Mesoscopic systems

Datta S 1997 Electronic Transport in Mesoscopic Systems (Cambridge Cambridge University Press)... 

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

Computer simulation techniques offer the ability to study the potential energy surfaces of chemical reactions to a high degree of quantitative accuracy [4]. Theoretical studies of chemical reactions in the gas phase are a major field and can provide detailed insights into a variety of processes of fundamental interest in atmospheric and combustion chemistry. In the past decade theoretical methods were extended to the study of reaction processes in mesoscopic systems such as enzymatic reactions in solution, albeit to a more approximate level than the most accurate gas-phase studies. 

Carbon nanotubes (CNTs) as well as fullerenes are splendid gift brought to the Earth from the red giant carbon stars in the long-distant universe through the spectroscopy. Moreover, those belong to new carbon allotropes of the mesoscopic scale with well-defined structures. In particular, CNTs are considered to be the materials appropriate to realise intriguing characteristics related to the mesoscopic system based on their size and physicochemical properties. 

In a mesoscopic system in which both classical- and quantum-mechanical pictures become compatible even for a short time is realised, its pragmatic significance would be very large considering technical level of today. This book is expected to offer the starting point of such new developments. In this sense. I like to express my wholehearted admiration to the eminent work of Dr. Sumio lijima who first discovered CNT. The timely contents of this book are readily conceivable by the excellent authors and I also appreciate the wisdom of my colleague editors. 

The synthesis of molecular carbon structures in the form of C q and other fullerenes stimulated an intense interest in mesoscopic carbon structures. In this respect, the discovery of carbon nanotubes (CNTs) [1] in the deposit of an arc discharge was a major break through. In the early days, many theoretical efforts have focused on the electronic properties of these novel quasi-one-dimensional structures [2-5]. Like graphite, these mesoscopic systems are essentially sp2 bonded. However, the curvature and the cylindrical symmetry cause important modifications compared with planar graphite. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

The sum in (4) runs over all the transverse channels of the system - that is, the channels that extend from the upstream to the downstream electrode. They normally are thought of (qualitatively) in terms of the molecular orbitals on the molecule, with appropriate modifications for mesoscopic systems. 

Imry Y (1986) Physics of mesoscopic systems. In Grinstein G, Mazenko G (ed) Directions in condensed matter physics. World Scientific, Singapore... 

The main objective of the Workshop was to bring together people working in areas of Fundamental physics relating to Quantum Field Theory, Finite Temperature Field theory and their applications to problems in particle physics, phase transitions and overlap regions with the areas of Quantum Chaos. The other important area is related to aspects of Non-Linear Dynamics which has been considered with the topic of chaology. The applications of such techniques are to mesoscopic systems, nanostructures, quantum information, particle physics and cosmology. All this forms a very rich area to review critically and then find aspects that still need careful consideration with possible new developments to find appropriate solutions. 

Keywords Quantum chaology photoelectric effect decoherence mesoscopic systems. 

The stability of scarred states to external noise and other environmental disturbances was the next natural issue that was raised and partially addressed earlier (L. Sirko, et.al., 1993 R. Scharf, et.al., 1994). The main conclusion was that scarred states are quite robust to reasonable levels of noise. This question took on added relevance with the coming of age of mesoscopic systems where, be it spontaneous emission in atom optics or leads or scattering and other forms of dissipation in heterostructures, the open nature of the system must be accounted for. These new experiments also provided non-ideal realizations of simple theoretical paradigms such as stadium billiards and the kicked rotor, with additional issues that had to be accounted for in the theory. 

Datta S (1995) Electronic transport in mesoscopic systems. Cambridge University Press, Cambridge... 

A many-atom system may contain hundreds of atoms, as in clusters, or macroscopic amounts of matter, as in the cases of condensed matter solutions or solid surface phenomena. Mesoscopic systems and nanostructures fall in between those two extremes. These objects may be embedded in a medium in thermodynamical equilibrium, which imposes constrains of temperature, pressure, or chemical potentials. The medium may alternatively be excited and near equilibrium, or even far from it, in which cases it may strongly affect the time evolution of the object of interest. A unified treatment of these situations can be done with the density operator and its L-vN equation of motion. 

Asymmetric conductors have isymmetric I — V curves. This phenomenon is known as the diode or ratchet effect and plays a major role in electronics. Recently much interest has been attracted by transport asymmetries in singlemolecule devices and other mesoscopic systems [1], The idea that asymmetric molecules can be used as rectifiers is rather old [2], however, it was implemented experimentally [3] only recently. Another experimental realization of a mesoscopic rectifier is an asymmetric electron waveguide constructed within the inversion layer of a semiconductor heterostructure [4]. The ratchet effect was observed in carbon nanotubes [5], and strongly asymmetric I — V curves were recently reported for the tunneling in the quantum Hall edge states [6]. These experimental advances have stimulated much theoretical activity [7, 8, 9, 10, 11] with the main focus on the simplest Fermi-liquid systems [12]. 

Supramolecular architectures are highly sensitive to chiral perturbations in general, and in systems that form liquid crystals in particular. Small amounts of enantiopure guest molecule added to a nematic host can induce a transition to a cholesteric phase, and the helical organization in the mesoscopic system is very sensitive to the structure of the guest molecule. Chiral amplification was successfully achieved in such liquid crystals, using CPL as the chiral trigger for the phase transition [183]. 

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