Quantum effect, macroscopic

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

Macroscopic descriptions of matter and radiation are adequate without taking the discontinuous nature of matter and/or radiation into account. However, when dealing with particles approaching the size of elementary quanta, the quantum effects become increasingly important and must be taken into account explicitly in the mechanical description of these particles. Unlike relativistic mechanics, quantum mechanics cannot be used to describe macroscopic events. There is a fundamental difference between classical and non-classical, or quantum, phenomena and the two systems are complimentary rather than alternatives. 

Dimensions between the atomic/molecular and the bulk macroscopic scales are sometimes called mesoscopic. Because the mesoscopic scale corresponds roughly to the electron free path, unusual phenomena such as quantum effects can be observed, some of which could be used in the development of single-electron devices or quantum computers. Top-down-type nanofabrication techniques are now capable of producing structures in this size range, and research on this subject has received significant attention, especially in the held of semiconductor science and technology. 

When first confronted with the oddities of quantum effects Bohr formulated a correspondence principle to elucidate the status of quantum mechanics relative to the conventional mechanics of macroscopic systems. To many minds this idea suggested the existence of some classical/quantum limit. Such a limit between classical and relativistic mechanics is generally defined as the point where the velocity of an object v —> c, approaches the velocity of light. By analogy, a popular definition of the quantum limit is formulated as h —> 0. However, this is nonsense. Planck s constant is not variable. 

We are now in the right position to reach a preliminary conclusion. Although the decoherence theory is an attractive and efficient way of defeating the emergence of quantum effects at a macroscopic level, the authors of Ref. 112 did not feel comfortable with it. The reason is that when the observer has the impression that a wave-function collapse occurs, actually the quantum mechanical coherence is becoming even more extended and macroscopic, since it spreads from the system to the environment, Eq. (256). 

The most common traditional definition of the quantum/classical limit is the point at which Planck s constant h - 0. However, this is an unreasonable stipulation [33] because h is not dimensionless and its value can therefore not be varied. A possible operational condition could be formulated in terms of a dimensionless parameter of the form h/S 1, where S is the action quantity in a given situation. It could be argued that for S sufficiently large compared to h, measurement at the macroscopic level cannot detect quantum effects because of limited instrument resolution. This argument implies that the coarse-grained appearance of a classical world is simply a question of experimental accuracy and that every physical system ultimately displays quantum features and that there is no classical limit. 

Atomic and sub-atomic particles behave fundamentally different from macroscopic objects because of quantum effects. The more closely an atom is confined the more classical its behaviour. (Compare 5.2.1). Mathematically, the boundary condition on the particle wave function ip —> 0 as r —> oo, is replaced by limr >ro xp — 0, where r0 oo. It means that the influence of the free particle has a much longer reach through its wave function than a particle confined to a bulk phase. Wave-mechanically, the wavelength of the particle increases and approaches infinity for a completely localized, or classical particle. Electrons and atoms in condensed phases, where their motion is... 

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. 

One of the remarkable properties of quantum mechanics is that the wave nature of matter completely escapes perception in our everyday life, although this feature is a cornerstone of the theory. The smallness of Planck s constant and therefore of the de Broglie wavelength of a macroscopic object is certainly largely responsible for the non-observability of quantum effects in the classical world. However, it is important to ask whether there are fundamental limits to quantum physics and how far we can push the experimental techniques to visualize quantum effects in the mesoscopic world for objects of increasing size, mass and complexity. Where are the fundamental limits on the way towards larger objects ... 

This auto-localization of an object by its own heat radiation is a fundamental process limiting the ultimate observability of quantum effects in macroscopic objects. However, for nanometer sized systems [Arndt 1999 Hackermiiller 2004 Clauser 1997] this mechanism becomes only relevant at high temperatures and it is not expected to be a limitation for the interference of objects which are even considerably larger than the fullerenes, such as proteins. 

Regarding the structure of nanodiamond, a distinction has to be made between the diamond core that usually features a cubic lattice and, on the other hand, the surface. Depending on particle size, the portion of surface atoms may amount to as much as 50%. Generally the surface structure plays a major role for the material properties observed. At particle dimensions of more than 2nm, the bandgap of nanodiamond corresponds to that of macroscopic diamond. Quantum effects are not observed, but there are interband states that can be attributed to partial surface graphitization and lattice defects, respectively. 

Quantum mechanics provides the law of motion for microscopic particles. Experimentally, macroscopic objects obey classical mechanics. Hence for quantum mechanics to be a valid theory, it should reduce to classical mechanics as we make the transition from microscopic to macroscopic particles. Quantum effects are associated with the de Broglie wavelength A = h/mv. Since h is very small, the de Broglie wavelength of macroscopic objects is essentially zero. Thus, in the limit A —> 0, we expect the time-dependent Schrddinger equation to reduce to Newton s second law. We can prove this to be so (see Problem 7.56). 

As many quantum effects are more pronounced in semiconductors compared to metals, attention will now be focused on the case of a semiconducting material. The changes that occur in the properties of a free electron gas change when the dimensions of the solid are reduced were described in Section 2.4. Although the model of the free electron gas does not include the nature of the solid, from a macroscopic point of view it is necessary to distinguish between metals, semiconductors, and insulators [15], Whilst the model of a free electron gas describes relatively well the case of electrons in the conduction band of metals, the electrons in an insulating material are only poorly described by the free electron model. In... 

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. 

Well, first of all, there are the ingenious experiments designed to show us that quantum effects can, indeed, appear in the macroscopic realm. In the form of SQUID devices, with their superimposed superconducting currents, such macroscopic quantum devices can become practical measuring instruments. And there are such delicate laboratory experiments such as the preparation of macroscopic collections of atoms in a single degenerate Bose-Einstein state. But now the claim might be that such quantum effects, if not limited to the microscopic, are, perhaps, limited to special, technically prepared situations of scientific artifacts. 

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