化学、生物学的システムの進歩のきっかけとなる開発 Development could spark advances in computing, electrochemical, biological systems

2023-02-23 ライス大学

ライス大学とオックスフォード大学の科学者によって開発された新しい数学理論は、複雑な量子系における秩序を混沌から分類することができるとされています。この理論は、光合成モデルの計算解析に基づいて検証され、量子系の運動の性質を予測することができることが示されています。この理論は、十分に複雑な量子系に適用でき、より優れた量子コンピューターの開発や、次世代の太陽電池やバッテリーの設計など、様々な応用分野において進歩をもたらす可能性があります。また、この研究は、米国科学アカデミー紀要に掲載されました。

<関連情報>

多次元量子系における表面交差とエネルギーフロー Surface crossing and energy flow in many-dimensional quantum systems

Chenghao Zhang, Martin Gruebele, David E. Logan and Peter G. Wolynes
Proceedings of the National Academy of Sciences  Published:February 23, 2023
DOI:https://doi.org/10.1073/pnas.2221690120

Significance

Quantum scrambling and energy redistribution are important in many problems ranging from photosynthetic energy flow to charge transfer at electrodes and in quantum dots. In mesoscopic systems such as large molecules, a transition from coherent organized quantum behavior to chaotic behavior can be found. Two of the key scrambling mechanisms, electronic surface crossing and vibrational anharmonic resonance, have usually been treated separately. Here, we develop a unified theory providing a transition criterion from localized to scrambled regimes. The criterion is easy to compute even for very complicated systems, and we test it by comparisons with numerical quantum dynamics simulations for a model inspired by bacteriochlorophyll dimers involved in photosynthesis.

Abstract

Energy flow in molecules, like the dynamics of other many-dimensional finite systems, involves quantum transport across a dense network of near-resonant states. For molecules in their electronic ground state, the network is ordinarily provided by anharmonic vibrational Fermi resonances. Surface crossing between different electronic states provides another route to chaotic motion and energy redistribution. We show that nonadiabatic coupling between electronic energy surfaces facilitates vibrational energy flow and, conversely, anharmonic vibrational couplings facilitate nonadiabatic electronic state mixing. A generalization of the Logan–Wolynes theory of quantum energy flow in many-dimensional Fermi resonance systems to the two-surface case gives a phase diagram describing the boundary between localized quantum dynamics and global energy flow. We explore these predictions and test them using a model inspired by the problem of electronic excitation energy transfer in the photosynthetic reaction center. Using an explicit numerical solution of the time-dependent Schrödinger equation for this ten-dimensional model, we find quite good agreement with the expectations from the approximate analytical theory.

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