Causal Quantum Evolution

Quantum states ) may be transformed one into other by the causal effect of a quantum evolution unitary operator, 

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The experimentally achievable localized excitations are typically described by one of the zero-order basis states (see Section 3.2), which are eigenstates of a part of the total molecular Hamiltonian. Localization can be in a part of the molecule or, more abstractly, in state space . The localized excitations are often described by extremely bad quantum numbers. The evolution of initially localized excitations is often more complex and fascinating than an exponential decay into a nondescript bath or continuum in which all memory of the nature of the initial excitation is monotonically lost. The terms in the effective Hamiltonian that give birth to esoteric details of a spectrum, such as fine structure, lambda doubling, quantum interference effects (both lineshapes and transition intensity patterns), and spectroscopic perturbations, are the factors that control the evolution of an initially localized excitation. These factors convey causality and mechanism rather than mere spectral complexity. 

Locally, Minkowski and universal space are identical as causal manifolds, but the universal time is not equivalent to the time registered in the local Minkowski frame. Quantum mechanically temporal evolution and energy are defined by conjugate operators. The operator —i d/dt), which defines the energy (or frequency) depends on the geometry of the stationary state. 

Finally, what can we measure in quantum mechanics The states themselves looses their causal evolution when interacting with an apparatus while achieving a sort of deterministic evolution therefore, the measurement is even not on the states but on operators that have an intrinsic role on the system structure from this point we recover the phenomenological idea that those operators that commutes with Hamiltonian of the system are observables and can be averaged on certain states to be measured (observed). Yet, other quantities may be measured on perturbed states of Ihe systems under investigation. 

Since during its evolution beyond the horizon, any dynamical change in the fluctuation spectra was causally forbidden, the fluctuating gravitational field experienced by the recombining hydrogen atoms was directly related to the fluctuation spectra of the inflationary epoch, determined by the quantum fluctuations of the field(s) of that era. This observation leads promptly to the conclusion that the spectra should be very close to the ZeTdovich-Harrison spectra. Detailed features of the power spectra seem to effectively rule out some of the concurrent inflationary models. 

Therefore, the classical treatment of the Borrmann effect has the quality of the immediate interpretation of the recorded fluorescence spectra (see Putz, 2014) but does not fully respond to what is happening with this energy, intimate-dynamically manifested in the anomalous absorption. Here s why, the quantum view can causally present the dififaction phenomenology in d5mamic evolution, where the asymmetrical propagation naturally derives fi om the quantum definition itself of diflBaction the coherent (dynamic) photonic transfer derivedfrom the dynamic localization, (5.312) and (5.313). 

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