Bose-Einstein condensate (BEC)
Fr.: condensat de Bose-Einstein
A state of matter in which a group of atoms or subatomic particles,
cooled to within → absolute zero,
coalesce into a single quantum mechanical entity
that can be described by a → wave function.
When a group of atoms are cooled down to very near
absolute zero, the atoms hardly move relative to each other, because
they have almost no free energy
to do so. Hence the atoms clump together and enter
the same → ground energy states.
They become identical and the whole group starts behaving as though it were a
single atom. A Bose-Einstein condensate results from a
→ quantum transition phase
called the → Bose-Einstein condensation.
This form of matter was predicted in 1924 by Albert Einstein on
the basis of the quantum formulations of the Indian physicist
Satyendra Nath Bose.
→ boson; → Einstein; → condensate.
Bose-Einstein condensation (BEC)
Fr.: condensation de Bose-Einstein
A → quantum phase transition during which the → bosons constituting a sufficiently cooled boson gas are all clustered in the → ground energy state. The phase transition results in a → Bose-Einstein condensate. This phenomenon occurs when the temperature becomes smaller than a critical value given by: Tc = (2πħ2 / km)(n / 2.612)2/3, where m is mass of each boson, ħ is the → reduced Planck's constant, k is → Boltzmann's constant, and n is the particle number density. When T ≤ Tc, the → de Broglie wavelength of bosons becomes comparable to the distance between bosons.
→ boson; → Einstein; → condensation.
Fr.: distribution de Bose-Einstein
For a → population of independent → bosons, a function that specifies the number of particles in each of the allowed → energy states.
→ boson; → Einstein; → distribution.
âmâr-e Bose-Einstein (#)
Fr.: statistique de Bose-Einstein
Same as → Bose-Einstein distribution.
→ boson; → Einstein; → statistics.
A unit of radiation energy sometimes used in the investigation of photochemical processes. The unit is defined as NAhν, where NA is → Avogadro's number and hν is the energy of a → quantum of the radiation. One einstein (or Einstein unit) is the energy per → mole of photons carried by a beam of monochromatic light.
Named for Albert Einstein (1879-1955).
Fr.: coefficient d'Einstein
A measure of the probability that a particular atomic transition leading to the formation of an atomic spectral line occurs. The coefficient of spontaneous emission is denoted by Aij, and the coefficient of stimulated emission by Bij, i representing the lower level and j is the upper level.
Named after Albert Einstein (1879-1955) who introduced the coefficients in 1916; → coefficient.
Fr.: croix d'Einstein
An image of a distant quasar (redshift 1.7) formed by a foreground spiral galaxy (redshift 0.039) through gravitational lensing. The image of the quasar is split into four point sources forming a cross at the center of the galaxy.
Einstein equivalence principle
parvaz-e hamug-arzi-ye Einstein
Fr.: principe d'équivalence d'Einstein
The → equivalence principle as stated by Einstein, on which is
based the theory of → general relativity. It comprises
the three following items:
→ Einstein; → equivalence; → principle.
Fr.: modèle d'Einstein
A model for the → specific heat of solids in which the specific heat is due to the vibrations of the atoms of the solids. The vibration energy is → quantized and the atoms have a single frequency, ν. Put forward in 1907 by Einstein, this model was the first application of → quantum theory to the solid state physics. The expression for the specific heat is given by: CV = 3Rx2ex/(ex -1)2, where R is the → gas constant, x = TE/T, TE = hν/k, h is → Planck's constant, and k is → Boltzmann's constant. TE is called the → Einstein temperature. This model could explain the temperature behavior of specific heat but not very satisfactorily at low temperatures. It has therefore been superseded by the → Debye model. See also → Dulong-Petit law.
Albert Einstein in 1907; → model.
Fr.: convention Einstein
A notation convention in → tensor analysis whereby whenever there is an expression with a repeated → index, the summation is done over that index from 1 to 3 (or from 1 to n, where n is the space dimension). For example, the dot product of vectors a and b is usually written as: a.b = Σ (i = 1 to 3) ai.bi. In the Einstein notation this is simply written as a.b = ai.bi. This notation makes operations much easier. Same as Einstein summation convention.
