The N-soliton interactions in the adiabatic approximation for the MM (V (x) = 0) can be modelled by CTC .
The adiabatic approximation holds true for both equations if the soliton parameters satisfy :
This goal matches the needs of: (i) going beyond the simplest adiabatic approximation -- commonly adopted in the description of ultrafast phenomena at the nanoscale; and(ii) dealing with the actual spatial inhomogeneities of many-electron systems at non-adiabatic level.
Adiabatic approximation partially or completely fails to describe a large class of physical phenomena, such as multiple excitations, charge-transfer and dissipation processes.
For this particular approach, we used effective mass approximation and adiabatic approximation.
For this reason, we used the adiabatic approximation to separate the Schrodinger equation into two equations, one depending on its "fast" motion (radial) and the other depending on its "slow" motion (axial).
The solution is proposed in terms of modes, propagating independently in the adiabatic approximation
, and described as a non-integer power series of a small parameter characterizing the stratified medium.
The authors use the Born-Oppenheimer adiabatic approximation
and show the parametric method for calculations for polyenes and acenes.
The time of flight was calculated for the proton and using the adiabatic approximation