Non-Hermitian quantum mechanics and exceptional points in molecular electronics
Bibliographic record
Abstract
In non-Hermitian (NH) quantum mechanics, Hamiltonians are studied whose eigenvalues are not necessarily real since the condition of hermiticity is not imposed. Certain symmetries of NH operators can ensure that some or all of the eigenvalues are real and thus suitable for the description of physical systems whose energies are always real. While the mathematics of NH quantum mechanics is well developed, applications of the theory to real quantum systems are scarce, and no closed system is known whose Hamiltonian is NH. Here, we consider the elementary textbook example of a NH Hamiltonian matrix, and we show how it naturally emerges as a simplifying concept in the modeling of molecular electronic devices. We analyze the consequences of non-Hermiticity and exceptional points in the spectrum of NH operators for the molecular conductance and the spectral density of simple models for molecules on surfaces.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".