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Asymptotic freedom and noninteger dimensionality.
1Oklahoma State University, Stillwater, Stillwater, USA. subhash.kak@okstate.edu.
Scientific Reports
|February 10, 2021
Summary
In low-dimensional spaces (below 3D), object potential decreases with increasing energy. Below 2D, forces vanish, revealing a new asymptotic freedom paradigm with potential applications in materials science.
Area of Science:
- Condensed matter physics
- Materials science
- Quantum mechanics
Background:
- Asymptotic freedom is crucial for understanding strange metals, unconventional superconductors, and fractional quantum Hall states.
- Anomalous mechanical effects are significant in metamaterials.
Purpose of the Study:
- To investigate the behavior of inter-object potential in low-dimensional spaces.
- To explore the implications of a new asymptotic freedom paradigm.
- To identify potential applications in condensed matter physics and materials science.
Main Methods:
- Theoretical analysis of inter-object potential as a function of dimensionality and energy levels.
- Mathematical modeling of force behavior in dimensions below two.
Main Results:
- A critical dimensionality between two and three was identified, below which potential decreases with increasing energy.
- For dimensions below two, the potential becomes constant, leading to the disappearance of force (asymptotic freedom).
Conclusions:
- The study reveals a novel form of asymptotic freedom in low-dimensional systems.
- This finding has potential applications in areas like strange metals, superconductors, and metamaterials.
- It offers new insights into anomalous mechanical effects relevant to metamaterials.
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