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The indistinguishability of all particles of each fundamental type ( say, electrons, or photons ) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle for fermions and in Bose-Einstein condensation for bosons.
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indistinguishability and particles
For example, the indistinguishability of particles has been proposed as a solution to Gibbs ' mixing paradox.
The indistinguishability of particles has a profound effect on their statistical properties.
The term " teleportation ", coined by Bennett, Brassard, Crépeau, Jozsa, Peres and Wootters, reflects the indistinguishability of quantum mechanical particles.
His resolution of the so-called " Gibbs paradox ," about the entropy of the mixing of gases, is now often cited as a prefiguration of the indistinguishability of particles required by quantum mechanics.
In statistical mechanics, a semi-classical derivation of the entropy that doesn't take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive ( is not proportional to the amount of substance in question ).
The paradox is averted by concluding the indistinguishability ( at least effective indistinguishability ) of the particles in the volume.
By Jaynes ' reasoning, if the particles are experimentally indistinguishable for whatever reason, Gibbs paradox is resolved, and quantum mechanics only provides an assurance that in the quantum realm, this indistinguishability will be true as a matter of principle, rather than being due to an insufficiently refined experimental capability.
The starting point of this formalism is the notion of indistinguishability of particles that bring us to use determinants of single-particle states as a basis of the Hilbert space of N-particles states.
We note here that, in this context, is computed quantum-mechanically, taking into account indistinguishability of particles.
He showed the equation to consist of stacking the entropy ( missing information ) due to four terms: positional uncertainty, momenta uncertainty, quantum mechanical uncertainty principle and the indistinguishability of the particles.
indistinguishability and photons
He was the first to take into account the distinguishability of photons in the statistical analysis of elementary processes, being a precursor of the notion of quantum indistinguishability.
indistinguishability and for
This obscures clues for a cryptanalyst, and can be used to increase cryptanalytic difficulty in naive cryptographic schemes ( however, most modern schemes contain more rigorous defences ; see Ciphertext indistinguishability ).
The property of indistinguishability under chosen plaintext attack is considered a basic requirement for most provably secure public key cryptosystems, though some schemes also provide indistinguishability under chosen ciphertext attack and adaptive chosen ciphertext attack.
indistinguishability and .
This indicates that the particle labels have no physical meaning, in agreement with our earlier discussion on indistinguishability.
Goldwasser / Micali subsequently demonstrated that semantic security is equivalent to another definition of security called ciphertext indistinguishability.
Generally speaking, information granules are collections of entities that usually originate at the numeric level and are arranged together due to their similarity, functional or physical adjacency, indistinguishability, coherency, or the like.
Independence relations between the quantified variables are modelled in the game tree as indistinguishability relations between game states with respect to a certain player.
Ciphertext indistinguishability is a property of many encryption schemes.
Intuitively, if a cryptosystem possesses the property of indistinguishability, then an adversary will be unable to distinguish pairs of ciphertexts based on the message they encrypt.
If any adversary can succeed in distinguishing the chosen ciphertext with a probability significantly greater than 1 / 2, then this adversary is considered to have an " advantage " in distinguishing the ciphertext, and the scheme is not considered secure in terms of indistinguishability.
Security in terms of indistinguishability has many definitions, depending on assumptions made about the capabilities of the attacker.
For a probabilistic asymmetric key encryption algorithm, indistinguishability under chosen plaintext attack ( IND-CPA ) is defined by the following game between an adversary and a challenger.
all and particles
The flux values are for all particles with masses greater than the given mass and are based on an estimate of the numbers of visual meteors.
In criticism of the latter's views, his conclusions were based upon dog lung injection studies in which all of the vascular channels were first filled with a solution under pressure and then were injected with various sized colored particles designed to stop at the arteriolar level.
The floc particles were all small as the heavier floc settled out.
in the 13th-century by the alchemist Pseudo-Geber ( Geber ), sometimes identified with Paul of Taranto, that all physical bodies possess an inner and outer layer of minute particles or corpuscles.
In 1924, Louis de Broglie proposed that all particles behave to an extent like waves.
If a system consists of several particles, the total angular momentum about a point can be obtained by adding ( or integrating ) all the angular momenta of the constituent particles.
where the total mass of all particles is given by
However, in quantum physics, there is another type of angular momentum, called spin angular momentum, represented by the spin operator S. Almost all elementary particles have spin.
Finally, there is total angular momentum J, which combines both the spin and orbital angular momentum of all particles and fields.
After inflation stopped, the Universe consisted of a quark – gluon plasma, as well as all other elementary particles.
Temperatures were so high that the random motions of particles were at relativistic speeds, and particle – antiparticle pairs of all kinds were being continuously created and destroyed in collisions.
The distribution begins as a Dirac delta function, indicating that all the particles are located at the origin at time t = 0, and for increasing times they become flatter and flatter until the distribution becomes uniform in the asymptotic time limit.
Assuming that all the particles start from the origin at the initial time t = 0, the diffusion equation has the solution
Baryons are strongly interacting fermions — that is, they experience the strong nuclear force and are described by Fermi − Dirac statistics, which apply to all particles obeying the Pauli exclusion principle.
A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration.
* Japanese: all particles, such as the genitive postposition の ( no ) and the topic marker は ( wa ).
Molecular diffusion, often called simply diffusion, is the thermal motion of all ( liquid or gas ) particles at temperatures above absolute zero.
And in 2012, researchers finally succeeded in correctly identifying the path each particle had taken without any adverse effects at all on the interference pattern generated by the particles.
Roughly speaking, all the forces involved in interactions between atoms can be explained by the electromagnetic force acting on the electrically charged atomic nuclei and electrons inside and around the atoms, together with how these particles carry momentum by their movement.
Either there was some interaction between the particles, even though they were separated, or the information about the outcome of all possible measurements was already present in both particles.
* L. Hardy, Nonlocality for two particles without inequalities for almost all entangled states.
If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made.
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