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Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

ABSTRACT: Whether quantum state transitions occur by instantaneous jumps (a la Bohr) or deterministic dynamics (Schrödinger's preference) has been intensely debated. Recent experimental measurements of shelved electrons have reignited the debate. We examine aspects of the time-dependent numerical solutions of the Schrödinger equation in quantum systems with two and three levels perturbed by a sinusoidal field. A geometrical construction involving quantum state phase differences illuminates the role of interstate phase differences in a deterministic, rather than random, process of multiphoton absorption. Alternate halves of the Rabi cycle exhibit phase reversals much like the classical beats of coupled oscillators. For non-zero detuning, population inversion does not occur because the exciting field drifts out of the proper phase before inversion is complete. A close correspondence with classical, coupled oscillator beats offers insights for interpretation of deterministic quantum dynamics and suggests an experimental test for the correctness of this picture depending on the long-time phase stability of exciting fields.

SUBMITTER: Shirts RB

PROVIDER: S-EPMC9434749 | biostudies-literature | 2022 Aug

REPOSITORIES: biostudies-literature

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Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

Shirts Randall B RB Welch John S JS

ACS omega 20220815 34

Whether quantum state transitions occur by instantaneous jumps (a la Bohr) or deterministic dynamics (Schrödinger's preference) has been intensely debated. Recent experimental measurements of shelved electrons have reignited the debate. We examine aspects of the time-dependent numerical solutions of the Schrödinger equation in quantum systems with two and three levels perturbed by a sinusoidal field. A geometrical construction involving quantum state phase differences illuminates the role of int ...[more]

PMID: 36061689

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Project description:BACKGROUND: Phase transition widely exists in the biological world, such as transformation of cell cycle phases, cell differentiation stages, disease development, and so on. Such a nonlinear phenomenon is considered as the conversion of a biological system from one phenotype/state to another. Studies on the molecular mechanisms of biological phase transition have attracted much attention, in particular, on different genotypes (or expression variations) in a specific phase, but with less of focus on cascade changes of genes' functions (or system state) during the phase shift or transition process. However, it is a fundamental but important mission to trace the temporal characteristics of a biological system during a specific phase transition process, which can offer clues for understanding dynamic behaviors of living organisms. RESULTS: By overcoming the hurdles of traditional time segmentation and temporal biclustering methods, a causal process model (CPM) in the present work is proposed to study the biological phase transition in a systematic manner, i.e. first, we make gene-specific segmentation on time-course expression data by developing a new boundary gene estimation scheme, and then infer functional cascade dynamics by constructing a temporal block network. After the computational validation on synthetic data, CPM was used to analyze the well-known Yeast cell cycle data. It was found that the dynamics of the boundary genes are periodic and consistent with the phases of the cell cycle, and the temporal block network indeed demonstrates a meaningful cascade structure of the enriched biological functions. In addition, we further studied protein modules based on the temporal block network, which reflect temporal features in different cycles. CONCLUSIONS: All of these results demonstrate that CPM is effective and efficient comparing to traditional methods, and is able to elucidate essential regulatory mechanism of a biological system even with complicated nonlinear phase transitions.

Dataset Information

Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

Publications

Quantum Interstate Phase Differences and Multiphoton Processes: Quantum Jumps or Dynamic Beats?

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