Transitions decoherence theory

In the Poisson case, the decoherence theory affords a more satisfactory justification for the correspondence principle [20]. Adopting the Wigner formalism, it is possible to express quantum mechanical problems in terms of the classical phase space, and the Wigner quasi-probability is expected to remain positive definite until the instant at which a quantum transition occurs, according to the estimate of Ref. 120, at the time... 

Thus, the assumption of the decoherence theory that there are no isolated systems, and that we have always to consider the influence of environmental fluctuations, would kill anomalous diffusion. Furthermore, the numerical results of Ref. 31 show that the quantum-induced transition from anomalous to ordinary diffusion is a quantum effect more robust than the localization phenomenon itself. This indicates that in the presence of a weak environmental fluctuation is now insufficient to reestablish the correspondence principle. 

Dugic, M., Rakovic, D., and Plavsic, M., The polymer conformational stability and transitions a quantum decoherence theory approach, in Finely Dispersed Particles Micro-, Nano- and Atto-Engineering, Spasic, A.M., Hsu, J.P., Eds., Marcel Dekker/CRC Press/Taylor Francis, Chap. 9. 

In this chapter, we describe the problem of polymer conformational stability and transitions in the framework of the so-called quantum decoherence theory. We propose a rather qualitative scenario yet bearing generality in the context of the quantum decoherence theory, enabling us to reproduce both, existence and stability of the polymers conformations, and the short time scales for the quantum-mechanical processes resulting effectively in the conformational transitions. The... 

In this chapter, we offer a new approach to the problem. Actually, we show that the fuUy quantum-mechanical approach within the decoherence theory [7] offers both, existence and stability of the molecules conformations, and the rather fast decoherence-like transition between the different conformations. Within our approach, the Levinthal s paradox completely disappears. 

At first sight, this approach may seem unreasonable, because it should simultaneously provide both existence and maintenance of the (stable) conformations in the stationary state of the system, and the model for fast conformational transitions. Fortunately enough, there is a quantum-mechanical theory meeting these criteria and requirements — the so-called decoherence theory [7]. Section V justifies this claim. In Section IV, we outline the fundamentals of the decoherence theory. 

We essentially make a couple of plausible assumptions or interpretations of the phenomenological data which allow the natural accounting for the decoherence effect in the composite system conformation + environment. These assumptions are worth repeating. First, we assume that every stationary state of the composite system — that is characterized by the constant values of the system s parameters — is characterized by the same land of interaction in the composite system (cf. (9.20)). Second, we assume that the external action — eventually giving rise to the conformational transitions — substantially change the kind of interaction in the (new) composite system (cf. (9.25)). It is a matter of the general decoherence theory straightforwardly to prove the final result (9.33), as well as (9.35) [7,14-16,19]. 

The LevinthaTs paradox is an open problem still. To avoid the core of the problem — it s kinema-tical aspect — we propose a new approach in this regard. Actually, we treat the macromolecules conformations as the quantum-mechanical observable. Bearing in mind the foundations of the decoherence theory, we are able to model both, existence and maintenance of the conformations as well as the conformational transitions in the rather short time intervals. Our model is rather qualitative yet a general one — while completely removing the LevinthaTs paradox — in contradistinction with the (semi-)classical approach to the issue. 

Introduces the quantum decoherence theory approach to polymer conformational stability and transitions... 

Part II continues with a section on various approaches and transitions. Chapter 6 covers polymer networks and transitions from nano- to macroscale by Plavsic. The following chapter is on the atomic scale imaging of oscillation and chemical waves at catalytic surface reactions by Elokhin and Gorodetskii. Then next chapter relates the characterization of catalysts by means of an oscillatory reaction written by Kolar-Anic, Anic, and Cupic. Then Dugic, Rakovic, and Plavsic address polymer conformational stability and transitions based on a quantum decoherence theory approach. Chapter 10 of this section, by Jaric and Kuzmanovic, presents a perspective of the physics of interfaces from a standpoint of continuum physics. 

Yet, some theoretical problems are left to be discussed to seek for the ultimate and idealistic features as a nonadiabatic-transition theory Although a trajectory thus hopping plural times converges to run on an adiabatic potential surface asymptotically, the off-diagonal density matrix element Pij t) does not vanish practically, as in the original SET. This is ascribed to an incomplete treatment of the nuclear-electronic entanglement. This issue, often referred to as the problem of decoherence, is originated from the nuclear wavepacket bifurcation due to different slopes of potential surfaces, which will be discussed more precisely below. 

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