Rotating unstable Langevin-type dynamics: linear and nonlinear mean passage time distributions

Area of Science:

• Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• Characterizing decay processes in unstable dynamical systems is crucial for understanding complex phenomena.
• Langevin-type dynamics, particularly rotating unstable systems with external forces, present significant analytical challenges.
• Existing theoretical frameworks may not fully capture the behavior of these systems across all timescales and force regimes.

Purpose of the Study:

• To develop and validate two novel theoretical descriptions for the decay process of linear rotating unstable Langevin-type dynamics.
• To analyze the influence of constant external forces on these dynamics using mean passage time distributions.
• To investigate both linear and nonlinear rotating unstable systems, including applications in laser physics and plasma physics.

Main Methods:

• Formulation of two matrix-based theoretical approaches: the Quasideterministic (QD) approach for long times and an alternative for shorter times.
• Utilizing a time-dependent rotation matrix to transform dynamics into a representation where noise and force are rotational.
• Validation of theories using a laser system (two variables) and theoretical considerations for three-variable systems, comparing with experimental and simulation data.

Main Results:

• The QD approach, when applied to non-forced systems, aligns with results for non-rotating unstable systems, particularly in the transformed y-representation.
• For forced systems, the QD approach is valid for weak forces, while the alternative theory is required for strong forces where rotational evolution dominates.
• Nonlinear corrections to linear systems are characterized as quantities evaluated in the deterministic limit.

Conclusions:

• The proposed theoretical frameworks provide effective tools for characterizing decay processes in rotating unstable Langevin dynamics.
• The choice of theoretical approach depends on the system's parameters, specifically the strength of the external force and the timescale of interest.
• The theories demonstrate broad applicability, with potential uses in laser physics, plasma physics, and other fields involving complex dynamical systems.