Fr.: rayon d'Einstein
In gravitational lens phenomenon, the critical distance from the → lensing object for which the light ray from the source is deflected to the observer, provided that the source, the lens, and the observer are exactly aligned. Consider a massive object (the lens) situated exactly on the line of sight from Earth to a background source. The light rays from the source passing the lens at different distances are bent toward the lens. Since the bending angle for a light ray increases with decreasing distance from the lens, there is a critical distance such that the ray will be deflected just enough to hit the Earth. This distance is called the Einstein radius. By rotational symmetry about the Earth-source axis, an observer on Earth with perfect resolution would see the source lensed into an annulus, called Einstein ring, centered on its position. The size of an Einstein ring is given by the Einstein radius: θE = (4GM/c2)0.5 (dLS/(dL.dS)0.5, where G is the → gravitational constant, M is the mass of the lens, c is the → speed of light, dL is the angular diameter distance to the lens, dS is the angular diameter distance to the source, and dLS is the angular diameter distance between the lens and the source. The equation can be simplified to: θE = (0''.9) (M/1011Msun)0.5 (D/Gpc)-0.5. Hence, for a dense cluster with mass M ~ 10 × 1015 Msun at a distance of 1 Gigaparsec (1 Gpc) this radius is about 100 arcsec. For a gravitational → microlensing event (with masses of order 1 Msun) at galactic distances (say D ~ 3 kpc), the typical Einstein radius would be of order milli-arcseconds.
Fr.: anneau d'Einstein
The apparent shape of a background source unsergoing the effect of → gravitational lensing as seen from Earth, provided that the source, the intervening lens, and the observer are in perfect alignement through → Einstein radius.
Fr.: modèle d'Einstein
Same as → Einstein model.
Einstein static Universe
giti-ye istâ-ye Einstein
Fr.: Univers stationnaire d'Einstein
A cosmological model in which a static (neither expanding nor collapsing) Universe is maintained by introducing a cosmological repulsion force (in the form of the cosmological constant) to counterbalance the gravitational force.
damâ-ye Einstein (#)
Fr.: température d'Einstein
A characteristic parameter occurring in the → Einstein model of → specific heats.
→ Einstein; → temperature.
tânsor-e Einstein (#)
Fr.: tenseur d'Einstein
A mathematical entity describing the → curvature of → space-time in → Einstein's field equations, according to the theory of → general relativity. It is expressed by Gμν = Rμν - (1/2) gμνR, where Rμν is the Ricci tensor, gμν is the → metric tensor, and R the scalar curvature. This tensor is both symmetric and divergence free.
Named after Albert Einstein (1879-1955); → tensor.
marpel-e zamâni-ye Einstein
Fr.: échelle de temps d'Einstein
The time during which a → microlensing event occurs. It is given by the equation tE = RE/v, where RE is the → Einstein radius, v is the magnitude of the relative transverse velocity between source and lens projected onto the lens plane. The characteristic time-scale of → microlensing events is about 25 days.
→ Einstein; → time-scale.
Fr.: ascenseur d'Einstein
A → thought experiment, involving an elevator, first conceived by Einstein to show the → principle of equivalence. According to this experiment, it is impossible for an observer situated inside a closed elevator to decide if the elevator is being pulled upward by a constant force or is subject to a gravitational field acting downward on a stationary elevator. Einstein used this experiment and the principle of equivalence to deduce the bending of light by the force of gravity.
→ einstein; elevator, from L. elevator, agent noun from p.p. stem of elevare "to lift up, raise," from → ex- "out" + levare "lighten, raise," from levis "light" in weight, → lever.
Bâlâbar, → lift.
Einstein's field equations
hamugešhâ-ye meydân-e Einstein
Fr.: équations de champ d'Einstein
A system of ten non-linear → partial differential equations in the theory of → general relativity which relate the curvature of → space-time with the distribution of matter-energy. They have the form: Gμν = -κ Tμν, where Gμν is the → Einstein tensor (a function of the → metric tensor), κ is a coupling constant called the → Einstein gravitational constant, and Tμν is the → energy-momentum tensor. The field equations mean that the curvature of space-time is due to the distribution of mass-energy in space. A more general form of the field equations proposed by Einstein is: Gμν + Λgμν = - κTμν, where Λ is the → cosmological constant.
Named after Albert Einstein (1879-1955); → field; → equation.
Einstein's gravitational constant
pâyâ-ye gerâneši-ye Einstein (#)
Fr.: constante gravitationnelle d'Einstein
The coupling constant appearing in → Einstein's field equations, expressed by: κ = 8πG/c4, where G is the Newtonian → gravitational constant and c the → speed of light.
→ einstein; → gravitational; → constant.