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In addition to an analogy with the Boltzmann factor of the OCP with inverse temperature \(\beta = 2\) , the GinUE eigenvalue PDF permits an interpretation as the absolute value squared of the ground state wave function for spinless fermions in the plane subject to a perpendicular magnetic field. More generally, for \(\beta \) twice an odd positive integer m the OCP Boltzmann factor occurs as proportional to the absolute value squared of Laughlin trial wavefunction in the theory of the fractional quantum Hall effect with filling fraction 1/m. In relation to the topic of chaotic behaviour in dissipative quantum systems, statistical properties of the now complex energy spectrum can be compared with those of bulk GinUE eigenvalues.

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Further Theory and Applications

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  • 出版模式：

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  • 发表日期：

    2025年

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  • Sung-Soo Byun,
  • Peter J. Forrester

摘要

In addition to an analogy with the Boltzmann factor of the OCP with inverse temperature \(\beta = 2\) , the GinUE eigenvalue PDF permits an interpretation as the absolute value squared of the ground state wave function for spinless fermions in the plane subject to a perpendicular magnetic field. More generally, for \(\beta \) twice an odd positive integer m the OCP Boltzmann factor occurs as proportional to the absolute value squared of Laughlin trial wavefunction in the theory of the fractional quantum Hall effect with filling fraction 1/m. In relation to the topic of chaotic behaviour in dissipative quantum systems, statistical properties of the now complex energy spectrum can be compared with those of bulk GinUE eigenvalues.