Interaction-free ergodicity-breaking driven by temporally hyperuniform noise
Phys. Rev. E 112, 054136 – Published 20 November, 2025
DOI: https://doi.org/10.1103/g921-ppyv
Abstract
We show that norm-conserving spin models driven by temporally hyperuniform noise exhibit a sharp ergodicity-breaking transition in the absence of interactions. In the nonergodic phase, the dynamics freeze into configurations determined by the initial condition. Our analysis demonstrates that such interaction-free ergodicity breaking arises generically whenever a global constraint is imposed and the driving noise is class-I hyperuniform, the strongest form in Torquato's classification. The transition can also be interpreted as a condensation of fluctuations into the zero-frequency mode, reminiscent of Bose–Einstein condensation in an ideal gas.
Physics Subject Headings (PhySH)
- Brownian motion
- Classical mechanics
- Classical statistical mechanics
- Critical phenomena
- Diffusion
- Dynamical phase transitions
- Lagrangian dynamics
- Noise
- Nonequilibrium statistical mechanics
- Phase transitions
- Random walks
- Stochastic processes
- Bose-Einstein condensates
- Classical spin models
- Dynamical systems
- Nonequilibrium systems
- Stochastic dynamical systems
- Brownian dynamics
- Langevin equation
- Non-Markovian processes
- Statistical methods
- Stochastic differential equations
- Time series analysis
