Coherent states thermodynamics

If the impurity potential is smooth, the process of scattering on them proceeds quasi-classically. In this case no real scattering takes place and the impurity effect may be reduced to the appearance of a random phase of the electron wave function. As has been shown by Zawadowski (1), such impurities do not affect the thermodynamics of the one-dimensional system, in which, however, no phase transitions exist. The finite temperature of the transition arises due to three-dimensional effects which establish the coherent state in the whole volume. The impurities cause the phase shift on each thread, and, as a result, the coherence drops and the transition temperature diminishes. 

The fascinating issues relating to polymer structures preceding crystallization are still largely open to investigation. More specific and articulated models of such states may provide a better understanding of polymer crystallization, both from the thermodynamic and the kinetic viewpoint. Furthermore, the different mechanisms that lead polymers to crystallize may eventually be understood in a coherent, more unified picture. 

The foregoing chapters mark a long and not yet finished journey through the special field of the chemical kinetics of solids. It differs from the more common textbooks on kinetics not only because of the immense variety of crystalline phases, but even more in view of the ambiguity in the definition of the correct number of independent thermodynamic state variables. This is the source of many difficulties and particularly with solids containing one or more immobile components or multiphase systems composed of coherent or semicoherent crystals. In coping with this inherent complexity in the foregoing chapters, we chose to restrict ourselves mainly to the fundamental aspects rather than to present many uncorrelated details. 

At the phenomenological thermodynamic level, when we go far from equilibrium, the striking new feature is that new dynamical states of matter arise. We may call these states dissipative structures as they present both structure and coherence and their maintenance requires dissipation of energy.6 Dissipative processes that destroy structure at and near equilibrium may create these structures when sufficiently far from equilibrium. 

In this article we approach the topic of coherent control from the perspective of a chemist who wishes to maximize the yield of a particular product of a chemical reaction. The traditional approach to this problem is to utilize the principles of thermodynamics and kinetics to shift the equilibrium and increase the speed of a reaction, perhaps using a catalyst to increase the yield. Powerful as these methods are, however, they have inherent limitations. They are not useful, for example, if one wishes to produce molecules in a single quantum state or aligned along some spatial axis. Even for bulk samples averaged over many quantum states, conventional methods may be ineffective in maximizing the yield of a minor side product. 

As we explore the interaction of cold-atom systems with microwave and terahertz radiation, we find that they have some unique properties as detectors. A comparison with superconductor-based detectors such as SQUlDs is instractive. Because of the third law of thermodynamics, i.e., a system in a single quantum state has zero entropy, the response of a SQUID is almost free of thermal noise. But an additional properly of SQUIDs is that they exhibit the phenomenon of coherence, i.e., wave interference, which leads to entirely new effects, e.g. the AC and DC Josephson effects. Cold atom clouds share this behavior, as we will discuss below. 

With the distinction now made between intensive and extensive variables, it is possible to rephrase the requirement for the complete specification of a thermodynamic state in a more coherent manner. The experimental observation is that the specification of two state variables uniquely determines the values of aifother state variables of an equilibrium, single-component, single-phase system. [Remember, however, that to determine the size of the system, that is, its mass or total volume, one must also specify the mass of the system, or"the value of one other extensive parameter (total volume, - total energy, etc.).] The implication of this statement is that for each substance there exist, in principle, equations relating each state variable to two others. For example. 

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