The first detection time of one-dimensional systems with long-range interactions

We studied the first detection problem of the quantum particle transition on a one-dimensional Levy crystal, which includes the long-range interactions and the transition process on the system can be described by the spatial fractional Schrodinger equation. The results demonstrate that the long-range interactions can be directly obtained for short time. The average detection times < n? and the corresponding variance var(n) are discontinuous with respect to the detection interval t, which could be caused by the beat of the detection frequency 1/t and the oscillation frequency of the first detection probability Fn.