Level Spacing Distributions and Quantum Chaos in Hermitian and non-Hermitian Systems
【摘要】：正 The correspondence between quantum level spacing distributions and classical motion of l-D PT symmetricnon-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potentialV_1(x)=(ix)~((2n+1)/m) and general polynomial potential V_2(x)=x~(2m)+ib_1x~(2M-1)+b_2x~(2m-2+…+ib_(2M-1)x. The levelspacing distribution of V_1 has two forms. When 2n+1-2m is positive, the level spacing distribution of real eigen valuesassumes 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 itselfin classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacingdistribution mentioncd above is not due to the spontaneous breaking down of PT symmetry. Level spacing distributionof V_2 assumes an increasing power function when order of the polynomial is greater than two.