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Brownian motion under noninstantaneous resetting in higher dimensions
Anna S Bodrova1,2,3, Igor M Sokolov1,4
1Department of Physics, Humboldt University, Newtonstrasse 15, 12489 Berlin, Germany.
This study examines Brownian motion with resetting in higher dimensions. While probability density function invariance is unique to 1D, mean-squared displacement invariance persists in higher dimensions.
Area of Science:
- Statistical Physics
- Physical Chemistry
- Mathematical Physics
Background:
- Brownian motion describes random particle movement.
- Resetting mechanisms introduce periodic returns to a starting point.
- Higher-dimensional systems exhibit complex behaviors compared to 1D.
Purpose of the Study:
- Investigate Brownian motion with constant-speed resetting in dimensions greater than one.
- Analyze the probability density function (PDF) and mean-squared displacement (MSD).
- Compare Poissonian and deterministic resetting protocols.
Main Methods:
- Mathematical modeling of resetting Brownian motion.
- Analysis of probability density functions (PDFs).
- Calculation and analysis of mean-squared displacement (MSD).
Main Results:
- The probability density function (PDF) invariance with return speed is unique to 1D Poissonian resetting.
- Mean-squared displacement (MSD) invariance can still be observed in higher dimensions.
- Both Poissonian and deterministic resetting protocols were analyzed.
Conclusions:
- Resetting Brownian motion in higher dimensions shows dimension-dependent properties.
- The invariance of physical observables like MSD can extend beyond 1D.
- Understanding these behaviors is crucial for applications in statistical physics and beyond.
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