Macroscopic quantum phenomenon

Before we can understand any experiment more complicated than a simple spectrum, we need to develop some theoretical tools to help us describe a large population of spins and how they respond to RF pulses and delays. The vector model uses a magnetic vector to represent one peak (one NMR line) in the spectrum. The vector model is easy to understand but because it represents a quantum phenomenon in terms of classical physics, it can describe only the simpler NMR experiments. It is important to realize that the vector model is just a convenient way of picturing the NMR phenomenon in our minds and is not really an accurate description of what is going on. As human beings, however, we need a physical picture in our minds and the vector model provides it by analogy to macroscopic objects. 

Similar mesoscopic quantum effects take place also in short hydrogen-bonded chains and in small clusters, which include hydrogen bonds. The phenomenon of large proton polarizability and fast oscillations of the polarization of the chain were studied experimentally by Zundel and coworkers [6,249,288,289]. A theoretical study of macroscopic tunneling of the chain polarization has been conducted in Refs. 319-322. 

The basic concept of the existence of a critical temperature for the onset of macroscopic occupation of a single quantum ground state of a boson system is applicable both for liquid He and for weakly interacting low-density atomic vapors. The phenomenon of Bose-Einstein condensation is not limited to an ideal Bose gas and prevails also in a strongly interacting boson system. The bridging between Bose-Einstein condensation in the low-density, weak... 

The characterization of the interrelations between chemical bonding and molecular shape requires a detailed analysis of the electronic density of molecules. Chemical bonding is a quantum mechanical phenomenon, and the shorthand notations of formal single, double, triple, and aromatic bonds used by chemists are a useful but rather severe oversimplification of reality. Similarly, the classical concepts of body and surface , the usual tools for the shape characterization of macroscopic objects, can be applied to molecules only indirectly. The quantum mechanical uncertainty of both electronic and nuclear positions within a molecule implies that valid descriptions of both chemical bonding and molecular shape must be based on the fuzzy, delocalize properties of electronic density distributions. These electron distributions are dominated by the nuclear arrangements and hence quantum mechanical uncertainly affects electrons on two levels by the lesser positional uncertainty of the more massive nuclei, and by the more prominent positional uncertainty of the electrons themselves. These two factors play important roles in chemistry and affect both chemical bonding and molecular shape. 

Electrochemical microsystem technology can be scaled down from macroscopic science to micro and further to nanoscale through EMST to ENT [1]. In ENT, electrochemistry involves in the production process to realize nanoproducts and systems which must have reproducible capability. The size of the products and systems must be in the submicron range. It considers electrochemical process for nanostructures formation by deposition, dissolution and modification. Electrochemical reactions combining ion transfer reactions (ITR) and electron transfer reactions (ETR) as applicable in EMST are also applied in ENT. Molecular motions play an important role in ENT as compared with EMST. Hence, mechanical driven system has to be changed to piezo-driven system to achieve nanoscale motions in ENT. Due to the molecular dimension of ENT, quantum effects are always present which is not important in the case of EMST. The double layer acts as an interface phenomenon between electrode and electrolyte in EMST, however, double layer in the order of few nanometers even in dilute electrolyte interferes with the nanostmcture in ENT. 

Bose-Einstein condensation A phenomenon occurring in a macroscopic system consisting of a large number of bosons at a sufficiently low temperature, in which a significant fraction of fee particles occupy a single quantum state of lowest energy (fee ground state). Bose-Einstein condensation can only take place for bosons whose total number is conserved in collisions. Because... 

Despite the fact that this phenomenon can be calculated correctly in physical terms only by the use of quantum mechanics (e. g. [31]), the macroscopic behavior of the spin ensembles can be described for many of the NMR experiments as a continuous magnetization vector. In this description the magnetization vector in the thermal equilibrium points in the direction of the static magnetic field of the magnet. The thermal equilibrium can be disturbed by an appropriate RF pulse. The subsequent relaxation after the RF field has been switched off can be described by the so-called relaxation times Ti and Tz [31]. Tj and Ti are measures of the interaction of a spin with its surroundings and the mobility of a spin, respectively. 

The paradox here is that if entropy is a state property of a system it cannot depend on what we happen to know about the system. Quantum mechanics has a similar-sounding, but quite different epistemological problem, which, in principle, placed limits on the precision by which certain pairs of properties are measured. Since measurement involves experimental design and choice of parameters of interest, in the quantum framework the observer is required to complete the phenomenon. In statistical thermodynamics, however, entropy is microscopic uncertainty and if we interpret entropy as lack of microscopic information about the macroscopic thermodynamic state we seem to get involved in the identity of that state alone, which would be a conflicting standpoint. Therefore, let us discuss all such viewpoints and inherent differences often arising from not fully congruous ideas, which try to enlighten the true interdisciplinary of the notion of entropy. 

The phenomenon of NMR is based on the property of nucleus to possess intrinsic angular momentum. It is often called spin angular momentum or simply spin. Spin is a form of the angular momentum that is not due to the rotation of the particle, but is an intrinsic property of the particle itself. The concept of spin is difficult to visualize, because it is a quantum mechanical property with no analogue in the macroscopic world. 

The electrons in an atom also have an intrinsic angular momentum in addition to their orbital angular momentum about the nucleus. This is called the electron spin or sometimes just referred to as spin. Even an electron in the / = 0 orbital that has zero angular momentum will have an intrinsic spin. The intrinsic spin of the electron is not a classical mechanical effect hence, it is not a correct picture to view the electron spinning about one of its axes, as the classical mechanical picture would indicate. The term spin is more of a name for this phenomenon rather than an actual description of the electron. Though the intrinsic spin of the electron is real, there is no example in the macroscopic world to form a visual model. The electron spin arises naturally when relativistic mechanics is combined with quantum mechanics. Since this text is confined to quantum mechanics, the concept of electron spin must be introduced as a hypothesis. 

Although continuum models have been quite sueeessful in assessing macroscopic optical response, they have intrinsie limitations for probing microscopie optical properties, such as molecular polarizability and photoconductivity. The limitations stem from the faet that eontinuum eleetrodynamies, as applied to metal nanostructures, are intended to deseribe the eolleetive motions of the electrons and are thus not applieable to any physieal phenomenon that occurs at small length scales (typieally a few nanometers for typieal eondensed-phase systems). For small length seales, many-body theories need to be applied to account for the quantum eharaeteristies of individual eleetronie transitions, for example, light absorption by an organie sensitizer and subsequent electron injection to semiconductor layer. 

In this section, we describe theoretical methods that describe the macroscopic optical properties of metal nanoparticles (a.k.a quantum dots). Recently, silver and gold nanoparticles have foimd tremendous use in biological assays, detection, labelling and sensing because of their sensitive optical spectra. While some works in the literature refer to these as quantum dots , in optical absorption experiments their quantized energy structure is not probed. The spectrum is a probe of the localized surface plasmon phenomenon, a collective electronic excitation that is localized in spatial extent owing to the small size of the nanoparticle compared with the wavelength. 

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