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Related Experiment Video

Updated: May 14, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Singular probability distribution of shot-noise driven systems.

Akihisa Ichiki¹, Yukihiro Tadokoro, M I Dykman

¹Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 16, 2013

Summary

Shot noise drives systems to exhibit power-law singularities in their coordinate distribution. These singularities form peaks, especially in the underdamped regime, revealing signatures of shot-noise fluctuations.

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Area of Science:

Statistical physics
Non-equilibrium systems
Stochastic processes

Background:

Understanding the behavior of systems subjected to random fluctuations is crucial.
Shot noise, characterized by discrete random pulses, introduces unique dynamics.
Previous studies have explored noise effects, but the specific impact of shot noise on probability distributions requires further investigation.

Purpose of the Study:

To investigate the stationary probability distribution of a system driven by shot noise.
To analyze the emergence and characteristics of singularities in the coordinate distribution.
To explore the influence of shot noise on both overdamped and underdamped regimes.

Main Methods:

Analytical derivation of the stationary probability distribution.
Identification of power-law singularities in the distribution.
Analysis of peak formation and position in both overdamped and underdamped systems.
Comparison of analytical findings with numerical simulations.

Main Results:

The coordinate distribution exhibits power-law singularities in its central part for both overdamped and underdamped systems.
These singularities manifest as distribution peaks at low noise pulse rates.
Peak positions in the underdamped regime follow a geometric progression.
The energy distribution in the underdamped case also shows multiple peaks with geometric progression positions.
Analytical results show excellent agreement with numerical simulations.

Conclusions:

Shot noise induces unique structures in the probability distribution of driven systems.
The observed power-law singularities and geometric progressions are signatures of shot-noise fluctuations.
The findings provide a deeper understanding of non-equilibrium statistical mechanics under shot noise conditions.