Transformation from adiabatic

One may now consider how changes can be made in a system across an adiabatic wall. The first law of thermodynamics can now be stated as another generalization of experimental observation, but in an unfamiliar form the M/ork required to transform an adiabatic (thermally insulated) system, from a completely specified initial state to a completely specifiedfinal state is independent of the source of the work (mechanical, electrical, etc.) and independent of the nature of the adiabatic path. This is exactly what Joule observed the same amount of work, mechanical or electrical, was always required to bring an adiabatically enclosed volume of water from one temperature 0 to another 02. 

In some cases the hypothesis fixes completely which special motions are to be considered as allowed. This occurs if the new class of motions are derived by means of an adiabatic transformation from some class of motions already known (Ehrenfest [1917]). 

Detonation, Rayleigh (or Mikhel son) Line and Transformation in. (Called here Rayleigh-MikheTson Line) The Chapman-Jouguet theory deals with adiabatic transformations in steady, non-viscous, onedimensional flows in stream tubes or ducts of constant cross-section. Such transformations can be called Rayleigh transformations. From the equation of continuity valid for flow of constant cross-section and from the momentum equation (Ref 1, p 117 Ref 2, p 99), with use of the formula c = y-Pv for sonic velocity in an ideal gas, can be derived the relationship ... 

Formally, we can write the unitary transformation from the adiabatic to the diabatic basis as... 

Assume next that the compression occurs so rapidly that the material has no time to respond before it is transformed from the undisturbed state to the steady state behind the shock front. In this event the transformation occurs adiabatically. 

In most of the cases, an ultrasonic wave propagates adiabatically, so the (20) looks more naturally its right-hand side represents the adiabatic (non-relaxed) modulus and non-adiabatic contribution to the dynamic modulus. Recall that the relaxed (or isothermal) modulus should be regarded as quasi-static one. Figure 1 shows the frequency-dependent factor of non-adiabatic contribution as function of cox. One can see that transformation from isothermal-like to adiabatic-like propagation occurs in the vicinity cox = 1. The velocity of ultrasound is increased in this region, while the attenuation reaches its maximum value. 

The unitary transformation from a basis of adiabatic electronic states to a basis of diabatic electronic states is given by... 

Generalized adiabatic modes can be transformed from normal mode space into Cartesian coordinate space according to Eq. (98)... 

As illustrated also in other Chapters of this book (see especially Chapters 3), the transformation from the adiabatic wavefunctions computed by ah initio methods to diabatic ones, is often the first task to be accomplished when approaching the study of the dynamics around a CI. The main historical reason for the preference given to the diabatic representation was the problem of the divergence of the coupling between adiabatic surfaces, as illustrated for example in the review of Ref. 1. This computational difficulty seems to have been overcome, judging from the increasing... 

The advantage of the quasiparticle transformations lies in the fact that they are more transparent than the global transformation of the whole Hamiltonian. The first transformation in (28.32) with generator Si is equivalent to the adiabatic quasiparticle transformation from the crude into the adiabatic representation, defined through new quasiparticles in adiabatic representation with double bar... 

The second transformation with generator S2 is equivalent to the nonadiabatic transformation from the adiabatic representation into the final one, which we shall call general , i.e. the representation that involves the adiabatic case as well as the nonadiabatic one. This representation is defined through new quasiparticles denoted simply without bar... 

Sadygov R G and Yarkony D R 1998 On the adiabatic to diabatic states transformation in the presence of a conical intersection a most diabatic basis from the solution to a Poisson s equation. I J. Chem. Rhys. 109 20... 

---