"' Figure 2 "'shows the dependence of the diabatic and adiabatic energies on the value of the magnetic field; note that for non-zero coupling the eigenvalues of the Hamiltonian cannot be below for approaches to calculating these probabilities.
42.
If the rate of change of the transverse-field is accelerated, the system may leave the ground state temporarily but produce a higher likelihood of concluding in the ground state of the final problem Hamiltonian, i . e ., diabatic quantum computation.
43.
For a rapidly increased spring constant, the system undergoes a diabatic process \ scriptstyle { \ left ( \ frac { dk } { dt } \ rightarrow \ infty \ right ) } in which the system has no time to adapt its functional form to the changing conditions.
44.
As a result, internal diabatic heating / cooling due to molecular diffusion explains why laboratory experiments show evidence of circulations developing as the result of surface heating / cooling ( Park and Whitehead, 2000 ) or even when the heating is above the cooling ( Coman et al ., 2006 ).
45.
The localized diabatic potential-energy surfaces describing intervalence charge transfer in the special pair ( P L P M ) of bacteriochlorophyll molecules that form the primary charge donor during bacterial photosynthesis, as well as the resulting Born-Oppenheimer adiabatic surfaces ( GS-ground state, HT-hole transfer state.
46.
Where \ scriptstyle { q } is the perturbation variable ( electric or magnetic field, molecular bond-length, or any other perturbation to the system ), and \ scriptstyle { E _ 1 } and \ scriptstyle { E _ 2 } are the energies of the two diabatic ( crossing ) states.
47.
In 1932 an analytic solution to the problem of calculating adiabatic transition probabilities was published separately by Lev Landau and Clarence Zener, for the special case of a linearly changing perturbation in which the time-varying component does not couple the relevant states ( hence the coupling in the diabatic Hamiltonian matrix is independent of time ).
48.
A 2005 National Research Council report concluded " regional variations in radiative forcing may have important regional and global climate implications that are not resolved by the concept of global mean radiative forcing . " and " Regional diabatic heating can cause atmospheric teleconnections that influence regional climate thousands of kilometers away from the point of forcing ."
49.
The diagonal elements are the energies of the diabatic states ( \ scriptstyle { E _ 1 ( t ) } and \ scriptstyle { E _ 2 ( t ) } ), however, as \ scriptstyle { \ mathbf { H } } is not a diagonal matrix, it is clear that these states are not eigenstates of the new Hamiltonian that includes the magnetic field contribution.
50.
With the field absent, the energetic separation of the diabatic states is equal to \ scriptstyle { \ hbar \ omega _ 0 }; the energy of state \ scriptstyle { | 1 \ rangle } increases with increasing magnetic field ( a low-field-seeking state ), while the energy of state \ scriptstyle { | 2 \ rangle } decreases with increasing magnetic field ( a high-field-seeking state ).
