Choice Of Basis States Research Articles

Pitfalls in the theory of carrier dynamics in semiconductor quantum dots: Single-particle basis versus the many-particle configuration basis

We analyze quantum dot models used in current research for misconceptions that arise from the choice of basis states for the carriers. The examined models originate from semiconductor quantum optics, but the illustrated conceptional problems are not limited to this field. We demonstrate how the choice of basis states can imply a factorization scheme that leads to an artificial dependency between two, actually independent, quantities. Furthermore, we consider an open quantum dot-cavity system and show how the dephasing, generated by the dissipator in the von Neumann Lindblad equation, depends on the choice of basis states that are used to construct the collapse operators. We find that the Rabi oscillations of the s-shell exciton are either dephased by the dissipative decay of the p-shell exciton or remain unaffected, depending on the choice of basis states. In a last step we resolve this discrepancy by taking the full system-reservoir interaction Hamiltonian into account.

Non-Hermiticity, Boson Realizations, and the Role of a Physical Subspace

I give a brief review of boson realizations in quantum many-body theory and how the Dyson-Maleev type mappings give rise to quasi- (or pseudo-) Hermitian structures. In this context it is emphasised that non-Hermiticity of a mapped Hamiltonian is directly linked to a choice of basis states (or the implied inner product). The role of a physical subspace and the necessity to have a formalism which can identify this subspace is highlighted.

Intrinsic resonance representation of quantum mechanics

The choice of basis states in quantum calculations can be influenced by several requirements, and sometimes a very natural basis suggests itself. However often one retreats to a “merely complete” basis, whose coefficients in the eigenstates carry little physical insight. We suggest here an optimal representation, based purely on classical mechanics. “Hidden” constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies the hierarchical structure of couplings between “zero-order” states. We present a (non-perturbative) method to obtain such a basis-state as solutions to a certain resonant Hamilton–Jacobi equation.

Spontaneous emission by a fully excited system of three identical atoms

The Lehmberg-Agarwal master equation is used to study cooperative spontaneous emission by a system of three identical two-level atoms. A choice of basis states is described which allows an exact solution to be obtained for any geometrical configuration, any sample size, and any initial conditions of the atomic system, fully including both near-field and super-radiance effects.

Erratum: Positive-parity excited baryons in a quark model with hyperfine interactions

A quark model suggested by quantum chromodynamics with strong spin-dependent forces of magnetic-dipole-magnetic-dipole character perturbing a flavor-independent confinement potential is applied to lowlying positive-parity excited baryons. SU(3) is broken only by quark masses, and this leads to a new choice of basis states in the hyperon sector; couplings to $\overline{K}N$ are especially transparent in this basis. The results, which are largely determined by previous analyses, are in good agreement with the known properties of these states. Spin-orbit forces are once again found to be negligible.

Positive-parity excited baryons in a quark model with hyperfine interactions

A quark model suggested by quantum chromodynamics with strong spin-dependent forces of magnetic-dipole-magnetic-dipole character perturbing a flavor-independent confinement potential is applied to lowlying positive-parity excited baryons. SU(3) is broken only by quark masses, and this leads to a new choice of basis states in the hyperon sector; couplings to $\overline{K}N$ are especially transparent in this basis. The results, which are largely determined by previous analyses, are in good agreement with the known properties of these states. Spin-orbit forces are once again found to be negligible.

A Peculiar Property of theJP=1+ρ0π−andε0π−States at LowM3πinπ−p→π+π−π−p

The usefulness of the isobar model for analysis of multiparticle final states depends a great deal on the choice of basis states with qualitatively different behavior in the relevant kinematic variables. We have discovered that the ${1}^{+}$ state formed in ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ near ${M}_{3\ensuremath{\pi}}=0.9$ GeV by a ${\ensuremath{\rho}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$ $S$-wave system is quite similar in many important features to that formed by an ${\ensuremath{\epsilon}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$ $P$-wave system, once symmetrization in the identical ${\ensuremath{\pi}}^{\ensuremath{-}}$ particles is accomplished. This similarity, which is quite marked for ${M}_{3\ensuremath{\pi}}<1.1$ GeV, is due to a combination of kinematical and dynamical effects. It makes partial-wave analysis of $3\ensuremath{\pi}$ data in this region rather tricky. Persons applying isobar-model analysis to other systems should be alert for similar difficulties.