Quantum adiabaticity

The limit equation governing limj -,o qc can be motivated by referring to the quantum adiabatic theorem which originates from work of Born and FOCK [4, 20] The classical position g influences the Hamiltonian very slowly compared to the time scale of oscillations of in fact, infinitely slowly in the limit e — 0. Thus, in analogy to the quantum adiabatic theorem, one would expect that the population of the energy levels remain invariant during the evolution ... 

Now, recall that for weak hydrogen bonds the high-frequency mode is much faster than the slow mode because 0 m 20 00. As a consequence, the quantum adiabatic approximation may be assumed to be verified when the anharmonic coupling parameter aG is not too strong. Thus, neglecting the diabatic part of the Hamiltonian (22) and using Eqs. (18) to (20), one obtains... 

Figure 11. The solid line depicts the quantum adiabatic free energy curve for the Fe /Fe electron transfer at the water/Pt(lll) interface (obtained by using the Anderson-Newns model, path integral quantum transition state theory, and the umbrella sampling of molecular dynamics. The dashed line shows the curve from the classical calculation as given in Fig. 5. (Reprinted from Ref 14.)...

Adiabatic process (quantum mechanics) — In quantum mechanics a process is called adiabatic if electrons equilibrate with nuclei as they move. The concept of quantum adiabaticity was introduced by Paul Ehrenfest (1880-1933) as early as 1917, using pre-Heisenberg quantum mechanics [i]. The idea survived the advent of post-Heisenberg quantum mechanics, and was brought into its modern form by -> Born [ii]. The existence of adiabatic processes is readily proved by considering... 

Various correlation and internuclear distance measurements are based on zero- or double quantum spin flips. The most efficient correlation methods are based on the adiabatic process, which is relatively insensitive to actual, orientation-dependent coupling strength. A double-quantum spin flip is generated by a sweep of the rf field amplitude, centred at half rotation frequency (the HORROR condition [9]). The increased rotation frequency leads to a crucial improvement in the broad-band character of the DREAM method [10]. The zero-quantum adiabatic spin flip process is considered in the next section. 

B. Simon, Holonomy, the quantum adiabatic theorem, and Berry s phase, Phys. Rev. Lett. 51 2167 (1983). 

Quantum Adiabatic Switching and Supersymmetric Approach to Excited States of Nonlinear Oscillators... 

Quantum adiabatic theorem (QAT) has been extensively explored since the birth of QM (Born and Fock 1928 Messiah 1962). The essence of QAT is as follows. Let Hi be the initial Hamiltonian at time t = 0, and let Hf be the final Hamiltonian after the lapse of a long time t = T. We can construct a time-dependent Hamiltonian H(t) that continuously and infinitesimally slowly interpolates between and Hf in the time interval 0<,t T ... 

Hazra, R. K., M. Ghosh, and S. P. Bhattacharyya. 2008. Quantum adiabatic switching route to the impurity modulated states of 2-D quantum dots with different switching functions. International Journal of Quantum Chemistry 108 (4) 719. 

Indeed, the reaction coordinate optimization typically 3delds a reduction in the predicted rate coefficient by about a factor of two from that obtained for a center-of-mass reaction coordinate. The quantum adiabatic channel calculations are generally restricted to an assumed center-of-mass separation for the reaction coordinate. 

This gravitational topological adiabatic quantum algorithm, constitutes an example of a quantum adiabatic speedup that relies on the topological order that it is inherent to the space-time in loop quantum gravity. 

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