Non-Markovian stationary probability density for a harmonic oscillator in an electromagnetic field.
← Research streamThe authors report an exact solution of the Fokker-Planck equation for the stationary-state probability density of a harmonic oscillator embedded in an electromagnetic field, with a constant magnetic field and a stochastic electric field modeled as Gaussian e…
Study snapshot
Abstract
We calculate the exact solution of the Fokker-Planck equation for the stationary-state probability density of a harmonic oscillator embedded in an electromagnetic field. The magnetic field is assumed to be a constant and the electric field an external stochastic force with the properties of a Gaussian and exponentially correlated noise (Ornstein-Uhlenbeck process). In this work, we first study the problem in the absence of the magnetic field, then we obtain the complete solution and corroborate that the latter reduces to the former when the magnetic field is suppressed.
AI evidence extraction
Structured fields below were generated from the paper’s abstract and metadata to make the evidence easier to inspect. Automated extraction may be incomplete or incorrect; verify important details against the original paper.
Main findings
The authors report an exact solution of the Fokker-Planck equation for the stationary-state probability density of a harmonic oscillator embedded in an electromagnetic field, with a constant magnetic field and a stochastic electric field modeled as Gaussian exponentially correlated (Ornstein-Uhlenbeck) noise. They also solve the case without magnetic field and state that the full solution reduces to the no-magnetic-field case when the magnetic field is suppressed.
Outcomes measured
- Stationary-state probability density of a harmonic oscillator (exact solution of Fokker-Planck equation)
Limitations
- The abstract describes a theoretical/mathematical model rather than biological or epidemiological outcomes.
- No exposure metrics (e.g., frequency, field strength, SAR) are provided in the abstract.
- No health-related endpoints are described.
View raw extracted JSON
{
"study_type": "other",
"exposure": {
"band": null,
"source": "other",
"frequency_mhz": null,
"sar_wkg": null,
"duration": null
},
"population": null,
"sample_size": null,
"outcomes": [
"Stationary-state probability density of a harmonic oscillator (exact solution of Fokker-Planck equation)"
],
"main_findings": "The authors report an exact solution of the Fokker-Planck equation for the stationary-state probability density of a harmonic oscillator embedded in an electromagnetic field, with a constant magnetic field and a stochastic electric field modeled as Gaussian exponentially correlated (Ornstein-Uhlenbeck) noise. They also solve the case without magnetic field and state that the full solution reduces to the no-magnetic-field case when the magnetic field is suppressed.",
"effect_direction": "unclear",
"limitations": [
"The abstract describes a theoretical/mathematical model rather than biological or epidemiological outcomes.",
"No exposure metrics (e.g., frequency, field strength, SAR) are provided in the abstract.",
"No health-related endpoints are described."
],
"evidence_strength": "insufficient",
"confidence": 0.74,
"peer_reviewed_likely": "yes",
"keywords": [
"Fokker-Planck equation",
"harmonic oscillator",
"electromagnetic field",
"magnetic field",
"stochastic electric field",
"Gaussian noise",
"Ornstein-Uhlenbeck process",
"non-Markovian",
"stationary probability density"
],
"suggested_hubs": []
}AI-extracted fields are generated from the abstract and metadata and may be incomplete or incorrect. This material is for informational purposes and is not medical advice.
Identifiers and source
DOI: 10.1103/physreve.86.061115
PubMed: 23367901
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