Related papers: Analysis of the Extended Coupled-Cluster Method in…
We formulate an atomistic-to-continuum coupling method based on blending atomistic and continuum forces. Our precise choice of blending mechanism is informed by theoretical predictions. We present a range of numerical experiments studying…
This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 that introduced the first local analysis of CC theory. We offer…
Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating…
Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schr\"odinger operators and control theory. We review recent results and announce new ones regarding…
We develop a simple and unified approach to investigate several aspects of the cluster statistics of random expansive (multi-)sets. In particular, we determine the limiting distribution of the size of the smallest and largest clusters, we…
An approach is developed, combining the ideas of quantum statistical mechanics and multichannel theory of scattering, for treating statistical systems whose constituents can possess different bound states realized as compact clusters. The…
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, to the problem of tracing the parameter dependence of bound and resonant states…
Mix-cumulants of conserved charge distributions are sensitive observables for probing properties of the QCD medium and phase transition in heavy-ion collisions. To perform precise measurements, efficiency correction is one of the most…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
The Schr\"odinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a differential equation whose flow can be split with benefit into…
A version of the method of accurate calculations for few valence-electron atoms which combines linearized single-double coupled cluster method with the configuration interaction technique is presented. The use of the method is illustrated…
We present a technique to identify exact analytic expressions for the multi-quantum eigenstates of a linear chain of coupled qubits. A choice of Hilbert subspaces is described which allows an exact solution of the stationary Schr\"{o}dinger…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
Quantum confinement is studied by numerically solving time-dependent Schr\"odinger equation. An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum.…
We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schr\"{o}dinger equations. Actually, using the classical Mountain Pass Theorem and minimization techniques, we prove the existence…
The (T) and [T] perturbative corrections are derived for multicomponent coupled-cluster theory with single and double excitations (CCSD). Benchmarking shows that multicomponent CCSD methods that include the perturbative corrections are more…
The recent quantum information boom has effected a resurgence of interest in unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ans\"atze prompted us to investigate the classical approach of…
The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…
We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by T.L. Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two…
Quantum entanglement serves as a fundamental resource in quantum information theory. This paper presents a comprehensive framework of separability criteria for detecting bipartite and multipartite entanglements. We construct a novel…