Jun-Qing Li, Yan-Gang Miao
By adding an imaginary interacting term proportional to ip_1p_2 to the
Hamiltonian of a free anisotropic planar oscillator, we construct a new model
which is described by the PT-pseudo-Hermitian Hamiltonian with the permutation
symmetry of two dimensions. We prove that our model is equivalent to the
Pais-Uhlenbeck oscillator and thus establish a relationship between our
PT-pseudo-Hermitian system and the fourth-order derivative oscillator model. We
also point out the spontaneous breaking of permutation symmetry which plays a
crucial role in giving a real spectrum free of interchange of positive and
negative energy levels in our model. Moreover, we find that the permutation
symmetry of two dimensions in our Hamiltonian corresponds to the identity (not
in magnitude but in attribute) of two different frequencies in the
Pais-Uhlenbeck oscillator, and reveal that the unequal-frequency condition
imposed as a prerequisite upon the Pais-Uhlenbeck oscillator can reasonably be
explained as the spontaneous breaking of this identity.
View original:
http://arxiv.org/abs/1110.2312
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