Related papers: Effective Hamiltonian for two-electron Quantum Dot…
These lecture notes introduce some simple effective Hamiltonians (also known as semi-empirical models) that have widespread applications to solid state and molecular systems. They are aimed as an introduction to a beginning graduate…
A quasi-unidimensional one-electron double quantum dot is studied within the framework of Shannon informational entropy. Its confinement potential, which is described by an asymmetric harmonic-gaussian function, consists of two wells…
Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron…
The dynamics of two ultra-cold bosons confined in a one-dimensional double-well potential is studied. We compare the exact dynamics governed by a full two-body Hamiltonian with the dynamics obtained in a two-mode model approximation. We…
Correlation among particles in finite quantum systems leads to complex behaviour and novel states of matter. One remarkable example is predicted to occur in a semiconductor quantum dot (QD) where at vanishing density the Coulomb correlation…
We present a study of the one dimensional Su-Schrieffer-Heeger model Hamiltonian by a diagrammatic perturbative method in the weak electron-phonon coupling regime. Exact computation of both the charge carrier effective mass and the electron…
Variational wave function is proposed to describe electronic properties of an array of one-dimensional conductors coupled by transverse hopping and interaction. For weak or intermediate in-chain interaction the wave function has the…
We study the formation of molecular states in a two-electron quantum dot as a function of the barrier potential dividing the dot. The increasing barrier potential drives the two electron system from an artificial helium atom to an…
We propose a new mechanism which can lead to ferromagnetism in Hubbard models containing triangles with different on-site energies. It is based on an effective Hamiltonian that we derive in the strong coupling limit. Considering a…
We consider a model Hamiltonian for a dimer including all the electronic one- and two-body terms consistent with a single orbital per site, a free Einstein phonon term, and an electron-phonon coupling of the Holstein type. The bare…
We consider a Kondo spin that is coupled antiferromagnetically to a large chaotic quantum dot. Such a dot is described by the so-called universal Hamiltonian and its electrons are interacting via a ferromagnetic exchange interaction. We…
This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each Hamiltonian refers to physically…
The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In…
Motivated by recent neutron and x-ray observations in V$_2$O$_3$, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t_{2g} states containing two electrons coupled to spin S = 1, and…
Starting from the Fock space representation of hadron bound states in a quark model, a change of representation is implemented by a unitary transformation such that the composite hadrons are redescribed by elementary-particle field…
It is difficult to calculate the energy levels and eigenstates of a large physical system on a classical computer because of the exponentially growing size of the Hilbert space. In this work, we experimentally demonstrate a quantum…
We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues…
We present and discuss in detail practical techniques in formulating effective models to describe the dynamics of low-energy electrons in generic bilayer graphene. Starting from a tight-binding model using the $p_z$ orbital of carbon atoms…
Exact diagonalization results are reported for the lowest rotational band of N=6 electrons in strong magnetic fields in the range of high angular momenta 70 <= L <= 140 (covering the corresponding range of fractional filling factors 1/5 >=…
We develop a theoretical model for the description of electron dynamics in coupled quantum wires when the local magnetic moment is formed in one of the wires. We employ a single-particle Hamiltonian that takes account of the specific…