SciPost Submission Page
Classical representation of the dynamics of quantum spin chains
by Tony Jin
Submission summary
| Authors (as registered SciPost users): | Tony Jin |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2502.10502v2 (pdf) |
| Date submitted: | Sept. 16, 2025, 2:52 p.m. |
| Submitted by: | Tony Jin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Since the advent of quantum mechanics, classical probability interpretations have faced significant challenges. A notable issue arises with the emergence of negative probabilities when attempting to define the joint probability of non-commutative observables. In this work, we propose a resolution to this dilemma for quantum spin chains, by introducing an exact representation of their dynamics in terms of classical continuous-time Markov chains (CTMCs). These CTMCs effectively model the creation, annihilation, and propagation of pairs of classical particles and antiparticles. The quantum dynamics then emerges by averaging over various realizations of this classical process.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1) The derivations are clearly presented and well motivated, facilitating understanding of the proposed construction.
2) Several numerical examples are convincing and support the main theoretical conclusions.
3) The framework is original and provides an interesting new angle on classical representations of quantum dynamics.
Weaknesses
Report
Overall, the article introduces a novel and promising framework for treating quantum dynamics and is presented in a clear and concise manner. The work clearly merits publication in SciPost.
Requested changes
1) To the best of my understanding, Eq.~(8) violates the conservation of the total probability $\sum\limits_{C} (p_C^{{\bullet}}+p_C^{{\circ}})$. Furthermore, the growth of the total probability contrasts with a physical Markovian dynamics and, to the best of my understanding, leads to a loss of numerical precision with the growth of the total number of particles.
As this is the main equation derived in this article, I suggest emphasizing this fact directly and providing a summary of the resulting dynamics, clearly separating its physical and non-physical properties.
2) I believe the article would benefit from a more careful discussion of the error estimate $\Delta \langle\hat{O}(t)\rangle \propto \frac{N_{tot}}{\sqrt{M}}$. In particular, while the appearance of the factor $N_{\mathrm{tot}}$ is intuitively clear, its precise origin is not fully obvious, and a more carefully motivated derivation would be helpful.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)