Adiabatic approximation on the impact-parameter model

S. Koval, C. J. Gazza

We analyse the validity ranges of the adiabatic and anti-adiabatic approximations for a model with electron - electron and electron - phonon interactions for a three-site cluster. This model describes the motion of apical oxygen atoms in . We show that the adiabatic approximation still applies for critical infrared coupling where the gap between the ground state and first excited electronic state becomes nearly equal to the double-well potential barrier. For this high coupling value, the motion of holes and ions is already highly correlated. We arrive at the non trivial conclusion that in this model the adiabatic approximation is valid even in a parameter region where the electronic energy scale is not much larger than the phononic energy scale. This approximation is able to describe polaronic effects which have been shown to appear in the infrared absorption spectrum in previous exact numerical calculations. We also investigate the range of validity of the anti-adiabatic approximation. We find that the window where none of the above-mentioned approximations is valid shrinks with decreasing on-site repulsion U until it closes at U = 0 in agreement with other work in the literature.

D. M. Tong, X. X. Yi, X.J. Fan +2 more

Alan C. Santos, M. S. Sarandy

The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard adiabatic theorem is specifically derived for closed quantum systems. In a realistic open system scenario, the inevitable system-reservoir interaction must be taken into account, which strongly impacts the generalization of the adiabatic behavior. In this paper, we introduce sufficient conditions for the adiabatic approximation in open quantum systems. These conditions are simple yet general, providing a suitable instrument to investigate adiabaticity for arbitrary initial mixed states evolving under time local master equations. We first illustrate our results by showing that the adiabatic approximation for open systems is compatible with the description of quantum thermodynamics at thermal equilibrium, where irreversible entropy production is vanishing. We also apply our sufficient conditions as a tool in quantum control, evaluating the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and the Landau-Zener model under decoherence.

G. F. Drukarev

Huazhong Li

Recent applications of quantum adiabatic approximation to quantum computation are reviewed.We discuss the adiabatic quantum algorithm and the recent discovery of inconsistency of quantum adiabatic theorem giving impact to this application.