The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potenti...The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potential V1 (x) = (ix)(2n+1)/m and general polynomial potential V2(x) = x2M + ib1x2M-1 + b2x2M-2 +... + ib2M-1x. The level spacing distribution of V1 has two forms. When 2n + 1 - 2m is positive, the level spacing distribution of real eigen values assumes a decreasing power function, while it behaves as an increasing power function when 2n + 1 - 2m is negative.The PT symmetry of this system is spontaneously broken as 2n + 1 - 2m becomes negative. This change manifests itself in classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacing distribution mentioned above is not due to the spontaneous breaking down of PT symmetry. Level spacing distribution of V2 assumes an increasing power function when order of the polynomial is greater than two.展开更多
文摘The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potential V1 (x) = (ix)(2n+1)/m and general polynomial potential V2(x) = x2M + ib1x2M-1 + b2x2M-2 +... + ib2M-1x. The level spacing distribution of V1 has two forms. When 2n + 1 - 2m is positive, the level spacing distribution of real eigen values assumes a decreasing power function, while it behaves as an increasing power function when 2n + 1 - 2m is negative.The PT symmetry of this system is spontaneously broken as 2n + 1 - 2m becomes negative. This change manifests itself in classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacing distribution mentioned above is not due to the spontaneous breaking down of PT symmetry. Level spacing distribution of V2 assumes an increasing power function when order of the polynomial is greater than two.
