Shortcuts to adiabaticity

Demirplak and Rice developed the counter-diabatic control protocol while studying control methods that efficiently transfer population between a selected initial state and a selected target state of an isolated molecule [11-13]. The protocol has been studied for manipulation of atomic and molecular states [11, 12, 19] and spin chain systems [20, 21]. Experiments with the counter-diabatic protocol have been demonstrated for the control of BECs [22] and the electron spin of a single nitrogen-vacancy center in diamond [23]. The counter-diabatic field (CDF) protocol is identical with the transitionless driving protocol, independently proposed by Berry a few years later [24]. A discussion of the relationship between these approaches and several of the other proposed shortcuts to adiabaticity can be found in the review by Torrontegui and coworkers [10]. 

There are many other quantum dynamics control protocols that we have not discussed see Ref. 10 for descriptions and a discussion of those that fall into the shortcuts to adiabaticity category, and Refs 1,2 for descriptions and discussion of other control methodologies. 

X. Chen, 1. Lizuain, A. Ruschhaupt, D. Gudry-Odelin, and J. G. Muga, Shortcut to adiabatic passage in two- and three-level atoms. Phys. Rev. Lett, 105(12) 123003—123006(2010). 

S. Deffner, C. Jarzynski, and A. del Campo. Classical and quanmm shortcuts to adiabaticity for scale-invariant driving. Phys. Rev. X, 4(2) 021013-021031(2014). 

S. Martfnez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga Shortcuts to adiabaticity in three-level systems using Lie transforms. Phys. Rev. A, 89(5) 053408—053415(2014). 

X. Chen and I. G. Muga. Transient energy excitation in shortcuts to adiabaticity for the time-dependent harmonic oscillator. Phys. Rev. A, 82(5) 053403-053409(2010). 

We develop instead a shortcut for the Second Law along the following lines Just as we were able to link the performance of work under adiabatic conditions to the existence of a function of state, the energy, so we will postulate that the transfer of heat under reversible conditions is related to another functions of state, termed the empirical entropy, symbolized by s (or, later, the metrical entropy, S), which will then found to be useful to characterize various processes. In short, it is claimed as part of the Second Law ofThermodynamics that... 

The flash is operating adiabatically at 20 bar. The bottom of the flash is separated in a shortcut column. In the shortcut column, the condenser and reboiler pressure is 20 bar. The light key component in distillate is HCI and its mole fraction in the bottom is set at 0.001. The heavy key is ethyl chloride and its composition in the distillate is very small in this example it is 0.001. The reflux ratio is 2. The bottom product is mostly pure ethylene chloride. The purge (stream 11) split fraction in the distillate is set at 0.1. The pressure of the recycle stream is reduced to 1 atm using a throttling valve. The exit stream from the valve is heated in a heater to the fresh feed temperature and linked with the fresh feed. The stream conditions and compositions are shown in Figure 9.10. 

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