相关论文: An Approximate Coupled Cluster Theory via Nonlinea…
The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analysed as a multivariate…
The iteration dynamics of the coupled cluster equations exhibits a synergistic relationship among the cluster amplitudes. The iteration scheme may be viewed as a multivariate discrete-time propagation of nonlinearly coupled equations, which…
The dynamics associated with the time series of the iteration scheme of coupled cluster theory has been analysed. The phase space analysis indicates the presence of a few significant cluster amplitudes, mostly involving valence excitations,…
In this paper, we have analysed the time series associated with the iterative scheme of a double similarity transformed Coupled Cluster theory. The coupled iterative scheme to solve the ground state Schr{\"o}dinger equation is cast as a…
Coupled cluster theory is one of the most accurate electronic structure methods for predicting ground and excited state chemistry. However, the presence of numerical artifacts at electronic degeneracies, such as complex energies, has made…
The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Dynamics of a cluster of chaotic oscillators on a network are studied using coupled maps. By introducing the association schemes, we obtain coupling strength in the adjacency matrices form, which satisfies Markov matrices property. We…
This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly…
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…
The Coupled-Cluster theory is one of the most successful high precision methods used to solve the stationary Schr\"odinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in…
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behaviour of a coupled cluster wavefunction representation…
We study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks, scale free networks, small world networks, tree networks, and random networks. For small coupling strengths nodes show…
In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
The complex behavior of many natural and engineered systems emerges from the interaction of a small number of effective degrees of freedom. Discovering the physical basis of the interactions between these degrees of freedom directly from…
Dynamical systems can be analyzed as computational devices capable of performing information processing. In coupled oscillators, enlarged capabilities are expected when the set of units is formed by subsets with collective behaviour within…
The cluster perturbation theory (CPT) is one of the simplest but systematic quantum cluster approaches to lattice models of strongly correlated electrons with local interactions. By treating the inter-cluster potential, in addition to the…
We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on decomposition of both amplitudes and two electron integrals, using a combination of tensor hypercontraction and…
We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…