Adiabatic switching

Reinhardt, W. P. (1989), Adiabatic Switching A Tool for Semiclassical Quantization and a New Probe of Classically Chaotic Phase Space, Adv. Chem. Phys. 73, 925. 

Further evaluation of Eq. (2.35) requires an expression connecting 0(g)) (assumed to be nondegenerate) with Ox 5 ) (also assumed to be nondegenerate). This link is established via the interaction-picture time-evolution operator i.e. by an adiabatic switching oiHi ... 

Multiphoton excitation using light pulses that are moderately strong may be treated directly using Eq. (1.51). Here we focus solely on cw excitation with an adiabatically switched interaction potential,... 

The adiabatic switching is introduced via the slowly varying e c term that guarantees that the interaction vanishes as t —> ice. It is the exact time-dependent analog of the procedure used in the iE derivation of the Lippmann-Schwinger equation [Eq. (2.52)] in the energy domain. 

Use of the interaction representation in time-dependent perturbation theory and an adiabatic switching, ( a 0> of the perturbation yields the evolution operator... 

Even more efficient single-scan zero-quantum dephasing is possible if adiabatically switched gradients are used in combination with on-resonance spin-locking. Experimental and theoretical details of this technique can be found in the paper by Davis et al. (1993). 

A weak lattice potential in the x-direction is then adiabatically switched on, so that the overall state is a product state... 

Closely related to TI is the adiabatic switching method of Watanabe and Reinhardt [49]. This approach involves following a thermodynamic path via a molecular dynamics simulation in which the parameter A. varies slowly with time. For a sufficiently slow variation, the process is adiabatic and the entropy of the initial and final states will be the same extensions of the basic idea permit evaluation of isothermal and other free-energy changes. The question of how slow the variation must be to remain an adiabatic process has been the subject of some study and analysis [50,51]. De Koning and Antonelli [52] have demonstrated its use by calculating the difference in free energy between two Einstein crystals. 

This leads to the Dirac variation-of-constants method [10]. Although generall> successful, an unsatisfying feature of this method can be seen when we consider an adiabatically switched-on static perturbation. By the adiabatic theorem [11] the perturbed wave function as t — -)-< has the form... 

The adiabatic switching semiclassical quantization method [60-62] may also be used to choose initial conditions for polyatomic reactants. This approach does not require an explicit determination of the topologically independent paths Ct and actions Jt for Eq. (3.36) and, in principle, may be more easily applied to larger polyatomics than the EBK semiclassical quantization approach described above. However, what is required is a separable zero-order Hamiltonian H0 that gives rise to the same kind of intramolecular motion as does the complete Hamiltonian [63,64]. 

Adiabatic switching is based on the Ehrenfest adiabatic theorem [65-67], which states that classical actions and quantum numbers are preserved in adiabatic, slow processes. It is assumed that the actual Hamiltonian H may be written as a sum of a separable zero-order Hamiltonian H0 and a nonseparable part AH ... 

In this section we describe several methods not pertaining to the techniques described earlier. We discuss the multicanonical method of Berg as applied to macromolecules, " " - and the adiabatic switching procedure of Rein-hardt, which is related to the thermodynamic integration approach but is based on different grounds. For completeness, we mention four additional techniques, three of which were developed originally for spin models. 

M. Watanabe and W. P. Reinhardt, Phys. Rev. Lett., 65,3301 (1990). Direct Dynamical Calculation of Entropy and Free Energy by Adiabatic Switching. 

The expectation value in Eq. (13.3) does not remain constant in time, because the bias operator does not commute with the hamiltonian. A quasiequilibrium is maintained through an adiabatic switching that turns on the bias via the integral representation... 

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

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