EmbeddingGemma 2: an open, lightweight multimodal embedding model
deepmind.google·6d ago
AI Engineering
Hacker News·Aug 13·5 min read
Graduate Student Proves a Quantum Uncertainty Principle for Fractals
TL;DR
Semyon Dyatlov has established a new uncertainty principle for quantum particles in relation to fractals, enhancing our understanding of their behavior in chaotic systems. This breakthrough could lead to universal mathematical tools for studying complex paths in higher dimensions.
✦ Why It Matters
Explore fractal patterns in your quantum simulations to enhance predictive accuracy.
Key Takeaways
- Investigate the implications of fractal uncertainty in your quantum mechanics projects.
- Consider how chaos theory applies to your current research or applications.
- Utilize insights from harmonic analysis to enhance your mathematical modeling.
- Stay updated on developments in fractal geometry and its applications.
How It Works
Cohen's proof involved isolating peaks from fractal-like functions and demonstrating that their Fourier transforms could not yield fractal structures. This required constructing a specialized damping function, which he achieved through innovative methods in complex analysis.