Application Of Adiabatic Approximation Research Articles

On the applicability of adiabatic approximation in multiphonon recombination theory

A recent paper by C. H. Henry and D. V. Lang claims that the adiabatic approximation breaks down in the neighborhood of the intersection of the adiabatic potential curves for the two electronic states, between which multiphonon transitions occur. It is shown that their claim is not justified; what they consider to be the sign of failure of the adiabatic approximation is no more than an indication of the fact that owing to the uncertainty principle, there is a finite neighborhood around the above mentioned point of intersection, throughout which multi-phonon transitions can occur. Direct calculation of the multi-phonon transition probability on the basis of the adiabatic approximation gives in fact a result identical with the result obtained with their version of the theory. Further discussions contend that in more general situations Henry and Lang’s formulation of the theory will no longer be applicable and a proper adiabatic approximation treatment by first lifting the degeneracy at the intersection point will be necessary.

Evidence of molecular states in single quantum dots with structural anisotropy under magnetic fields

The present work reports on the analysis of the effect of the structural anisotropy of a self-assembled quantum dot of InAs/GaAs, on the energy spectrum of an electron and in the presence of an external magnetic field applied along growth direction. The anisotropy is modeled by periodic variations in the dot height with respect to the azimuthal angle. First, we considered a problem of an axially symmetric lens-shaped quantum dot that could be resolved completely by the application of adiabatic approximation. Secondly, we resolved the problem of the anisotropic quantum dot by using the Galerkin method based on the solution of the axially symmetric lenticular dot. We found that for structures with symmetries C2 and C4, the degeneration of the levels observed in the isotropic case was destroyed, and anti-crosses appear between the levels due to the rupture of the rotational symmetry. The dependency of energy levels corresponding to low-lying states of the quantum dot, as a function of the strength of a magnetic field and of the dot size, for different anisotropy configurations is analyzed. Our results reveal that the presence of some degree of structural anisotropy in a single QD has the potential to generate molecular states such as those arising in systems of coupled quantum dots.

Applicability of adiabatic approximation on neutron noise analysis in molten salt reactor

In this paper, the applicability of the adiabatic approximation on the neutron noise analysis in the molten salt reactor (MSR) is investigated. The neutronic model considering the fuel recirculation is established based on one-group neutron diffusion theory. In linear perturbation theory, the fluctuation equations are derived due to the smallness of the perturbation. Following the standard procedure, the kinetic equations for the fluctuations of amplitude factors, which are dependent on the unknown fluctuations of shape functions, are obtained. If the fluctuations of shape functions are neglected, the solutions of both the total neutron noise and its point kinetic term are inaccurate. In order to estimate the effects of the fluctuations of shape functions and the interference between the point kinetic and space-dependent terms, the adiabatic approximation is applied. The solutions are compared to the exact ones and those obtained in the point kinetic approximation to figure out the applicability of the adiabatic approximation. The results show that the adiabatic approximation is accurate enough for low velocities. With higher velocities, the solutions obtained in both the point kinetic and adiabatic approximations gradually deviate from the exact ones, whereas the adiabatic approximation can still provide good estimation of the frequency- and space-dependent behavior of neutron noise in the plateau region. In particular, the spatial oscillation of the amplitude of neutron noise can be well reconstructed. Moreover, the characteristic peak, which is related to the inverse of fuel recirculation, is absent in the point kinetic approximation but can be observed in the adiabatic approximation. Therefore, the adiabatic approximation can be regarded as an effective tool for reconstructing and interpreting the neutron noise in MSR.