RECORD
Spectral properties of stochastic processes possessing finite propagation velocity
Statistical Mechanics · Submitted 21 Jul 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A generic spectral feature of these processes is the lower-boundedness of the real part of the eigenvalue spectrum, corresponding to an upper limit for the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson-Kac processes and L\'evy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. A generic spectral feature of these processes is the lower-boundedness of the real part of the eigenvalue spectrum, corresponding to an upper limit for the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. We analyze also Generalized Poisson-Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. In this case, there exists a critical value of the wavevector above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. This model can be extended to the quantum case and, in point of fact, it represents a simple and highlighting example of a sub-quantum dynamics with hidden variables.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. | contribution 0.97 | 0.86 | 0.06 | asserted 0.89 |
| s1 | Generalized Poisson-Kac processes and L\'evy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. | method 0.47 | 0.42 | 0.04 | asserted 0.99 |
| s2 | A generic spectral feature of these processes is the lower-boundedness of the real part of the eigenvalue spectrum, corresponding to an upper limit for the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. | result 0.97 | 0.67 | 0.41 | asserted 1.00 |
| s3 | We analyze also Generalized Poisson-Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. | contribution 0.96 | 0.78 | 0.04 | asserted 0.94 |
| s4 | In this case, there exists a critical value of the wavevector above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. | result 1.00 | 0.84 | 0.18 | asserted 1.00 |
| s5 | This model can be extended to the quantum case and, in point of fact, it represents a simple and highlighting example of a sub-quantum dynamics with hidden variables. | interpretation 0.99 | 0.43 | 0.11 | asserted 0.87 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
This article investigates the spectral structure of the evolution operators associated with the statistical description of stochastic processes possessing finite propagation velocity. Generalized Poisson-Kac processes and L\'evy walks are explicitly considered as paradigmatic examples of regular and anomalous dynamics. A generic spectral feature of these processes is the lower-boundedness of the real part of the eigenvalue spectrum, corresponding to an upper limit for the spectral dispersion curve, physically expressing the relaxation rate of a disturbance as a function of the wave vector. We analyze also Generalized Poisson-Kac processes possessing a continuum of stochastic states parametrized with respect to the velocity. In this case, there exists a critical value of the wavevector above which the point spectrum ceases to exist, and the relaxation dynamics becomes controlled by the essential part of the spectrum. This model can be extended to the quantum case and, in point of fact, it represents a simple and highlighting example of a sub-quantum dynamics with hidden variables.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 1 sentence without a confident label
Cites as support 1 paper
-
This was shown especially for LWs by the recent work of Fedotov [ref] (see also [ref] ), and by the unifying theory of Extended Poisson-Kac processes developed by Giona and collaborators [ref] .
Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity · Introduction · 0.99
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.