SciPost Submission Page
Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
by Jeferson D. da Silva, Diego Tapias, Peter Sollich, Fernando L. Metz
Submission summary
| Authors (as registered SciPost users): | Fernando Metz |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2408.13322v2 (pdf) |
| Date accepted: | 2025-01-13 |
| Date submitted: | 2024-12-12 13:19 |
| Submitted by: | Metz, Fernando |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We study the spectral properties and eigenvector statistics of the Laplacian on highly-connected networks with random coupling strengths and a gamma distribution of rescaled degrees. The spectral density, the distribution of the local density of states, the singularity spectrum and the multifractal exponents of this model exhibit a rich behaviour as a function of the first two moments of the coupling strengths and the variance of the rescaled degrees. In the case of random coupling strengths, the spectral density diverges within the bulk of the spectrum when degree fluctuations are strong enough. The emergence of this singular behaviour marks a transition from non-ergodic delocalized states to localized eigenvectors that exhibit pronounced multifractal scaling. For constant coupling strengths, the bulk of the spectrum is characterized by a regular spectral density. In this case, the corresponding eigenvectors display localization properties reminiscent of the critical point of the Anderson localization transition on random graphs.
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
Author comments upon resubmission
We resubmit hereby the manuscript entitled "Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks" for publication in SciPost Physics. We have answered to all points raised by the referees and the paper has been modified accordingly. We hope that the resubmitted version of the manuscript will be accepted for publication.
Sincerely,
Fernando Metz
(corresponding author)
List of changes
All changes in the manuscript have been specified in the replies to the referees.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)