Heat bath system operator

In the previous section we discussed the effective Hamiltonian method a main feature of this method is that it results in the appearance of damping operator T in the Liouville equation. However, the damping operator is introduced in an ad hoc manner. In this section we shall show that the damping operator results from the interaction between the system and heat bath. 

The parameter is the damping constant, and (n) is the mean number of reservoir photons. The quantum theory of damping assumes that the reservoir spectrum is flat, so the mean number of reservoir oscillators (n) = ( (O)bj(O j) = ( (1 / ) — 1) 1 in the yth mode is independent of j. Thus the reservoir oscillators form a thermal system. The case ( ) = 0 corresponds to vacuum fluctuations (zero-temperature heat bath). It is convenient to consider the quantum dynamics of the system (56)-(59) in the interaction picture. Then the master equation for the density operator p is given by... 

In Chapter VI, Ferrario et al. discuss the precise conditions under which the heat bath driven by the operator of Eq. (2.8) allows the correlation function (/) to be exponential [Eq. (2.25)]. In this case, the system of Eq. (2.1) can be replaced by the reduced model... 

Solution Since the problem does not specify the states before and after the process, we cannot use eq. (6. g l. However, we may still answer this problem by noting that ideal work corresponds to a reversible process that accomplishes the given task while using the surroundings as the only heat bath. We will do this by operating a Carnot cycle between the surroundings at T , and the system at T. Application of the first and second law to this Carnot cycle gives ... 

FIG. V-28 Electric heated vaporizer Circulating pumped water bath. System inciudes etectric immersion water heater, pump, piping, controls, and expansion tank, all factory piped up and delivered on skid ready to operate. (Source Armstrong Engineering Associates.)... 

Atmospheric evaporators are more commonly used. They are open systems that use process heat and warm air to evaporate water. These evaporators are relatively inexpensive, require low maintenance and are self-operating. Under the right conditions, they can evaporate water from virtually any plating bath or rinse. A packed-bed evaporator is an example of an atmospheric evaporator. 

For column operation at very low temperatures, constant temperature baths using chillers and ethanol or ethylene glycol baths have been used [56,57,65], The operation of these systems to temperatures as low as -70°C has been shown. At the opposite extreme, researchers working in the range from 100°C to 200°C have often used GC ovens for column heating. 

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