Spontaneous breaking of permutation symmetry in pseudo-hermitian quantum mechanics

Jun-Qing Li, Yan-Gang Miao

By adding an imaginary potential proportional to $$ip_1p_2$$ to the hamiltonian of an anisotropic planar oscillator, we construct a model which is described by a non-hermitian hamiltonian with PT pseudo-hermiticity. We introduce the mechanism of the spontaneous breaking of permutation symmetry of the hamiltonian for diagonalizing the hamiltonian. By applying the definition of annihilation and creation operators which are PT pseudo-hermitian adjoint to each other, we give the real spectra.

http://arxiv.org/abs/1110.2312
Quantum Physics (quant-ph)

Jun-Qing Li, Yan-Gang Miao

By adding an imaginary potential proportional to ip_1p_2 to the hamiltonian of an anisotropic planar oscillator, we construct a model which is described by a non-hermitian hamiltonian with PT pseudo-hermiticity. We introduce the mechanism of the spontaneous breaking of permutation symmetry of the hamiltonian for diagonalizing the hamiltonian. By applying the definition of annihilation and creation operators which are PT pseudo-hermitian adjoint to each other, we give the real spectra.

http://arxiv.org/abs/1110.2312

Quantum Physics (quant-ph)