Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities

We investigate operator growth in a bipartite kicked coupled tops (KCT) system with out-of-time ordered correlators (OTOC). Due to the conservation of total magnetization, the system admits a decomposition into distinct invariant subspaces. Initially focusing on the largest invariant subspace, we observe that, under strong coupling, the OTOC growth rate correlates remarkably well with the classical Lyapunov exponent. For the case of scrambling in the mixed phase space, we invoke Percival's conjecture to partition the eigenstates of the Floquet map into regular and chaotic. We notice that the scrambling rate in the chaotic subspace is quantified by OTOCs calculated with respect to a random state constructed from the mixture of chaotic eigenstates described above. We then consider the total system and study OTOCs for different types of initial operators, including the case of random operators where the operators are chosen randomly from the Gaussian unitary ensemble. We observe that the presence of a conserved quantity results in different types of scrambling behaviors for various choices of initial operators depending on whether the operators commute with the symmetry operator. When the operators are random, the averaged OTOC is related to the linear entanglement entropy of the Floquet operator, as found in earlier works. More importantly, we derive a simple expression for the averaged OTOC when random operators commute with the symmetry operator. Our results offer (i) fresh insights into scrambling in mixed-phase space - a domain that has not been comprehensively explored before and (ii) implications of the conserved quantities on the scrambling of information.Comment: 12 pages, 12 figures, 1 table, improved versio