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Incertidumbres de posición-momento en sistemas clásicos

Dipesh K Singh1, P K Mohanty1

  • 1Indian Institute of Science Education and Research Kolkata, Department of Physical Sciences, Mohanpur 741246, India.

Physical review. E
|December 23, 2025
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Resumen
Este resumen es generado por máquina.

Desarrollamos un novedoso baño térmico que preserva el momento angular, lo que lleva a una incertidumbre mínima en la posición y el momento de las partículas. Este límite inferior está directamente relacionado con el momento angular medio, ofreciendo nuevas perspectivas sobre la mecánica cuántica.

Palabras clave:
mecánica estadísticamecánica cuánticamecánica clásicabaño térmicomomento angularincertidumbre de posición-momento

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Área de la Ciencia:

  • Mecánica estadística
  • Mecánica cuántica
  • Mecánica clásica

Sus antecedentes:

  • Comprender el comportamiento de los sistemas en baños térmicos es crucial en la mecánica estadística.
  • El papel del momento angular en la definición de las propiedades del sistema requiere una mayor investigación.
  • Los baños térmicos existentes a menudo conducen a un momento angular medio cero, lo que limita ciertas aplicaciones.

Objetivo del estudio:

  • Diseñar un baño térmico que pueda preservar o controlar el momento angular de un sistema.
  • Investigar las implicaciones de un momento angular medio distinto de cero en las incertidumbres de las partículas.
  • Establecer un límite inferior fundamental para las incertidumbres de posición-momento relacionadas con el momento angular.

Principales métodos:

  • Desarrollo de un baño térmico especializado.
  • Análisis teórico de partículas clásicas dentro de este baño.
  • Derivación de las relaciones de incertidumbre de posición-momento.

Principales resultados:

  • El baño térmico diseñado mantiene una distribución de energía de Boltzmann en el estado estacionario.
  • Las partículas en este baño exhiben incertidumbres de posición-momento con un límite inferior estrictamente positivo.
  • Este límite inferior es proporcional al valor absoluto del momento angular medio.
  • Una constante adimensional 'c' caracteriza esta proporcionalidad, acotada universalmente por la unidad.
  • Para partículas en potenciales centrales, c es precisamente igual a 1/2.

Conclusiones:

  • El estudio introduce un novedoso baño térmico con implicaciones para la mecánica estadística y cuántica.
  • Se establece una relación directa entre el momento angular y las incertidumbres fundamentales de las partículas.
  • Los hallazgos sugieren nuevos marcos teóricos para sistemas con momento angular conservado o controlado.