Related papers: Harmonic oscillator eigenfunction expansions, quan…
The widely used large-scale diagonalization method using harmonic oscillator basis functions (an instance of the Rayleigh-Ritz method, also called a spectral method, configuration-interaction method, or ``exact diagonalization'' method) is…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach…
We present a configuration interaction method optimized for Fock-Darwin states of two-dimensional quantum dots with an axially symmetric, parabolic confinement potential subject to a perpendicular magnetic field. The optimization explicitly…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
The method of effective interaction, traditionally used in the framework of an harmonic oscillator basis, is applied to the hyperspherical formalism of few-body nuclei (A=3-6). The separation of the hyperradial part leads to a state…
The random-phase approximation has been used to compute the properties of parabolic two-dimensional quantum dots beyond the mean-field approximation. Special emphasis is put on the ground state correlation energy, the symmetry restoration…
A system of two or more quantum dots interacting with a dissipative plasmonic nanostructure is investigated in detail by using a cavity quantum electrodynamics approach with a model Hamiltonian. We focus on determining and understanding…
Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods.…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
A system of harmonic oscillators coupled via nonlinear interaction is a fundamental model in many branches of physics, from biophysics to electronics and condensed matter physics. In quantum optics, weak nonlinear interaction between light…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
In the context of a two-parameter $(\alpha, \beta)$ deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined…
The ability to coherently couple arbitrary harmonic oscillators in a fully-controlled way is an important tool to process quantum information. Coupling between quantum harmonic oscillators has previously been demonstrated in several…
We present a new high-performance configuration interaction code optimally designed for the calculation of the lowest energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong…
In this study, a variety of methods are tested and compared for the numerical solution of the Schr\"odinger equation for few-body systems with explicitely time-dependent Hamiltonians, with the aim to find the optimal one. The configuration…
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two…
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting…
We present a method to calculate many-body states of interacting carriers in million atom quantum nanostructures based on atomistic tight-binding calculations and a combination of iterative selection of configurations and perturbation…