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Quantum Chaotic Systems and Random Matrix Theory
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2019
Akhilesh Pandey, Avanish Kumar, Sanjay Puri
Subsequently, Mcdonald-Kaufman [34] and Berry [35] considered stadium and Sinai billiards, respectively, and showed that their quantum spectra display level repulsion. Classically, a billiard system refers to a free particle moving in a two-dimensional region, obeying classical reflection rules at the boundary of the region. For the corresponding quantum billiard, the eigenfunctions are solutions of the free-particle Schrodinger equation which vanish at the boundary of the region. The energy levels are discrete.
Nonlinear Systems Analysis and Modeling
Published in Naim A. Kheir, Systems Modeling and Computer Simulation, 2018
Recall the last example, a ball rolling around on the inner wall of the basin. It can be seen that the ball starting from an initial point will always keep its total energy (kinetic energy plus potential energy) unchanged in the case without friction, or the total energy is reduced gradually until the ball stops at the bottom point if there is rolling friction. As a counterpart, if the ball is placed on the top point of a smooth hill-like surface, then it will no longer be back to the top point once the ball is pushed down the hill with a small force. In fact, the ball will keep rolling down the hill and the kinetic energy can be increased unboundedly. This example implies that every dynamic system commonly tends to the minimum energy state. In other words, the lower the energy level, the more stable the system is supposed to be. Therefore, we are inspired to explore an energy-like function associated with the system equation for its stability determination.
Electrical Properties
Published in Mary Anne White, Physical Properties of Materials, 2018
The wide variety of electrical conductivities in different materials is associated with the availability of energy levels directly above the filled energy levels in the material. The presence (and width) of a gap between the filled electronic states and the next available electronic states leads to very different electrical properties for insulators and conductors.
Photon bunching from an equilateral triangle of atoms
Published in Journal of Modern Optics, 2023
A single atom (black blob) in the triad is driven by a resonant coherent field having a Rabi frequency . The coherent external field propagates orthogonal to the plane of the system of atoms. Radiated photon pairs generated at the same time are recorded in the far-field regime. Two photodetectors located at distances and , respectively, record the radiation scattered by the atoms. Pairs of photons are detected utilising photo-detectors situated in a plane orthogonal to the direction in which the dipole moments of the atoms align, , the radiation pattern in the horizontal plane. The internal levels of an excited atom are presented in the lower right inset while the upper right inset depicts any atom which is not driven (white blob). () signify the upper (lower) energy level of an atom, respectively.
Computational analysis for temperature separation and correlations prediction for dual-inlet-sections vortex tube
Published in Numerical Heat Transfer, Part B: Fundamentals, 2023
Ravi Kant Singh, Achintya Kumar Pramanick, Subhas Chandra Rana
The energy level in the substance depends on many factors along with temperature, such as specific heat and mass of substance, and it contributes to the energy content and sensible heat of a substance. Therefore, to calculate the appropriateness of VT in certain applications, it is important to estimate the cooling power capacity along with the cold exit temperature gradient. The cooling power is calculated to analyze the thermal performance of the counter flow VT. It relies on the temperature difference, mass flow rate, and specific heat and is given as
FEA Based Design and Stability Study of Electroless Ni-P Coating Plated over a Stepped Shaft under Thermal Load
Published in Australian Journal of Mechanical Engineering, 2023
Tarik Hassan, Subhasish Sarkar, Tapendu Mandal, Nitesh Mondal, Gautam Majumdar
A separate study is performed to analyse results along a straight line in the model which is a very helpful tool to check the variation of data along that line. The values of equivalent stress () and strain energy (SE) are evaluated along the four different paths as discussed earlier, and the data are plotted against the radial distance with respect to the axis of the shaft as shown in Figures 9 and 10, respectively. The prime objective of finding the data along a path is to calculate the change in the values of and SE between the coating and the shaft. This change may be a helpful measure to predict the design stability of the coating over the surface of the substrate. From the atomic scale to a macro-scale substance, everything is connected to energy in various ways. It is also an important scientific fact that the energy level is indirectly proportional to the level of stability. Therefore, every object in this universe is trying to minimise its energy to gain better stability, like the electron in the outer orbit of an atom is very unstable and mainly responsible for chemical bonding because of its higher energy state while the reverse happens to the inner orbit electron due to lower energy level (Xu et al. 2018; Rohrlich 1960; Saville et al. 2011). In the case of elastic material, strain energy is one form of potential energy which is generated in a deformed body due to the generation of stress. The body which has higher SE or induced stress is capable of performing higher elastic work, making itself less stable and more prone to cause failure. Han et al. (2021) used the advanced concept of strain and resonance energy to analyse the stability and performance of explosives. Similarly, the ligand strain energy of the metal-organic framework (MOF) is compared with its stability by Shustova, Cozzolino, and Dinca (2012). The main objective here is to justify that the strain energy is an important determining parameter for the design stability of an elastic body.