Singular probability distribution of shot-noise driven systems.

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.