Quantum object examples

A consequent 5-dimensional treatment would require Unified Theory of Quantum Mechanics and General Relativity. This unified theory is not available now, and we know evidences that present QM is incompatible with present GR. The well-known demonstrative examples are generally between QFT and GR (e.g. the notion of Quantum Field Theory vacua is only Lorentz-invariant and hence come ambiguities about the existence of cosmological Hawking radiations [19]). But also, it is a fundamental problem that the lhs of Einstein equation is c-number, while the rhs should be a quantum object. 

The variables describing electrons and nuclei are termed electronic and nuclear. For the majority of problems which arise in chemistry, the nuclear variables can be thought to be the Cartesian coordinates of the nuclei in the physical three-dimensional space. Of course the nuclei are in fact inherently quantum objects which manifest in such characteristics as nuclear spins - additional variables describing internal states of nuclei, which do not have any classical analog. However these latter variables enter into play relatively rarely. For example, when the NMR, ESR or Mossbauer experiments are discussed or in exotic problems like that of the ortho-para dihydrogen conversion. In a more common setting, such as the one represented by the... 

Unfortunately, a rigorous derivation of stochastic pure-state dynamics is still lacking. Nevertheless it is gratifying that such stochastic dynamics are important and in fact form the basis of a quantum theory of individual (quantum) objects. One hint in this direction comes from single-molecule spectroscopy (SMS), where single molecule always is to be understood as a single molecule embedded into a polymorphic matrix or a crystal.The example used in Fig. 9 is a single... 

Neutron scattering has provided several examples of situations where it is evident that, on a short time scale, protons in solids or liquids cannot be considered as independent quantum objects. Without going into the detailed reason for the inseparability (except for the obvious correlations imposed when the neutron scatters on a set of indistinguishable particles), we will now consider the mechanisms by which coherence is lost over times much larger than rcoh. 

P3 A Quantum Object Set Ordering exists. In Section 6 it has been explained how an Object Set Ordering exists. This has been applied for several Quantum System examples in Section 9. It has been demonstrated how this ordering can be associated with the set by means of several techniques. 

Density Functions play a fundamental role in the definition of Quantum Theory, due to this they are the basic materials used in order to define Quantum Objects and from this intermediate step, they constitute the support of Quantum Similarity Measures. Here, the connection of Wavefunctions with Extended Density Functions is analysed. Various products of this preliminary discussion are described, among others the concept of Kinetic Energy Distributions. Another discussed set of concepts, directly related with the present paper, is constituted by the Extended Hilbert Space definition, where their vectors are defined as column structures or diagonal matrices, containing both wavefunctions and their gradients. The shapes of new density distributions are described and analysed. All the steps above summarised are completed and illustrated, when possible, with practical application examples and visualisation pictures. 

After the seminal structure building of the QS formalism, several additional studies appeared over time, which developed new theoretical details. Especially noteworthy is the concept of vector semispace (VSS). This mathematical construction will be shown to be the main platform on which several QS ideas are built, related in turn, to probability distributions and hence to quantum mechanical probability density functions. Such quantum mechanical density distributions form a characteristic functional set, which can be easily connected to VSS properties. Construction of the so-called quantum objects (QO) and their collections the QO sets (QOS) (see, for example, Carbo-Dorca ), easily permit the interpretation of the nature of quantum similarity measures for relationships between such quantum mechanically originated elements. Within quantum similarity context, QOS appear as a particular kind of tagged sets, where objects are submicroscopic systems and their density functions become tags. 

Analogously, the unit of information in Quantum Information and Quantum Computation is the quantum bit, or qubit, for short. A qubit can assume the logical values 0 or 1. However, it can also be in a logical state containing any linear combination of them, thanks to laws of quantum mechanics [8], Physically, qubits can be represented by any quantum object with two well defined and distinct eigenstates. Examples of qubits are the photon polarization states, electrons in two-level atoms (as an approximation) and nuclear spins under the influence of a magnetic field. 

Finally, in the last chapter (Chapter 12) of Part II of this book, Ramon has studied the molecular quantum similarity (QS) measures involving three density functions. The necessary algorithms have been described here. General theory and computational feasibility of a h3q)ermatricial or tensorial representation of molecular structures associated to any molecular quantum object set (MQOS) have been nicely explained in this chapter. Secondly, generalized Carbo similarity indices (CSI) have also been studied. The theoretical and computational approaches have been supported by various suitable applicative examples. 

How is physics, as it is currently practiced, deficient in its description of nature Certainly, as popularizations of physics frequently reniiiid us, theories such as Quantum Electrodynamics are successful to a reinarkiible degree in predicting the results of experiments. However, any reasonable measure of success requires that wc add the caveat, ...in the domain (or domains) for which the theory was developed. For example, classical Newtonian physics is perfectly correct in its description of slow-moving, macroscopic objects, but is fundamentally incorrect in its description of quantum and/or relativistic systems. 

I have reported this last example not for the sake of completeness in our discussion, but to underline a different point. Quantum chemistry, in the work of CTOup 1 and even more in the work of group II, put the emphasis on some properties which by tradition are not object of direct experimental determination. Electron charge distribution and MEP arejust two examples. The use of these quantities by theoreticians has spurred the elaboration of experimental methods able to measure them. This positive feedback between theory and experiment is an indication that quantum and experimental chemistry do not live in separate worlds. 

Bunz et al. pointed out that it would be of interest to develop materials that combine the stability, electron affinity, and high emissive quantum yield of PPEs with the excellent hole injection capabilities of poly(p-phenylene vinylene)s (PPVs) [48]. In line with this notion,recent synthetic activities have focused on the engineering of the band gap, conduction band, and valence band of PAEs with the objective to render these materials more useful for practical applications that exploit their electrically (semi)conducting nature. Examples of materials that emerged from these efforts are discussed in detail in other portions of this volume (in particular the chapters by Bunz, Klemm, and Yamamoto). They include, among others, poly(heteroarylene ethynylenes) such... 

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