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Relevant bibliographies by topics / Fermi-Dirac distribution

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Academic literature on the topic 'Fermi-Dirac distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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Journal articles on the topic "Fermi-Dirac distribution"

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Fannin, H. B., J. J. Hurly, and F. R. Meeks. "Quantum-Statistical Modeling of ICPs: He(I)." Applied Spectroscopy 42, no. 7 (September 1988): 1181–86. http://dx.doi.org/10.1366/0003702884430065.

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Relative populations of excited states of He(I) in reduced-pressure ICPs have been shown to obey Fermi-Dirac statistical counting. A single thermodynamic temperature—2000 K—defines the distribution. The experimental relative populations and the Fermi-Dirac distributions agree within fractions of one percent.

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Boé, Jean-Marie, and Fabrice Philippe. "Partitions and the Fermi–Dirac Distribution." Journal of Combinatorial Theory, Series A 92, no. 2 (November 2000): 173–85. http://dx.doi.org/10.1006/jcta.2000.3059.

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Wildberger, K., P. Lang, R. Zeller, and P. H. Dederichs. "Fermi-Dirac distribution inab initioGreen’s-function calculations." Physical Review B 52, no. 15 (October 15, 1995): 11502–8. http://dx.doi.org/10.1103/physrevb.52.11502.

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MOLINARI, V., D. MOSTACCI, and F. PIZZIO. "QUANTUM–RELATIVISTIC DISTRIBUTION FUNCTION FOR BOSONS AND FERMIONS." International Journal of Modern Physics B 26, no. 12 (May 8, 2012): 1241004. http://dx.doi.org/10.1142/s0217979212410044.

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In the present work, quantum–relativistic equilibrium distribution functions are derived for bosons above the critical temperature and for weakly degenerate fermions, extending to the relativistic case the Bose–Einstein and Fermi–Dirac distributions.

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Melrose, D. B., and A. Mushtaq. "Plasma dispersion function for a Fermi–Dirac distribution." Physics of Plasmas 17, no. 12 (December 2010): 122103. http://dx.doi.org/10.1063/1.3528272.

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Moussa, Jonathan E. "Minimax rational approximation of the Fermi-Dirac distribution." Journal of Chemical Physics 145, no. 16 (October 28, 2016): 164108. http://dx.doi.org/10.1063/1.4965886.

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Rosser, W. G. V. "The Fermi-Dirac and Bose-Einstein distribution functions." European Journal of Physics 7, no. 4 (October 1, 1986): 297–98. http://dx.doi.org/10.1088/0143-0807/7/4/116.

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Brunel, Vivien. "From the Fermi–Dirac distribution to PD curves." Journal of Risk Finance 20, no. 2 (March 18, 2019): 138–54. http://dx.doi.org/10.1108/jrf-01-2018-0009.

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Purpose In machine learning applications, and in credit risk modeling in particular, model performance is usually measured by using cumulative accuracy profile (CAP) and receiving operating characteristic curves. The purpose of this paper is to use the statistics of the CAP curve to provide a new method for credit PD curves calibration that are not based on arbitrary choices as the ones that are used in the industry. Design/methodology/approach The author maps CAP curves to a ball–box problem and uses statistical physics techniques to compute the statistics of the CAP curve from which the author derives the shape of PD curves. Findings This approach leads to a new type of shape for PD curves that have not been considered in the literature yet, namely, the Fermi–Dirac function which is a two-parameter function depending on the target default rate of the portfolio and the target accuracy ratio of the scoring model. The author shows that this type of PD curve shape is likely to outperform the logistic PD curve that practitioners often use. Practical implications This paper has some practical implications for practitioners in banks. The author shows that the logistic function which is widely used, in particular in the field of retail banking, should be replaced by the Fermi–Dirac function. This has an impact on pricing, the granting policy and risk management. Social implications Measuring credit risk accurately benefits the bank of course and the customers as well. Indeed, granting is based on a fair evaluation of risk, and pricing is done accordingly. Additionally, it provides better tools to supervisors to assess the risk of the bank and the financial system as a whole through the stress testing exercises. Originality/value The author suggests that practitioners should stop using logistic PD curves and should adopt the Fermi–Dirac function to improve the accuracy of their credit risk measurement.

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BROWN, S. R., and M. G. HAINES. "Transport in partially degenerate, magnetized plasmas. Part 1. Collision operators." Journal of Plasma Physics 58, no. 4 (December 1997): 577–600. http://dx.doi.org/10.1017/s0022377897006041.

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The quantum Boltzmann collision operator is expanded to yield a degenerate form of the Fokker–Planck collision operator. This is analysed using Rosenbluth potentials to give a degenerate analogue of the Shkarofsky operator. The distribution function is then expanded about an equilibrium Fermi–Dirac distribution function using a tensor perturbation formulation to give a zeroth-order and a first-order collision operator. These equations are shown to satisfy the relevant conservation equations. It is shown that the distribution function relaxes to a Fermi–Dirac form through electron–electron collisions.

