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We investigate dynamical properties of the magnetization plateau state in the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction. The dynamical structure factor shows characteristic behavior depending on the next-nearest-neighbor interaction α and the bond alternation δ. The static structure factor takes the largest value at q=π for small δ. With increasing δ, the wave number of the largest value shifts towards q=π/2, taking the incommensurate value.

On the basis of a resonating valence-bond description, we investigate the excitation spectrum caused by the Raman process in cuprate two-leg spin ladders with a cyclic four-spin interaction. Owing to a cyclic four-spin interaction, the S = 0 three-triplet excitation energy is reduced and becomes smaller than the S = 0 two-triplet excitation energy around the end of the Brillouin zone. Possible interpretations for the change in the lowest-lying mode are discussed. We show that such a change in the lowest-lying mode yields the shoulder structure at the lower edge in the phonon-assisted optical absorption spectrum.

We calculate the field dependence of dynamical structure factors of the S = 1 bond-alternating Heisenberg-chain compound Ni(C9D24N4)(NO2)ClO4 and the S = 1 Haldane-gap compound Ni(C5D14N2)2N3(PF6). We show that in the former system the highest magnon branch vanishes at H ∼0.63Hc and one gapped branch emerges in H > Hc, where Hc is the critical field for the energy-gap closing. In the latter system, by contrast, three distinct magnon branches appear below and above Hc. The results are in qualitative agreement with recent experimental findings.

Dynamical structure factors of the S =1 bond-alternating spin chains in the dimer state are calculated at finite temperature using the pair dynamical correlated-effective-field approximation. At T =0, the delta-function-type peak corresponding to the one-magnon mode appears. When temperature increases, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.

We calculate the dynamical structure factor of the S = 1/2 two-leg spin ladder system, using a continued fraction method based on Lanczos algorithm. Characteristics of the lowest excited states are discussed from strong to weak interchain-coupling regions.