The concepts of statistical physics have been used to study fermionic systems rapidly after the birth of the “new" quamtum mechanics in 1925. This proved to be extremely fruitful and led to major advances in atomic and solid state physics. Fermi-Dirac statistics was introduced in 1926 by Enrico Fermi and Paul Dirac. It was used by Ralph Fowler in 1926 to describe the collapsed state of a star (a so-called white dwarf ) and by Arnold Sommerfeld in 1928 to describe conduction electrons in solids. This chapter first presents some general results and then discusses a choice of specific systems.
The concepts of statistical physics have been used to study fermionic systems rapidly after the birth of the “new" quamtum mechanics in 1925. This proved to be extremely fruitful and led to major advances in atomic and solid state physics. Fermi-Dirac statistics was introduced in 1926 by Enrico Fermi and Paul Dirac. It was used by Ralph Fowler in 1926 to describe the collapsed state of a star (a so-called white dwarf ) and by Arnold Sommerfeld in 1928 to describe conduction electrons in solids. This chapter first presents some general results and then discusses a choice of specific systems.
Abstract Quantum statistical mechanics governs metals, semiconductors, and neutron stars. Statistical mechanics spawned Planck’s invention of the quantum, and explains Bose condensation, superfluids, and superconductors. This chapter briefly describes these systems using mixed states, or more formally density matrices, and introducing the properties of bosons and fermions. We discuss in unusual detail how useful descriptions of metals and superfluids can be derived by ignoring the seemingly important interactions between their constituent electrons and atoms. Exercises explore how gregarious bosons lead to superfluids and lasers, how unsociable fermions explain transitions between white dwarfs, neutron stars, and black holes, how one calculates materials properties in semiconductors, insulators, and metals, and how statistical mechanics can explain the collapse of the quantum wavefunction during measurement.
Abstract In this paper, we deal with the historical origins of Fermi–Dirac statistics, focusing on the contribution by Enrico Fermi of 1926. We argue that this statistics, as opposed to that of Bose–Einstein, has been somewhat overlooked in the usual accounts of the old quantum theory. Our main objective is to offer a critical analysis of Fermi’s seminal paper and its immediate impact. Secondly, we are also interested in assessing the status of the particle concept in the years 1926–1927, especially regarding the germ of quantum indistinguishability. We will see, for example, that the first applications of the Fermi–Dirac statistics to the study of metals or stellar matter had a technical nature, and that their main instigators barely touched upon interpretative matters. Finally, we will discuss the reflections and remarks made in these respects in two famous events in physics of 1927, the Como conference and the fifth Solvay congress.
Some fundamental changes have been introduced into statistical theory since the publication of a paper by Bose in 1924. The characteristic features of the new statistics, including that of Bose and Einstein, and the later one of Fermi and Dirac, are pointed out in this lecture and compared with the classical statistics. A number of recent applications of the new ideas are described, including the work of Thomas and Fermi on the distribution of electrons in atoms, and the work of Sommerfeld and others on the electron theory of metals. An account is also given of some recent results obtained by the author and H. J. Woods on the distribution of electrons in a metal.
Under conditions of high temperature and low density, we shall nd that it does not matter whether classical or quantum mechanical descriptions are used for a system of particles. At high densities and low temperatures this is no longer true, because of the overlap of the particles’ wave functions and quantum mechanics must be used, giving rise to quantum statistics. Under high-density, low-temperature conditions, the properties of a system depend in a crucial way on whether the particles that make up the system are fermions or bosons. Many fascinating phenomena occur in condensed matter as the temperature is lowered. Examples are ferromagnetism, superconductivity, and super uidity. ese important new properties appear fairly abruptly at phase transitions. Progress in the microscopic understanding and description of the behavior of these systems involves quantum mechanics and statistical physics ideas. Applications of quantum statistics are not conned to terrestrial systems and include astrophysical phenomena such as the microwave background radiation from the Big Bang and the mass-radius relationships for white dwarf stars and neutron stars. An important concept in thermal physics is that of entropy, which, as we shall see, increases with time as systems become more disordered. e increase of the entropy of the universe with the passage of time provides what is termed time’s arrow. An interesting and unanswered question arises as to why the entropy of the universe was so low at the beginning of time.
Aim of this paper is to retrace the path that led the young Enrico Fermi to write his paper on the statistics of an ideal monatomic gas. This discovery originated in his interest, which he had shown since his formative years, in the absolute entropy constant and in the problems he highlighted in Sommerfeld's quantization in the case of identical particle systems. The fundamental step taken by Fermi in writing his work on statistics was to apply the Exclusion Principle, formulated for electrons in an atom and which could therefore have been a pure effect due to dynamics, to a system of non-interacting particles.
Chapter 3 provides a brief review of a few concepts from classical Newtonian physics, and how this fails to explain phenomena at the nanoscopic scale. As is detailed within, the classical mechanical model is able to describe all observed physical phenomena; however, when it comes to the nanoscale this model breaks down, because the properties of the materials change dramatically. At this scale, the surface-to-volume ratio increases, gravitational forces become negligible and random molecular motion becomes more important. This changes the properties of the material and affects the devices that are fabricated at this scale. It is hence necessary to develop a new model that can explain such physical phenomena. This has led to a new branch of physics, i.e. quantum physics (QP) or quantum mechanics, which is able to explain the behavior observed at nanoscale. QP enables us to explain phenomena such as the photoelectric effect, Compton effect. etc. In this chapter, we introduce quantum mechanics and how it evolved in the late 19th and early 20th centuries. Further, light’s behaviour as a particle as well as a wave is described by the photoelectric effect and Young’s double-slit experiment, respectively. Further, the dual nature of the particle is explained using the de Broglie principle. Schrodinger’s equation is then explained, which gives the probability of finding a subatomic-scale particle at a certain position in a quantum well. In addition to the formulation of Schrodinger’s equation, its solution, the concept of a potential well, the characteristics of the wave function and its interpretation and significance, and, finally, the application of Schrodinger’s equation in the structure of an atom form subsequent parts of this chapter. The equation serves as a basis with which to understand band theory. Band theory explains the difference between conductors, insulators and semiconductors. Materials are distinguished according to the differences in their band gaps. Adding impurities or varying temperature changes the band gap in semiconductors, which consequently changes the properties of the semiconductor and its electrical conduction. One more important measure to understand and exploit the properties and behaviour of materials is Fermi–Dirac statistics. It is useful to acquire the probability of electrons at a given energy level at a specific temperature. These concepts can be utilised by physicists and chip makers to make more energy-efficient devices. Hence, this chapter details the fundamentals of quantum physics and how they relate to the electrical properties of nanodevices.