Mesoscopic system quantum

Even though the expressions nanomaterials or nanocomposites are recent (and very successful), these industrial materials have existed for at least a century and apparently always existed in nature (in minerals and vegetables). These small particles range in size from a few to several tens of nanometres and are called quasi zero-dimensional mesoscopic systems, quantum dots, quantized or Q particles, etc According to Jordan et al. nano-sized inclusions are defined as those that have at least one dimension in the range 1 100 mn. In materials research, the development of polymer nanocomposites is rapidly emerging as a multidisciplinary research activity whose results could broaden the applications of polymers to the great benefit of many different industries. 

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]. 

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 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. 

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]. 

Spin-orbit(SO) coupling is an important mechanism that influences the electron spin state [1], In low-dimensional structures Rashba SO interaction comes into play by introducing a potential to destroy the symmetry of space inversion in an arbitrary spatial direction [2-6], Then, based on the properties of Rashba effect, one can realize the controlling and manipulation of the spin in mesoscopic systems by external fields. Recently, Rashba interaction has been applied to some QD systems [6-8]. With the application of Rashba SO coupling to multi-QD structures, some interesting spin-dependent electron transport phenomena arise [7]. In this work, we study the electron transport properties in a three-terminal Aharonov-Bohm (AB) interferometer where the Rashba interaction is taken into account locally to a QD. It is found that Rashba interaction changes the quantum interference in a substantial way. 

These assumptions restrict the validity of NET, but as stated above, they have a wide range of validity. It has long been known that the Navier-Stokes equations are contained in NET. More recently, NET has been extended to deal with transport across surfaces, quantum mechanical systems, and mesoscopic systems see Chapter 2. We have chosen to illustrate NET with cases of transport through surfaces in the following sections. 

The frozen Rydberg gas corresponds to a quantum mesoscopic system, where the coherence of the two-level system is shared with the ensemble of the other atoms, offering an interesting example of decoherence through interaction with the environment [Joos 2003]. 

Vandersypen L. M. K. et al., Quantum computing and quantum bits in mesoscopic systems, (Kluwer, New York, 2003). 

S. Datta, Electric Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995). S. Datta, Quantum Transport Atom to Transistor, (Cambridge University Press, Cambridge, 2005). A. Nitzan, Electron transmission through molecules and molecular interfaces, Ann. Rev. Phys. Chem. 

The symmetric group S(n) is of fundamental importance in quantum chemistry as well in nuclear models and symplectic models of mesoscopic systems. One wishes to discuss the properties of the symmetric group for general n and concentrate on stable results that are essentially n—independent. Here the reduced notation(6)-(9) proves to be very useful. The tensor ir-reps A of S(n) are labelled by ordered partitions(A) of integers where A I- n. In reduced notation the label Ai, A2,. .., Ap for S(n) is replaced by (A2,...,AP). Kronecker products can then be fully developed in a n-independent manner and readily programmed. Thus one finds, for example, the terms arising in the reduced Kronecker product (21) (22) are... 

The field of clusters and fullerenes represents areas of modern science where the properties are determined by the reduced coordination. This will modify the functional properties when clusters are used in disperse forms or as units in cluster assembled materials. Examples of applications can be catalysts, sensor materials, units in nanophase/nanocrystalline materials with improved mechanical, electrical, magnetic or optical properties, of cluster based materials for sun protection, solar energy conversion, as an alternative to quantum dots produced with traditional techniques, fabrication of mesoscopic systems etc. The hope is to tune the properties with cluster size, making cluster based materials with characteristics more advanced than those of conventional materials. Production of these types of cluster and exploration of their properties of free as well as deposited clusters are a challenging task of basic and applied science which will be covered in the following sections of this article. 

We analyze theoretically the phenomenon of photon-assisted quantum transport in superconductor(S)- semiconductorfN) mesoscopic system. Sub-gap structures in the I-V characteristics could be explained by multiple Andreev reflections. The electrical properties are strongly determined by the interface between superconductor and semiconductor. The current - voltage characteristics were found to be very sensitive to the photon frequency. 

When dealing with micro- or mesoscopic systems behaving according to the laws of quantum mechanics, one has to use the quantum mechanical expression for the electron flux (current-density operator) [33],... 

Volume 254—Quantum Coherence in Mesoscopic Systems edited by B. Kramer... 

Hausler, W., L. Kecke, and A.H. MacDonald. 2001. Strongly Correlated Electrons Mesoscopic Systems and Quantum Hall Effect, cond-mat/0108290. 

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