Dynamic symmetries at the critical point

Area of Science:

• Nuclear physics
• Quantum mechanics
• Mathematical physics

Background:

• Dynamic symmetries offer powerful frameworks for understanding complex quantum systems.
• Shape phase transitions in nuclei, particularly between U(5) and SO(6) symmetries, are critical phenomena.
• Bessel functions appear in various physical contexts, including nuclear models.

Purpose of the Study:

• To introduce a new class of dynamic symmetries.
• To propose utilizing these symmetries to describe nuclear spectra at critical points.
• To generalize the application to systems undergoing second-order phase transitions between specific algebraic structures.

Main Methods:

• Introduction of a novel class of dynamic symmetries.
• Association of symmetry elements with zeros of Bessel functions.
• Application to the description of nuclear spectra.

Main Results:

• A new class of dynamic symmetries has been successfully introduced.
• The proposed symmetry class effectively describes nuclear spectra at the U(5)-SO(6) critical point.
• The framework is generalizable to other second-order phase transitions between U(n-1) and SO(n) structures.

Conclusions:

• The newly introduced dynamic symmetries provide a valuable tool for analyzing critical phenomena in quantum systems.
• The connection to Bessel function zeros offers a unique mathematical avenue for spectral description.
• This work advances the understanding of phase transitions in nuclear and other quantum systems.