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Yasuda, Makoto, Takeshi Furuhashi, and Shigeru Okuma. "Phase Transitions in Fuzzy Clustering Based on Fuzzy Entropy." Journal of Advanced Computational Intelligence and Intelligent Informatics 7, no. 3 (October 20, 2003): 370–76. http://dx.doi.org/10.20965/jaciii.2003.p0370.

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We studied the statistical mechanical characteristics of fuzzy clustering regularized with fuzzy entropy. We obtained Fermi-Dirac distribution as a membership function by regularizing the fuzzy c-means with fuzzy entropy. We then formulated it as direct annealing clustering, and determined the meanings of the Fermi-Dirac function and fuzzy entropy from the statistical mechanical point of view, and showed that this fuzzy clustering is a part of Fermi-Dirac statistics. We also derived the critical temperature at which phase transition occurs in this fuzzy clustering. Then, with a combination of cluster divisions by phase transitions and an adequate division termination condition, we derived fuzzy clustering that automatically determined the number of clusters, as verified by numerical experiments.

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Dissertations / Theses on the topic "Fermi-Dirac distribution"

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FURUHASHI, Takeshi, and Makoto YASUDA. "Fuzzy Entropy Based Fuzzy c-Means Clustering with Deterministic and Simulated Annealing Methods." Institute of Electronics, Information and Communication Engineers, 2009. http://hdl.handle.net/2237/15060.

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Rimgailaitė, Edita. "Kietojo kūno fizikos reiškinių kompiuterinis modeliavimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050603_162608-70551.

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Master’s thesis on “Simulation of processes in physic of solid state using computer programs” consists of an introduction, 3 chapters, conclusions, 22 references of literature, 15 appendixes and 1 compact disc. There are presented 3 tables and 31 pictures in the work as well. The work comprises 56 pages (with appendixes there are 93 pages). The aim of this work is seeking to create demonstrations for lectures in physic of solid state using the mathematical computer system. The first chapter deals with the possibility to use the computer programs in simulation of varied processes and phenomena and put into practice at lectures of solid state physics. The second chapter deals with particular phenomena. There are described the simulations of these phenomena as well. The computer mathematical system MathCAD was used to simulate and analyze the density of band states, Fermi – Dirac and Bolcman functions in the various temperature (5 K < T < 500 K). If we use the state destiny, Fermi – Dirac and Bolcman functions, we will get a distribution of free electrons by values of energy. Dynamic graph of functions is presented, which shows a variation probability of electron to be in E energy state subject to variations of temperature T. There is analyzing dependence of molar heat of solid state against to temperature T. The simulation of Fermi layer and concentration of charge at intrinsic and at impurity semiconductor are composed in this work as well. The using of simulations in lectures... [to full text]

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Oltean, Elvis. "Modelling income, wealth, and expenditure data by use of Econophysics." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/20203.

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In the present paper, we identify several distributions from Physics and study their applicability to phenomena such as distribution of income, wealth, and expenditure. Firstly, we apply logistic distribution to these data and we find that it fits very well the annual data for the entire income interval including for upper income segment of population. Secondly, we apply Fermi-Dirac distribution to these data. We seek to explain possible correlations and analogies between economic systems and statistical thermodynamics systems. We try to explain their behaviour and properties when we correlate physical variables with macroeconomic aggregates and indicators. Then we draw some analogies between parameters of the Fermi-Dirac distribution and macroeconomic variables. Thirdly, as complex systems are modelled using polynomial distributions, we apply polynomials to the annual sets of data and we find that it fits very well also the entire income interval. Fourthly, we develop a new methodology to approach dynamically the income, wealth, and expenditure distribution similarly with dynamical complex systems. This methodology was applied to different time intervals consisting of consecutive years up to 35 years. Finally, we develop a mathematical model based on a Hamiltonian that maximises utility function applied to Ramsey model using Fermi-Dirac and polynomial utility functions. We find some theoretical connections with time preference theory. We apply these distributions to a large pool of data from countries with different levels of development, using different methods for calculation of income, wealth, and expenditure.

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Books on the topic "Fermi-Dirac distribution"

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Solymar, L., D. Walsh, and R. R. A. Syms. The free electron theory of metals. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0006.

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The model of the free electron theory is presented. The density of states and the Fermi–Dirac distribution function are discussed, leading to the specific heat of the electrons, the work function, thermionic emission, and the Schottky effects. As examples of applications the field-emission microscope and quartz–halogen lamps are discussed. The photoelectric effect and the energy diagrams relating to the junction between two metals are also discussed.

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Horing, Norman J. Morgenstern. Quantum Mechanical Ensemble Averages and Statistical Thermodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0006.

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Chapter 6 introduces quantum-mechanical ensemble theory by proving the asymptotic equivalence of the quantum-mechanical, microcanonical ensemble average with the quantum grand canonical ensemble average for many-particle systems, based on the method of Darwin and Fowler. The procedures involved identify the grand partition function, entropy and other statistical thermodynamic variables, including the grand potential, Helmholtz free energy, thermodynamic potential, Gibbs free energy, Enthalpy and their relations in accordance with the fundamental laws of thermodynamics. Accompanying saddle-point integrations define temperature (inverse thermal energy) and chemical potential (Fermi energy). The concomitant emergence of quantum statistical mechanics and Bose–Einstein and Fermi–Dirac distribution functions are discussed in detail (including Bose condensation). The magnetic moment is derived from the Helmholtz free energy and is expressed in terms of a one-particle retarded Green’s function with an imaginary time argument related to inverse thermal energy. This is employed in a discussion of diamagnetism and the de Haas-van Alphen effect.

