It was theoretically described by physicists such as Arnold Sommerfeld and Léon Brillouin.

One of the most famous responses to this question was suggested in 1929 by Leó Szilárd, and later by Léon Brillouin.

Later, Léon Brillouin shortened the phrase to negentropy, to express it in a more " positive " way: a living system imports negentropy and stores it.

The concept of a Brillouin zone was developed by Léon Brillouin ( 1889 – 1969 ), a French physicist.

Brillouin scattering, named after Léon Brillouin, occurs when light in a medium ( such as air, water or a crystal ) interacts with time-dependent optical density variations and changes its energy ( frequency ) and path.

Inelastic scattering of light by acoustic phonons was first predicted by Léon Brillouin in 1922.

* Léon Brillouin, Ann.

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

* H. Armagnat and Léon Brillouin Les mesures en haute fréquence ( Chiron, 1924 )

* Léon Brillouin Les Statistiques Quantiques Et Leurs Applications.

* Léon Brillouin La Théorie des Quanta et l ' Atome de Bohr ( Presse Universitaires de France, 1922, 1931 )

* Léon Brillouin Conductibilité électrique et thermique des métaux ( Hermann, 1934 )

* Léon Brillouin Notions Elementaires de Mathématiques pour les Sciences Expérimentales ( Libraires de l ' Academie de Médecine, 1939 )

* Léon Brillouin The Mathematics of Ultra-High Frequencies Radio ( Brown University, 1943 )

* Léon Brillouin Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices ( McGraw – Hill, 1946 ) ( Dover, 1953, 2003 )

* Léon Brillouin Les Tenseurs en mécanique et en élasticité: Cours de physique théorique ( Dover, 1946 )

* Léon Brillouin Mathématiques ( Masson, 1947 )

* Léon Brillouin Notions élémentaires de mathématiques pour les sciences expérimentales ( Masson, 1947 )

* Léon Brillouin Propagation des ondes dans les milieux périodiques ( Masson – Dunod, 1956 )

* Léon Brillouin La science et la théorie de l ' information ( Masson, 1959 )

* Léon Brillouin Vie Matière et Observation ( Albin Michel, 1959 )

* Léon Brillouin Wave Propagation and Group Velocity ( Academic Press, 1960 )

* Léon Brillouin Science and Information Theory ( Academic Press, 1962 ) ( Dover, 2004 )

* Léon Brillouin Scientific Uncertainty and Information ( Academic Press, 1964 )

* Léon Brillouin Relativity Reexamined ( Academic Press, 1970 )

There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions ( all with the same volume ) at increasing distances from the origin, but these are used less frequently.

The sinc function for a non-Cartesian lattice ( e. g., hexagonal lattice ) is a function whose Fourier transform is the indicator function of the Brillouin zone of that lattice.

He also studied the propagation of monochromatic light waves and their interaction with acoustic waves, i. e., scattering of light with a frequency change, which became known as Brillouin scattering.

* Mosseri, Rémy Léon Brillouin à la croisée des ondes ( Belin, Paris, 1999 ) ISBN 2-7011-2299-6

The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone.

Since it is time-consuming to calculate the energy for a molecule, it is even more time-consuming to calculate them for the entire list of points in the Brillouin zone.

* Leon Brillouin, Science and Information Theory, Mineola, N. Y .: Dover, 1962 2004.

The most important consequence of the periodic potential is the formation of a small band gap at the boundary of the Brillouin zone.

In the nearly free correction of the model, box-like Brillouin zones are added to k-space by the periodic potential experienced from the ( ionic ) lattice.

The most common way of producing optical phase conjugation is to use a four-wave mixing technique, though it is also possible to use processes such as stimulated Brillouin scattering.

The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to the wave vectors confined to the Brillouin zone.

In this expression, W < sub > c, v </ sub >( E ) represents the product of the Brillouin zone-averaged transition probability at the energy E with the joint density of states, J < sub > c, v </ sub >( E ); φ is a broadening function, representing the role of scattering in smearing out the energy levels.

Similar arguments were subsequently generalized to many glass forming substances using Brillouin scattering.

To U-process to occur the decaying phonon to have a wave vector q < sub > 1 </ sub > that is roughly half of the diameter of the Brillouin zone, because otherwise quasimomentum would not be conserved.

Inelastic scattering includes Brillouin scattering, Raman scattering, inelastic X-ray scattering and Compton scattering.

* Brillouin zone, the primitive cell of a lattice in reciprocal space.

It is also closer in principle to the more sophisticated approaches used when dealing with real bulk crystalline solids, where the first step is either to integrate contributions to the ECD over constant energy surfaces in a wave-vector space ( k-space ), or to integrate contributions over the relevant surface Brillouin zone.

The Forbes approach is equivalent either to integrating over a spherical surface in k-space, using the variable K < sub > p </ sub > to define a ring-like integration element that has cylindrical symmetry about an axis in a direction normal to the emitting surface, or to integrating over an ( extended ) surface Brillouin zone using circular-ring elements.

For the picture shown to the right, corresponds to the band-structure of a 1D DBR with air-core interleaved with a dielectric material of relative permittivity 12. 25, and a lattice period to air-core thickness ratio ( d / a ) of 0. 8, is solved using 101 planewaves over the first irreducible Brillouin zone.

The energies associated with the index n vary continuously with wave vector k and form an energy band identified by band index n. The eigenvalues for given n are periodic in k ; all distinct values of ϵ < sub > n </ sub >( k ) occur for k-values within the first Brillouin zone of the reciprocal lattice.

The plane wave vector ( Bloch wave vector ) k, which when multiplied by the reduced Planck's constant is the particle's crystal momentum, is unique only up to a reciprocal lattice vector, so one only needs to consider the wave vectors inside the first Brillouin zone.

The band structure is the collection of energy eigenstates within the first Brillouin zone.