Papers by Keyword: Periodic System

Abstract: The Dirac contour representation functions fk(z) and fb(z) are employed to represent theket states |f ⟩ and bra states ⟨f |, respectively, in quantum systems with a finite-dimensional Hilbertspace H_2j+1. The scalar product within these quantum systems is defined using a contour integral.Moreover, a numerical approach is utilized to examine the time evolution of both periodic and non-periodic systems, utilizing several Hamiltonian matrices. Furthermore, the stability of periodic systemsis investigated. In addition to these aspects, we study the most significant application of the Dirac con-tour representation, which is its capability to handle an extended Hilbert space, suitable for describingquantum physics at negative temperatures.

Abstract: In a mechanical system that has periodically repeated subcomponents, premature failures or malfunctions often occur. Due to slight irregularities of parameters of periodic systems, maximal frequency responses of a few subcomponents become often significantly larger than those of other subcomponents. These phenomena, called frequency response localization, need to be comprehended for reliable designs of the periodic systems. In the present study, the effects of parameter distribution patterns on the frequency response localization are investigated. Probabilistic results of the frequency response localization characteristics with two distinct parameter distribution patterns are exhibited.