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Brillouin and Langevin functions, the Glossary

Index Brillouin and Langevin functions

The Brillouin and Langevin functions are a pair of special functions that appear when studying an idealized paramagnetic material in statistical mechanics.[1]

Table of Contents

  1. 25 relations: Arithmetico-geometric sequence, Azimuthal quantum number, Bohr magneton, Boltzmann constant, Boltzmann distribution, Catastrophic cancellation, Expected value, G-factor (physics), Geometric series, Introduction to Solid State Physics, Journal of Applied Physics, Léon Brillouin, Magnetic field, Magnetic moment, Magnetization, Padé approximant, Paramagnetism, Partition function (statistical mechanics), Paul Langevin, Special functions, Statistical mechanics, Taylor series, Total angular momentum quantum number, Vacuum permeability, Zeeman effect.

  2. Eponymous laws of physics

Arithmetico-geometric sequence

In mathematics, arithmetico-geometric sequence is the result of term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression.

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Azimuthal quantum number

In quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital.

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Bohr magneton

In atomic physics, the Bohr magneton (symbol) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by its orbital or spin angular momentum.

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Boltzmann constant

The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas.

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Boltzmann distribution

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system.

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Catastrophic cancellation

In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers.

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Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

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G-factor (physics)

A g-factor (also called g value) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus.

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Geometric series

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

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Introduction to Solid State Physics

Introduction to Solid State Physics, known colloquially as Kittel, is a classic condensed matter physics textbook written by American physicist Charles Kittel in 1953.

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Journal of Applied Physics

The Journal of Applied Physics is a peer-reviewed scientific journal with a focus on the physics of modern technology.

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Léon Brillouin

Léon Nicolas Brillouin (August 7, 1889 – October 4, 1969) was a French physicist.

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Magnetic field

A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. Brillouin and Langevin functions and magnetic field are magnetism.

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Magnetic moment

In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. Brillouin and Langevin functions and magnetic moment are magnetism.

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Magnetization

In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material.

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Padé approximant

In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order.

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Paramagnetism

Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. Brillouin and Langevin functions and Paramagnetism are magnetism.

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Partition function (statistical mechanics)

In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium.

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Paul Langevin

Paul Langevin (23 January 1872 – 19 December 1946) was a French physicist who developed Langevin dynamics and the Langevin equation.

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Special functions

Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications.

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Statistical mechanics

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities.

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Taylor series

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

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Total angular momentum quantum number

In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).

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Vacuum permeability

The vacuum magnetic permeability (variously vacuum permeability, permeability of free space, permeability of vacuum, magnetic constant) is the magnetic permeability in a classical vacuum.

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Zeeman effect

The Zeeman effect is the effect of splitting of a spectral line into several components in the presence of a static magnetic field.

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See also

Eponymous laws of physics

References

[1] https://en.wikipedia.org/wiki/Brillouin_and_Langevin_functions

Also known as Brillouin Function, Langevin Formula, Langevin Function, Langevin paramagnetic equation.