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Mirror symmetry breaking as a problem in dynamic critical phenomena
David Hochberg1, María Paz Zorzano
1Centro de Astrobiología (CSIC-INTA), Carretera Ajalvir Kilómetro 4, 28850 Torrejón de Ardoz, Madrid, Spain. hochbergd@inta.es
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
The Frank model
Area of Science:
- Theoretical Chemistry
- Chemical Physics
- Statistical Mechanics
Background:
- Spontaneous chiral synthesis is crucial for life.
- Understanding the Frank model's critical properties is key.
- Field theoretic renormalization group (RG) offers powerful analytical tools.
Purpose of the Study:
- To analyze the critical properties of the Frank model for spontaneous chiral synthesis.
- To apply renormalization group (RG) methods to understand universal behaviors.
- To identify RG fixed points (FPs) governing the model's dynamics.
Main Methods:
- Application of field theoretic renormalization group (RG) techniques.
- Analysis of long-time and long-wavelength properties.
- Comparison with multicolored directed percolation universality classes.
Main Results:
- The Frank model shares universality with directed percolation processes.
- Identified three types of RG fixed points (FPs): unstable, saddle, and two stable.
- Stable FPs correspond to unidirectional couplings, breaking chiral symmetry.
Conclusions:
- Homochirality emerges naturally from reaction noise in the critical regime.
- The Frank model provides insights into spontaneous chiral symmetry breaking.
- Critical dynamics are governed by specific RG fixed points (FPs).
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