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Invariancia de escala: una puerta de entrada a las transiciones de fase
1Departamento de Física, Universidade Estadual Paulista (UNESP), Av. 24A, 1515, São Paulo 13506-900, SP, Brazil.
Entropy (Basel, Switzerland)
|August 28, 2025
Resumen
Este estudio revela la invarianza de escala en los sistemas dinámicos que pasan de la regularidad al caos. Este comportamiento refleja una transición de fase continua, evidenciada por la susceptibilidad divergente cerca del punto crítico.
Área de la Ciencia:
- Dinámica no lineal
- Mecánica estadística
- Teoría del caos
Sus antecedentes:
- Los sistemas dinámicos pueden hacer la transición entre estados ordenados (regulares) y desordenados (caóticos).
- Los sistemas hamiltonianos, caracterizados por variables de acción y ángulo, a menudo se utilizan para modelar tales transiciones.
- Las transiciones de fase en los sistemas físicos implican fenómenos críticos y leyes de escala.
Objetivo del estudio:
- Investigar la invarianza de escala en una clase específica de mapeos no lineales de 2D que preservan el área.
- Para caracterizar la transición del comportamiento regular al caótico en estos sistemas.
- Para determinar si esta transición exhibe las propiedades de una transición de fase continua.
Principales métodos:
- Utilizó un mapeo no lineal bidimensional que conserva el área en el espacio de fase.
- Analizó el comportamiento de las variables de acción y ángulo bajo la variación de un parámetro de control.
- Calculó la acción cuadrada promedio y la susceptibilidad dentro del régimen caótico.
Principales resultados:
- Invarianza de escala observada en la acción cuadrada promedio en la región caótica.
- Se ha identificado un parámetro de orden que se acerca a cero en el punto de transición.
- Se ha demostrado que la susceptibilidad diverge a medida que el parámetro de orden se acerca a cero.
Conclusiones:
- La transición de la regularidad al caos en estos sistemas exhibe características de una transición de fase de segundo orden o continua.
- La invarianza de escala proporciona evidencia de universalidad en la transición al caos.
- La susceptibilidad divergente apoya aún más la analogía con las transiciones de fase en la mecánica estadística.
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