Entanglement and co-tunneling of two equivalent protons in hydrogen bond pairs
Bibliographic record
Abstract
A theoretical study is reported of a system of two identical symmetric hydrogen bonds, weakly coupled such that the two mobile protons can move either separately (stepwise) or together (concerted). It is modeled by two equivalent quartic potentials interacting through dipolar and quadrupolar coupling terms. The tunneling Hamiltonian has two imaginary modes (reaction coordinates) and a potential with a single maximum that may turn into a saddle-point of second order and two sets of (inequivalent) minima. Diagonalization is achieved via a modified Jacobi-Davidson algorithm. From this Hamiltonian the mechanism of proton transfer is derived. To find out whether the two protons move stepwise or concerted, a new tool is introduced, based on the distribution of the probability flux in the dividing plane of the transfer mode. While stepwise transfer dominates for very weak coupling, it is found that concerted transfer (co-tunneling) always occurs, even when the coupling vanishes since the symmetry of the Hamiltonian imposes permanent entanglement on the motions of the two protons. We quantify this entanglement and show that, for a wide range of parameters of interest, the lowest pair of states of the Hamiltonian represents a perfect example of highly entangled quantum states in continuous variables. The method is applied to the molecule porphycene for which the observed tunneling splitting is calculated in satisfactory agreement with experiment, and the mechanism of double-proton tunneling is found to be predominantly concerted. We show that, under normal conditions, when they are in the ground state, the two porphycene protons are highly entangled, which may have interesting applications. The treatment also identifies the conditions under which such a system can be handled by conventional one-instanton techniques.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".