Quantum object

If population analysis is not synonymous with the concept of an AIM, it becomes necessary to introduce a proper set of requirements before one can speak of an AIM. An AIM is a quantum object and as such has an electron density of its own. This atomic electron density must obviously be positive definite and the sum of these atomic densities must equal the molecular density. Each atomic density pA(r) can be obtained from the molecular density p(r) in the following way ... 

It can be shown that Equation 15.15 means no less than the QCT AIM itself is a quantum mechanical object within the global quantum object. A common misunderstanding is that the AIM in this case becomes a closed system. This is incorrect. The QCT AIM should be seen as an open system [54], free to exchange electronic charge, for instance. 

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. 

These devices allow utilizing new computational algorithms based on quantum superposition of states, allowing simultaneous representing many different numbers (so-called quantum computation). In a quantum computer information is loaded as a string of qubits (quantum mechanical representation of bits), which are quantum objects that can occupy different quantum states. A material implementation of qubits requires finding a medium, which can keep superpositional states from the destruction by interaction with the... 

The question then arises if a convenient mixed quantum-classical description exists, which allows to treat as quantum objects only the (small number of) degrees of freedom whose dynamics cannot be described by classical equations of motion. Apart in the limit of adiabatic dynamics, the question is open and a coherent derivation of a consistent mixed quantum-classical dynamics is still lacking. All the methods proposed so far to derive a quantum-classical dynamics, such as the linearized path integral approach [2,6,7], the coupled Bohmian phase space variables dynamics [3,4,9] or the quantum-classical Li-ouville representation [11,17—19], are based on approximations and typically fail to satisfy some properties that are expected to hold for a consistent mechanics [5,19]. 

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... 

A system of this type is not holistic, but partially holistic, which means that pairwise interaction occurs between the holistic units. The distinction drawn here between holistic and partially holistic systems is not in line with the terminology used in general philosophic discourse and in order to avoid any confusion it is preferable to distinguish between systems that interact either continuously, or discontinuously, with the quantum potential field. Quantum potential, like the gravitational potential, occurs in the vacuum, presumably with constant intensity. The quantum potential energy of a quantum object therefore only depends on the wave function of the object. 

The archetype of quantum objects is the photon. It is massless, has unit spin, carries no charge, and responds to the quantum potential field. By comparison, an electron is a massive fermion with half-spin and unit negative charge. It responds to both classical and quantum potentials. The only property that these two entities have in common is their wave nature,... 

The appearance of a quantum-potential field is related to the gauge, or phase, transformation of a quantum wave. It is assumed that the wave field of a quantum object that moves through space suffers a change of phase, such that... 

The remedy is not to attempt the reduction of chemistry to the one-particle solutions of quantum physics, without taking the emergent properties of chemical systems into account. Chemical reactions occur in crowded environments where the presence of matter in molar quantities is not without effect on the behaviour of the quantum objects that mediate the interactions. It is only against this background that quantum theory can begin to make a useful contribution to the understanding of chemical systems. 

The box-Hilbert space is now rigged with the asymptotic states that can be probed at the laboratory as if they were space separate quantum objects. 

The vacuum interface is the source of all quantum effects. Interaction with the interface causes particles to make excursions into time and bounce back with time-reversal and randomly perturbed space coordinates. Different from classical particles, quantum objects can suffer displacement in space without time advance. They can appear to be in more than one place at the same time, as in a two-slit experiment. 

Exploration of intramolecular non-local effects could be the beginning of more far-reaching studies. Neural receptors with the ability to exchange information via the quantum-potential field in the vacuum interface, could be another level of quantum object that might eventually explain para-psychic phenomena. 

Placzek s theory (1934) which treats molecules as quantum objects and electromagnetic fields classically, satisfactorily describes the Raman effect on the condition that the exciting frequency differs considerably from the frequencies of electronic as well as of vibrational transitions. 

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... 

The overall picture of an individual quantum object developed here may be summed up as follows ... 

The individual quantum object is in a pure state, which may be unstable under external influences. The dynamics is not only given by the Schrodinger equation, but specified by additional stochastic terms (cf. ref. 11). The probability distribution of pure states in a... 

Carbo, R. and Calabuig, B. (1992a). Molecular Quantum Similarity Measures and N-Dimen-sional Representation of Quantum Objects. I. Theoretical Foundations. Int.JQuant.Chem., 42, 1681-1693. 

The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications or matter-wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. 

Abstract Interaction between a quantum system and its surroundings - be it another similar quantum system, a thermal reservoir, or a measurement device - breaks down the standard unitary evolution of the system alone and introduces open quantum system behaviour. Coupling to a fast-relaxing thermal reservoir is known to lead to an exponential decay of the quantum state, a process described by a Lindblad-type master equation. In modern quantum physics, however, near isolation of individual quantum objects, such as qubits, atoms, or ions, sometimes allow them only to interact with a slowly-relaxing near-environment, and the consequent decay of the atomic quantum state may become nonexponential and possibly even nonmonotonic. Here we consider different descriptions of non-Markovian evolutions and also hazards associated with them, as well as some physical situations in which the environment of a quantum system induces non-Markovian phenomena. 

Formally, we describe the state of the particle during the propagation as a coherent superposition of states, in particular of position states, that are classically mutually exclusive. A classical object will either take one or the other path with certainty. A quantum object cannot be said to do that since the in-... 

Decoherence theory explains that a quantum object may loose some of its particular quantum properties due to the interaction with its environment. This phenomenon is investigated along two fines. First the authors study the influence of small angle collisions exerted by a dilute thermal gas on the molecules in the interferometer. They also focus on a novel property which is unique to large objects with many internal degrees of freedom, namely the thermal emission of photons. If sufficiently many photons of sufficiently short wavelength... 

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. 

The basic equations that rule the mechanics of H-bonds are developed in this appendix. They have been already established in the appendix of Ch. 5 but take here a slightly different form that makes the role of the mass m of the H-atom more apparent, in view of predicting effects of an H/D substitution. The formation of an H-bond is the result of an electrostatic interaction between the electrons and the nuclei of two molecules X-H and Y. Molecules are quantum objects that are ruled by an Hamiltonian H that depends on the coordinates r of electrons, q of the H(D)-atom that establishes an H(D)-bond and Q that defines the relative positions of the two molecular components X-H and Y. r stands for aU coordinates of all electrons e. The relative coordinates q and Q of the nuclei are defined in Figure 2.1. Q stands for all three intermonomer coordinates Q, Qg and defined in this figure. The quantum description is necessary for this H-bond, because a classical description fails to describe any chemical bond. This Hamiltonian H writes ... 

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