Low-dimensional system

For low-dimensional equation systems, the investigation of such time-scales can be carried out through a non-dimensionalization process. For example, consider the 2-variable scheme  

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In low-dimensional systems, such as quantum-confined. semiconductors and conjugated polymers, the first step of optical absorption is the creation of bound electron-hole pairs, known as excitons [34). Charge photogcncration (CPG) occurs when excitons break into positive and negative carriers. This process is of essential importance both for the understanding of the fundamental physics of these materials and for applications in photovoltaic devices and photodctcctors. Since exciton dissociation can be affected by an external electric field, field-induced spectroscopy is a powerful tool for studying CPG. 

More subtle effects of the dielectric constant and the applied bias can be found in the case of semiconductors and low-dimensionality systems, such as quantum wires and dots. For example, band bending due to the applied electric field can give rise to accumulation and depletion layers that change locally the electrostatic force. This force spectroscopy character has been shown by Gekhtman et al. in the case of Bi wires [38]. 

The calculations discussed above considered spin magnetic moments but not the orbital magnetic moments. However, it is known that orbital correlation has a strong effect in low-dimensional systems, which leads to orbital polarized ground states.67-69 Based on this fact, Guirado-Lopez et al.69 and... 

Maksimenko SA, Slepyan GY, Nemilentsau AM, Shuba MV (2008) Carbon nanotube antenna far-field, near-field and thermal-noise properties. Physica E Low-dimensional Systems and Nanostructures 40 2360-2364. 

Yoffe, A. D. Semiconductor quantum dots and related systems Electronic, optical, luminescence and related properties of low dimensional systems. Adv. Phys. 50, 1-208 (2001). 

This property may not be possessed by many other approximate methods based on, e.g., mean field or semielassieal approaehes. Also, in low dimensional systems, the above property is not true for CMD, so to apply CMD to such systems is not consistent with spirit of the method (though perhaps still useful for testing purposes). 

No harmonic term is present in this potential, so it represents a good test case as to whether the CMD method can reproduce inherently nonlinear oscillations. Along these lines, Krilov and Beme have independently explored the accuracy of CMD for hard potentials in low dimensional systems and also as a basis for improving the accuracy of other numerical approaches. ... 

Low-dimensional Solids. - 2.10.1 Introduction. The magnetic properties of one and two-dimensional arrays of localized spins coupled by Heisenberg exchange interactions have been studied as a rather specialized branch of theoretical physics since the earliest days of quantum mechanics. However, recent advances in theory, and the preparation of real materials that are a good approximation to the theoretical models, have made low-dimensional systems much more central to condensed-matter science. There is enormous scope for synthetic chemistry in this area and, as will be seen later in this section, many new materials have been discovered recently. 

We have now seen how local stability analysis can give us useful information about any given state in terms of the experimental conditions (i.e. in terms of the parameters p and ku for the present isothermal autocatalytic model). The methods are powerful and for low-dimensional systems their application is not difficult. In particular we can recognize the range of conditions over which damped oscillatory behaviour or even sustained oscillations might be observed. The Hopf bifurcation condition, in terms of the eigenvalues k2 and k2, enabled us to locate the onset or death of oscillatory behaviour. Some comments have been made about the stability and growth of the oscillations, but the details of this part of the analysis will have to wait until the next chapter. 

The same is true for low-dimensional systems, d — 1 and 2. The point is not only that for such systems the better statistics could be achieved accompanied with reasonable computational time spent for it. Another circumstance is that we can expect here that the superposition approximation gives greater errors. For example, for one-dimensional contact recombination the so-called bus effect is known [17] given particles A and B can react only after particles separating them disappear during reaction. This topological effect is not foreseen by the superposition approximation but can affect considerably the reaction rate. 

The obtained analytical results create a solid basis for the interpretation of experimental data on defect irradiation kinetics in solids of arbitrary nature, as well as in the low-dimensional systems [15, 57]. 

The quantum-classical Liouville equation in the force basis has been solved for low-dimensional systems using the multithreads algorithm [42,43]. Assuming that the density matrix is localized within a small volume of the classical phase space, it is written as linear combination of matrices located at L discrete phase space points as... 

The research on organized organic thin films extends back for more than a century [75]. However, since 1980s, the interest in these systems has increased dramatically due to the development of new methods of preparation of such systems and advances in scientific instrumentation. Langmuir and LB films are of great fundamental interest as low-dimensionality systems. 

Unfortunately, the author has not come so far across any publication on concerning inorganic semiconductor surfaces (2D) or linear ID systems. The problem of correct measurement of local densities or distances between PCs in nanostructured low-dimensional systems is even more complicated. Indeed, using modem EPR technique, one can measure 1/T2 values up to 5-6 nm [124]. But it is the very size of colloidal and aggregated nanoparticles Is it possible to use the pure 2D model in this case, or is it necessary to take into consideration an input of 3D interaction Our group is working on this problem now, trying to understand where is a border between 3D and 2D cases in terms of quantitative analysis of dipole-dipole interaction. 

Since the classical treatment has its restrictions and the applicability of the quantum OCT is limited to low-dimensional systems due to its formidable computational cost, it would be very desirable to incorporate the semiclassical method of wavepacket propagation like the Herman-Kluk method [20,21] into the OCT. Recently, semiclassical bichromatic coherent control has been demonstrated for a large molecule [22] by directly calculating the percent reactant as a function of laser parameters. This approach, however, is not an optimal control. 

The hyperfine field is directly proportional to the sublattice magnetization. Moreover, the appearance of the sextuplet(s) of 57Fe in the ordered regions provides the 3-D ordering temperature. In the case of low-dimensional systems, zero-point spin reduction is often observed. 

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