One of the unitary forms of the quantum mechanical time evolution operator is given by Cayley's approximation. A numerical implementation of the same involves the replacement of second derivatives in Hamiltonian with the three-point formula, which leads to a tridiagonal system of linear equations. In this work, we invoke the highly accurate five-point stencil to discretize the wave function onto an Implicit-Explicit pentadiagonal Crank-Nicolson scheme. It is demonstrated that the resultant solutions are significantly more accurate than the standard ones. We also discuss the resolution of bipartite wavepacket dynamics and derive conditions under which a product state from the laboratory perspective remains a product state from the center-of-mass point of view. This has profound applications for decoupling complicated bipartite dynamics into two independent single-particle problems.

The nonequilibrium properties of strongly correlated materials present a target in the search for new phases of matter. It is important to observe the types of excitations that exist in these materials and their associated relaxation dynamics. We have studied the photoexcitations in a spin-orbit assisted Mott insulator alpha-RuCl3 using time-resolved two-photon photoemission spectroscopy and transient reflection spectroscopy. We find that photoexcited carriers (doublons) in the upper Hubbard band rapidly relax to Mott-Hubbard excitons on a timescale of less than 200 fs. Subsequently, further relaxation of these lower-energy quasiparticles occurs with an energy-dependent time constant of that ranges from 370 to 600 fs due to exciton cooling. The population of Mott-Hubbard excitons persists for timescales up to several microseconds.

Driving superconductors out of equilibrium is a promising avenue to study their equilibrium properties as well as to control the superconducting state. Nonequilibrium superconductors are often studied using time-resolved optical conductivity measurements. Thus, the characterization of a superconducting state in a pump driven nonequilibrium state requires careful attention in the time domain. We calculate the time-resolved optical conductivity of a pumped superconducting state using a nonequilibrium Keldysh approach. Through functional derivation, the optical conductivity is obtained with full vertex corrections and used to characterize the transient superconducting state. The transient optical conductivity shows the suppression of the superconducting order parameter in the time domain. The subsequent recovery of the order parameter exhibits oscillatory behavior that corresponds to the Higgs amplitude mode, and may be seen in several parts of the spectrum.

Time-resolved optical conductivity is an often used tool to interrogate quantum materials driven out of equilibrium. Theoretically calculating this observable is a complex topic with several approaches discussed in the literature. Using a nonequilibrium Keldysh formalism and a functional derivative approach to the conductivity, we present a comparison of two particular approaches to the calculation of the optical conductivity and their distinguishing features, as applied to a pumped superconductor. The two methods are distinguished by the relative motion of the probe and gate times; either the probe or gate time is kept fixed while the other is swept. We find that both the methods result in same qualitative features of the time-resolved conductivity after pump is over. However, calculating the conductivity by keeping the gate fixed removes artifacts inherent to the other method. We provide software that, based on data for the first method, is able to construct the second approach.

Electron-boson scattering that is peaked in the forward direction has been suggested as an essential ingredient for enhanced superconductivity observed in FeSe monolayers. Here, we study the superconducting state of a system dominated by forward scattering in the time-domain and contrast its behavior against the standard isotropic BCS case for both s- and d-wave symmetries. An analysis of the electron's dynamics in the pump-driven non-equilibrium state reveals that the superconducting order in the forward-focused case is robust and persistent against the pump-induced perturbations. The superconducting order parameter also exhibits a non-uniform melting in momentum space. We show that this behavior is in sharp contrast to the isotropic interaction case and propose that time-resolved approaches are a potentially powerful tool to differentiate the nature of the dominant coupling in correlated materials.

In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability p t , i.e. the network changes occur locally and independently at each node. Secondly we consider the case where the entire connectivity matrix changes with probability p t , i.e. the change is global. We show that network changes, occuring both locally and globally, yield an enhanced range of synchronization. When the connections are changed slowly (i.e. p t is low) the nodes display nearly synchronized intervals interrupted by intermittent unsynchronized chaotic bursts. However when the connections are switched quickly (i.e. p t is large), the intermittent behavior quickly settles down to a steady synchronized state. Furthermore we find that the mean time taken to reach synchronization from generic random initial states is significantly reduced when the underlying links change more rapidly. We also analyse the probabilistic dynamics of the system with changing connectivity and the stable synchronized range thus obtained is in broad agreement with those observed numerically.

In this work we investigate the spatiotemporal behaviour of lattices of coupled chaotic logistic maps, where the coupling between sites has a nonlinear form. We show that the stable range of the spatiotemporal fixed point state is significantly enhanced for increasingly nonlinear coupling. We demonstrate this through numerical simulations and linear stability analysis of the synchronized fixed point. Lastly, we show that these results also hold in coupled map lattices where the nodal dynamics is given by the Gauss Map, Sine Circle Map and the Tent Map.