1/3 Power-Law Universality Class out of Stochastic Driving in Interacting Systems

Area of Science:

• Statistical mechanics
• Quantum many-body systems
• Dynamical systems

Background:

• Many-body systems often exhibit complex dynamics.
• Stochastic fluctuations in interactions can significantly alter system behavior.
• Understanding universal behaviors in such systems is crucial for theoretical and experimental advancements.

Purpose of the Study:

• To investigate the mean-field dynamics of many-body systems with stochastically fluctuating interactions.
• To identify universal features in the system's order parameter decay.
• To elucidate the underlying mechanisms driving this universality.

Main Methods:

• Mean-field theory analysis.
• Investigation of stochastic processes.
• Self-consistent determination of system parameters.
• Analysis of order parameter evolution over time.

Main Results:

• A universal algebraic decay of the order parameter, m(t) ~ t^{-χ}, with χ=1/3 was discovered.
• This decay exponent is independent of stochastic driving strength, energy spectrum, initial states, and driving protocols.
• The universality class is linked to a diffusive process with a self-consistently determined time-dependent diffusion coefficient.

Conclusions:

• The findings demonstrate a broad dynamical universality in stochastically interacting many-body systems.
• The identified mechanism provides a fundamental understanding of order parameter decay.
• The results have implications for experimental systems like cavity quantum electrodynamics (QED).