Hamiltonian noninteracting model

A system without vibrons is described as before by a basis set of states a) with energies ea and inter-state overlap integrals l fi, the model Hamiltonian of a noninteracting system is... 

An isolated noninteracting nanosystem is described as a set of discrete states a) with energies ea and inter-orbital overlap integrals tap by the following model Hamiltonian ... 

This model is quite universal, describing a variety of correlated electron systems coupled to the leads the Anderson impurity model, the multilevel quantum dot with diagonal noninteracting Hamiltonian quantum dots, when the off-diagonal matrix elements of eap describe hopping between individual dots, and, finally, the ID and 2D quantum point contacts. 

The /V-electron Hamiltonian is H = f + U + V, where T is kinetic energy, U, the interelectronic Coulomb interaction, and V. the external potential term. A system of N interacting electrons is modeled by a system of N noninteracting electrons moving in a self-consistent mean field. This requires a postulated mapping rule by... 

The mathematical issues relevant to the definition of density functional derivatives can be considered in the simple model of noninteracting electrons. As in the KSC [4], this singles out the kinetic energy. The /V-electron Hamiltonian operator is H = T + V. Orbital functional derivatives determine the noninteracting OEL equations... 

The weak-coupling limit takes as its starting point the conventional semiconductor noninteracting band picture, introduced in Chapter 3. The ground state is an occupied valence-band and an empty conduction-band. A bound conduction band electron and valence band hole move through the lattice as an effective-particle. In this section we derive the effective-particle model, discuss its solutions and compare them to essentially exact calculations on the same Hamiltonian (Barford et al. 2002b). We develop this theory for a linear, dimerized chain. 

Throughout this book electronic models of conjugated polymers are developed within the number or second quantization representation. This representation is particularly powerful for treating many-body problems. However, as it is less familiar than a first quantization approach, this appendix explains the equivalence of the two approaches for single particle Hamiltonians. We take two examples the fermion noninteracting (or Hiickel) Hamiltonian and the exciton transfer model. 

It makes an input trial density operator p, which is nearly idempotent, into a new purified version p , which is more nearly idempotent. Li et al. used Pm and constructed the following variational energy functional for a noninteracting N-electron system with a Hamiltonian h (or for a tight-binding model with a nonself-consistent h) ... 

Not surprisingly, the kinetic energy contributions in Eqs. (2.45) and (2.46) are identical to the thermodynamic results for the ideal gas, the idealized model for noninteracting particles [E(X)=0]. In the applications presented in the following chapters, we will omit these contributions, but we have to keep in mind that they must be added to make any statistical analysis of a Hamiltonian system quantitatively correct. 

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