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Book chapters on the topic "Fermi-Dirac distribution"

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Srinivasan, Ganesan. "Fermi–Dirac Distribution." In Undergraduate Lecture Notes in Physics, 55–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-45384-7_5.

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Merhav, Neri. "Quantum Statistics – The Fermi–Dirac Distribution." In Statistical Physics for Electrical Engineering, 47–63. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62063-3_3.

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Efird, Jimmy Thomas, and Francisco Pardo. "A Non-Parametric Two-Sample Survival Test Based on a Single Occupancy Fermi-Dirac Model for the Discrete Range Distribution." In Lifetime Data: Models in Reliability and Survival Analysis, 93–97. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-5654-8_14.

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Vincze, I., and R. Tőrös. "The Joint Energy Distributions of the Bose-Einstein and of the Fermi-Dirac Particles." In Advances in Combinatorial Methods and Applications to Probability and Statistics, 441–49. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4140-9_26.

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Wartak, Marek S., and Ching-Yao Fong. "Fermi–Dirac Distribution." In Field Guide to Solid State Physics. SPIE, 2019. http://dx.doi.org/10.1117/3.2510243.ch24.

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"Consequences of the Fermi-Dirac Distribution." In Einstein's Other Theory, 132–48. Princeton University Press, 2020. http://dx.doi.org/10.2307/j.ctv131bw9t.11.

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"Eight. Consequences of the Fermi-Dirac Distribution." In Einstein's Other Theory, 132–48. Princeton University Press, 2005. http://dx.doi.org/10.1515/9780691216409-009.

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Brooker, Geoffrey. "The Boltzmann distribution and molecular gases." In Essays in Physics, 242–47. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198857242.003.0020.

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“The Boltzmann distribution and molecular gases” explains why an “ordinary” gas has its molecules Boltzmann-distributed. The most concentrated Fermi–Dirac gas, helium 3 at its boiling point, is still in a “dilute limit”, dilute enough to be approximately Boltzmann. Similarly, the most concentrated Bose–Einstein gas, helium 4 at its boiling point, is also approximately Boltzmann.

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Brooker, Geoffrey. "Electrons and holes in semiconductors." In Essays in Physics, 321–36. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198857242.003.0025.

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“Electrons and holes in semiconductors” applies band theory to electrons in the conduction band, and to holes in the valence band. Holes are described by an upside-down Fermi–Dirac distribution. An incorrect model (cinema-queue model) for a hole is discredited and replaced by a correct discussion. Both (conduction-band) electrons and (valence-band) holes are examples of quasi-particles. Both can be assigned their own group velocities and effective masses.

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Manton, Nicholas, and Nicholas Mee. "Thermodynamics." In The Physical World. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198795933.003.0011.

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This chapter is about thermodynamics, or statistical mechanics, which explains macroscopic features of the world in terms of the motion of vast numbers of particles on the atomic scale. It discusses how macroscopic variables such as temperature and entropy were originally introduced, before presenting modern definitions of temperatures and entropy and the Laws of Thermodynamics. Alternative thermodynamic variables, including enthalpy and the Gibbs free energy, are defined and the Gibbs distribution is explained. The Maxwell distribution is derived. The chemical potential is introduced and the pressure and heat capacity of an electron gas is calculated, The Fermi–Dirac and Bose–Einstein functions are derived. Bose–Einstein condensation is explained. Black body radiation is discussed and the Planck formula is derived. Lasers are explained. Spin systems are used to model magnetization. Phase transitions are briefly discussed. Hawking radiation and the thermodynamics of black holes is explained.

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Conference papers on the topic "Fermi-Dirac distribution"

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Karkri, Aboulkacem, Mohammed Hadrami, Mohammed Benaichi, and Abdelaziz Chetouani. "Numerical modelling of degenerate and nondegenerate semiconductors with the Fermi-Dirac distribution." In 2016 International Conference on Electrical and Information Technologies (ICEIT). IEEE, 2016. http://dx.doi.org/10.1109/eitech.2016.7519601.

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Kim, Heung Soo, Anindya Ghoshal, Jaehwan Kim, and Seung-Bok Choi. "Transient analysis of delaminated smart composite structures by incorporating Fermi-Dirac distribution function." In Smart Structures and Materials, edited by Ralph C. Smith. SPIE, 2005. http://dx.doi.org/10.1117/12.592163.

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Ghoshal, Anindya, Heung Soo Kim, William H. Prosser, Hsiang Tai, Mark J. Schulz, and Goutham Kirikera. "Modeling delamination in composite structures by incorporating the Fermi-Dirac distribution function and hybrid damage indicators." In NDE for Health Monitoring and Diagnostics, edited by Tribikram Kundu. SPIE, 2004. http://dx.doi.org/10.1117/12.538270.

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