Universal spectral behavior of x(2)(ix)(epsilon) potentials

作者：Bender Carl M^*; Hook Daniel W

来源：Physical Review A, 2012, 86(2): 022113.

DOI：10.1103/PhysRevA.86.022113

The PT-symmetric Hamiltonian H = p(2) + x(2)(ix)(epsilon) (epsilon real) exhibits a phase transition at epsilon = 0. When epsilon >= 0, the eigenvalues are all real, positive, discrete, and grow as e increases. However, when epsilon < 0 there are only a finite number of real eigenvalues. As epsilon approaches - 1 from above, the number of real eigenvalues decreases to 1, and this eigenvalue becomes infinite at epsilon = -1. In this paper it is shown that these qualitative spectral behaviors are generic and that they are exhibited by the eigenvalues of the general class of Hamiltonians H-(2n) = p(2n) + x(2)(ix)(epsilon) (epsilon real, n = 1,2,3, ... ). The complex classical behaviors of these Hamiltonians are also examined.

• 出版日期2012-8-17