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Lecture Notes: Many-body quantum dynamics with MCTDH-X
by Paolo Molignini, Sunayana Dutta, Elke Fasshauer
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Submission summary
| Authors (as registered SciPost users): | Paolo Molignini |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00007v2 (pdf) |
| Date submitted: | 2024-12-29 13:20 |
| Submitted by: | Molignini, Paolo |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The lecture notes on “Many-body Quantum Dynamics with MCTDH-X”, adapted from the 2023 Heidelberg MCTDH Summer School, provide an in-depth exploration of the Multiconfigurational Time-Dependent Hartree approach for indistinguishable particles. They serve as a comprehensive guide for understanding and utilizing the MCTDH-X software for both bosonic and fermionic systems. The tutorial begins with an introduction to the MCTDH-X software, highlighting its capability to handle various quantum systems, including those with internal degrees of freedom and long-range interactions. The theoretical foundation is then laid out on how to solve the time-dependent and time-independent Schrödinger equations for many-body systems. The workflow section provides practical instructions on setting up and executing simulations using MCTDH-X. Detailed benchmarks against exact solutions are presented, showcasing the accuracy and reliability of the software in ground-state and dynamic simulations. The notes then delve into the dynamics of quantum systems, covering relaxation processes, time evolution, and the analysis of propagation for both bosonic and fermionic particles. The discussion includes the interpretation of various physical quantities such as energy, density distributions, and orbital occupations. Advanced features of MCTDH-X are also explored in the last section, including the calculation of correlation functions and the creation of visualizations through video tutorials. The notes conclude with a Linux/UNIX command cheat sheet, facilitating ease of use for users operating the software on different systems. Overall, these lecture notes provide a valuable resource for researchers and students in the field of quantum dynamics, offering both theoretical insights and practical guidance on the use of MCTDH-X for studying complex many-body systems.
Author comments upon resubmission
List of changes
The reply to the referees is contained in the attached document.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2025-1-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202408_00007v2, delivered 2025-01-23, doi: 10.21468/SciPost.Report.10539
Strengths
1. Clarity in presenting the basics of MCTDH-X theory:
these lecture notes are structured to guide the reader through the Multiconfigurational Time-Dependent Hartree approach for both bosonic and fermionic systems. They clearly introduce the theoretical framework, emphasizing the contrast between MCTDH and mean-field theories like Gross-Pitaevskii or Hartree-Fock
2. Effectiveness in guiding the reader through complicated many-body problems: the article provides comprehensive benchmarks and step-by-step workflows, including exact solutions for specific model problems (the Harmonic Interaction Model) . It not only introduces the time-independent and time-dependent cases but also illustrates how to handle complex systems using numerical methods, with a balance between practical and theoretical aspects
3. Completeness: the coverage of both imaginary- (for ground state) and real-time dynamics, as well as advanced analysis features like correlation functions, is thorough. The authors further includes discussion of delicate topics like symmetry-breaking and restoration.
Weaknesses
None
Report
I have carefully reviewed the authors’ reply letter and the revised version of the manuscript. I appreciate the authors’ efforts to address all the concerns raised by the reviewers in the first round and to amend the manuscript accordingly. The final version is significantly improved, and the addition of the new graphs with a more appropriate log scale is particularly illuminating. I am confident that this manuscript will be a valuable contribution to the field, and I am pleased to recommend its publication
Requested changes
Minor issue remaining:
- below eq. 9 in p 5, please reconsider the statement "In chemistry, these localized orbitals...". It is not obvious (and indeed it is not true) that the natural orbtial are localized. Localization ("of the eigenvectors") becomes possible when there is degeneracy in the eigenvalues, i.e. in the natural population, to within some fixed accuracy. It is this freedom that it is exploited in the localization process.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)