Fermi gas - Citizendia

A Fermi gas, or Free electron gas, is a collection of non-interacting fermions. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. It is the quantum mechanical version of an ideal gas, for the case of fermionic particles. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion Electrons in metals and semiconductors and neutrons in a neutron star can be approximately considered Fermi gases. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The M acro E xpansion T emplate A ttribute L anguage complements TAL, providing macros which allow the reuse of code across A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. The energy distribution of the fermions in a Fermi gas in thermal equilibrium is determined by their density, the temperature and the set of available energy states, via Fermi-Dirac statistics. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature In Statistical mechanics, Fermi-Dirac statistics is a particular case of Particle statistics developed by Enrico Fermi and Paul Dirac that By the Pauli principle, no quantum state can be occupied by more than one fermion, so the total energy of the Fermi gas at zero temperature is larger than the product of the number of particles and the single-particle ground state energy. The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925 For this reason, the pressure of a Fermi gas is nonzero even at zero temperature, in contrast to that of a classical ideal gas. This so-called degeneracy pressure stabilizes a neutron star (a Fermi gas of neutrons) or a White Dwarf star (a Fermi gas of electrons) against the inward pull of gravity. Degenerate matter is matter which has sufficiently high Density that the dominant contribution to its Pressure rises from the Pauli Exclusion A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type A white dwarf, also called a degenerate dwarf, is a small Star composed mostly of Electron-degenerate matter. Gravitation is a natural Phenomenon by which objects with Mass attract one another

It is possible to define a Fermi temperature below which the gas can be considered degenerate. The Fermi energy is a concept in Quantum mechanics usually referring to the energy of the highest occupied Quantum state in a system of Fermions at This temperature depends on the mass of the fermions and the energy density of states. In statistical and Condensed matter physics, the density of states ( DOS) of a system describes the number of states at each energy level that are available For metals, the electron gas's Fermi temperature is generally many thousands of kelvins, so they can be considered degenerate. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic The maximum energy of the fermions at zero temperature is called the Fermi energy. The Fermi energy is a concept in Quantum mechanics usually referring to the energy of the highest occupied Quantum state in a system of Fermions at The Fermi energy surface in momentum space is known as the Fermi surface.

Since interactions are neglected by definition, the problem of treating the equilibrium properties and dynamical behaviour of a Fermi gas reduces to the study of the behaviour of single independent particles. As such, it is still relatively tractable and forms the starting point for more advanced theories (such as Fermi liquid theory or perturbation theory in the interaction) which take into account interactions to some degree of accuracy. Fermi liquid is a generic term for a quantum mechanical Liquid of Fermions that arises under certain physical conditions when the Temperature In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system

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