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Tunable Lower Critical Fractal Dimension for a Nonequilibrium Phase Transition.
Mattheus Burkhard1, Luca Giacomelli1, Cristiano Ciuti1
1CNRS, Université Paris Cité, Matériaux et Phénomènes Quantiques, 75013 Paris, France.
Physical Review Letters
|June 7, 2026
Summary
This study explores how spatial dimensions and driving frequency influence phase transitions in quantum systems. Researchers found that fractal dimensions and driving frequency can tune critical behavior in these complex systems.
Area of Science:
- Quantum physics
- Condensed matter physics
- Non-equilibrium statistical mechanics
Background:
- Driven-dissipative systems exhibit complex quantum phenomena.
- Phase transitions in quantum systems are crucial for understanding emergent behavior.
- Spatial dimensionality plays a key role in determining system properties.
Purpose of the Study:
- To investigate the influence of spatial dimension and driving frequency on non-equilibrium phase transitions.
- To explore the possibility of fractal spatial dimensions in driven quantum systems.
- To determine the lower critical dimension of these transitions.
Main Methods:
- Theoretical investigation using numerical simulations of multimode dynamics.
- Analytical statistical mean-field treatment.
- Analysis of system-size dependence of asymptotic decay rates.
Main Results:
- Spatial dimension can be non-integer and fractal, dictated by the driving field's geometry.
- Critical slowing down characterizes the onset of criticality.
- The lower critical dimension was determined and found to be tunable.
Conclusions:
- Non-equilibrium phase transitions in driven-dissipative bosonic systems are sensitive to spatial dimensionality and driving frequency.
- Fractal dimensions can emerge and influence critical behavior.
- Continuous tuning of the critical dimension is achievable via frequency detuning.
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