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arXiv · 1206.5100

PT phase transition in multidimensional quantum systems

Carl M. Bender·David J. Weir
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Abstract

Non-Hermitian PT-symmetric quantum-mechanical Hamiltonians generally exhibit a phase transition that separates two parametric regions, (i) a region of unbroken PT symmetry in which the eigenvalues are all real, and (ii) a region of broken PT symmetry in which some of the eigenvalues are complex. This transition has recently been observed experimentally in a variety of physical systems. Until now, theoretical studies of the PT phase transition have generally been limited to one-dimensional models. Here, four nontrivial coupled PT-symmetric Hamiltonians, $H=p^2/2+x^2/2+q^2/2+y^2/2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2+igx^2y$, $H=p^2/2+x^2/2+q^2/2+y^2/2+r^2/2+z^2/2+igxyz$, and $H=p^2/2+x^2/2+q^2/2+y^2+r^2/2+3z^2/2+igxyz$ are examined. Based on extensive numerical studies, this paper conjectures that all four models exhibit a phase transition. The transitions are found to occur at $g\approx 0.1$, $g\approx 0.04$, $g\approx 0.1$, and $g\approx 0.05$. These results suggest that the PT phase transition is a robust phenomenon not limited to systems having one degree of freedom.

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Carl M. Bender, David J. Weir. 2012-06-22. PT phase transition in multidimensional quantum systems. https://doi.org/10.1088/1751-8113/45/42/425303

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