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Nanoelectronics and Mesoscopic Physics
Published in Vinod Kumar Khanna, Introductory Nanoelectronics, 2020
The heart and soul of nanoelectronics is mesoscopic physics. Meso means ‘intermediate or middle’. Mesoscopic physics is the physics of structures of intermediate dimensions falling between the microscopic (individual atoms and molecules) and macroscopic (bulk matter) kingdoms, i.e. covering the submicron and nanoscale sizes. Mesoscopic physics bridges the microscopic and macroscopic regions (Das 2010). It is a branch of condensed matter physics. In contrast to the microscopic dominion, objects of both the mesoscopic and macroscopic realms contain a large number of atoms, mesoscopic less and macroscopic more. Below we mention some distinguishing features of mesoscopic objects that distinctly tell them apart from macroscopic ones.
Quantum Chaotic Systems and Random Matrix Theory
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2019
Akhilesh Pandey, Avanish Kumar, Sanjay Puri
Mesoscopic physics deals with systems which are intermediate in size between the atomic scale and the macroscopic scale. The transport properties of metals and insulators at very small scales have given new insights in understanding mesoscopic physics. The quantities of special interest in this context are the conductance fluctuations and distributions. In this section, we briefly discuss the application of RMT to understand transport properties of mesoscopic systems. There has been extensive study of these systems in the literature, and we refer the interested reader to some important review articles [5-7,57,61].
Constructive solution of the inverse spectral problem for the matrix Sturm–Liouville operator
Published in Inverse Problems in Science and Engineering, 2020
We have imposed the boundary conditions (2), since the problem (1)–(2) generalizes eigenvalue problems for Sturm–Liouville operators on a star-shaped graph (see, e.g. [1,2]). Differential operators on geometrical graphs, also called quantum graphs, have applications in mechanics, organic chemistry, mesoscopic physics, nanotechnology, theory of waveguides and other branches of science and engineering (see Refs. [3–7] and references therein).
Inverse problems for Sturm–Liouville operators on a star-shaped graph with mixed spectral data
Published in Applicable Analysis, 2020
Yu Ping Wang, Chung-Tsun Shieh
In this paper, we are concerned with an inverse spectral problem of Sturm–Liouville operators defined on a star-shaped graph. Denote G a star-shaped graph with vertices every edge which joins the internal vertex and boundary vertex is identified with the interval the value x=0 corresponds to the boundary vertex and x=1 corresponds to the internal vertex for where Denote L the following Sturm–Liouville equations: on the graph G together with the Dirichlet conditions on the boundary vertices and the standard matching conditions on the internal vertexes where λ is the spectral parameter. We shall assume , the potential is a real function and , . The inverse spectral theory on the graph G consists in recovering L from its spectral characteristics, which is a generalization of the classical inverse spectral theory on a finite interval [1–3]. Direct and inverse problems for differential operators on quantum graphs are originated from mathematics itself and some applications, such as organic chemistry, mesoscopic physics, nanotechnology, microelectronics, acoustics and other fields of science and engineering (see [4–6] and references therein). So far, there are rich researches in this topics (see [4–25] and references therein), In particular, Pivovarchik [19] considered the star-shaped graph with three edges and proved that if that the potential is known on one or two edges, then two or one spectra, respectively, uniquely determine the potential on the remaining edges; Yang [20, 21] studied partial inverse problems on graphs, it was showed that some fractional part of the spectrum is sufficient to determine the potential on one edge of the star-shaped graph if the potential is known on the other edges; recently, Bondarenko [11] recovered one potential on the graph G provided potentials on other edges are known a priori, both algorithms for solution and sufficient conditions for the solvability of the partial inverse problems.
Quantum effect of cooling down the environment temperature of mesoscopic LC circuit
Published in Journal of Modern Optics, 2018
In recent years, due to the rapid progress of mesoscopic physics and the eager expectation for making up quantum computers, much interest has been brought in quantization scheme of mesoscopic LC circuits (1–3). For a fundamental LC ‘cell’, Louisell (4) quantized it in the way that charge q is taken as canonical coordinate, while the current multiplied by the inductance L is taken as canonical momentum, . By imposing the quantization condition , the quantized Hamiltonian for LC circuit is By setting Equation (1) converts into . When the LC circuit is in the bare vacuum state , the quantum fluctuation is However, one should not just focus on fluctuations of charge and current at zero (5–7). In fact, any practical electric circuit work in a finite temperature environment, so the effect of temperature should be taken into account in calculating quantumaverages. Generally speaking, each mesoscopic LC circuit is immersed in an environment which contains a certain number of quanta in excitation, the creation of excitation quanta is denoted by , and the ground state is no longer in the bare vacuum, but in a thermo vacuum (8) where k is the Boltzmann constant, is annihilated both by a and , is temperature dependent. By introducing so the thermo vacuum is expressed as where is its form is like a two-mode squeezing operator, so we name the thermo squeezing operator, which changes the vacuum at zero temperature to the thermo vacuum at temperature T. It is noticed that since a two-mode squeezed state is also an entangled state, can be looked as if mode is entangled with mode . Equation (4) can be also expressed as and shows Bose–Einstein distribution.