Basis dependence of approximative energy levels in a strongly driven two-level system
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We introduce the diabatic and the adiabatic bases of a strongly driven superconducting two-level system. The multiphoton resonance conditions, the Rabi couplings, and the energy levels are calculated in both bases using the rotating wave approximation, and the results are compared with the corresponding numerical values. We show the basis dependence of the approximate energy levels and deduce the validity regions for both bases. We demonstrate a parameter region where neither of the bases is sufficient for calculations in the rotating wave approximation.Keywords:
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Basis (linear algebra)
Adiabatic theorem
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(1980). Electronic non-adiabatic transitions derivation of the general adiabatic-diabatic transformation matrix. Molecular Physics: Vol. 40, No. 4, pp. 1011-1013.
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We apply a recently developed quasi-diabatic (QD) scheme to the symmetric quasi-classical (SQC) approach for accurate quantum dynamics propagation. By using the adiabatic states as the quasi-diabatic states during a short-time quantum dynamics propagation, the QD scheme allows directly interfacing diabatic SQC method with commonly used adiabatic electronic structure calculations, thus alleviate tedious theoretical efforts to reformulate SQC in the adiabatic representation. Further, the QD scheme ensures a stable propagation of the dynamics and allows using a much larger time step compared to directly propagating SQC dynamics in the adiabatic representation. This is due to the fact that the QD scheme does not explicitly require non-adiabatic couplings that could exhibit highly peaked values during non-adiabatic dynamics propagation. We perform the QD-SQC calculations with a wide range of model non-adiabatic systems to demonstrate the accuracy of the proposed scheme. This study opens up the possibility for combining accurate diabatic quantum dynamics methods such as SQC with any adiabatic electronic structure calculations for non-adiabatic on-the-fly propagations.
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In the present study we introduce a time-dependent wave packet method to treat electronically non-adiabatic processes explicitly in the coupled adiabatic state representation. The method is applied to the predissociation of the MgCl (A2II) state and is shown to be easy to implement, with the computational effort being comparable to the corresponding calculation in the diabatic basis. © 1992 John Wiley & Sons, Inc.
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Accurate positions and nonradiative lifetimes of states belonging to the adiabatic A state of LiH are estimated. The results coming from a Golden Rule treatment in the adiabatic scheme present excellent agreement with those obtained through a diabatic close coupling calculation. That confirms the accuracy reached in both approaches and also in the treatment of the diabatic–adiabatic transformation. It involves, in particular, an effective phase control that is needed to properly estimate nonadiabatic couplings. Also, a powerful numerical procedure to obtain energy profiles in the diabatic close coupling frame is described and applied in this work.
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A general algorithm for determining diabatic representations from adiabatic energies, energy gradients and derivative couplings using neural networks is introduced.
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Born–Oppenheimer approximation
Adiabatic theorem
Vibronic coupling
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A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. {As an example}, the potential energy surfaces of $^{208}$Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. {It is shown that} the diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, {to follow the evolution of single-particle orbits till very deformed region}, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.
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The relationship between the adiabatic and diabatic representations used in the calculation of electronic and vibration-rotation energy levels of molecules is explored and the details of the transformations between them investigated. It is demonstrated explicitly that applying the Smith transformation (Phys. Rev., 1969, 179, 111) on the complete adiabatic basis simply reproduces the original basis from which the Born-Oppenheimer channels were constructed. When the transformation is applied to a limited set of channels the coupling between the neglected channels provides a small correction to the potential. With this term included the transformation of a single Born-Oppenheimer channel gives the adiabatic (or diagonally corrected adiabatic) approximation.
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Unitary transformation
Born–Oppenheimer approximation
Adiabatic theorem
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