In quantum computing, a qubit or quantum bit (sometimes qbit) is the basic unit of quantum information: R

Radio wave

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 gigahertz (GHz) to as low as 30 hertz (Hz). At 300 GHz, the corresponding wavelength is 1 mm (shorter than a grain of rice); at 30 Hz the corresponding wavelength is 10,000 km (longer than the radius of the Earth). Like all other electromagnetic waves, radio waves travel at the speed of light in vacuum (and close to the speed of light in the Earth’s atmosphere, which acts as the transmission media for the vast majority of terrestrial use). Radio waves are generated by charged particles undergoing acceleration, such as time-varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects.

Radio waves are generated artificially by transmitters and received by radio receivers, using antennas. Radio waves are very widely used in modern technology for fixed and mobile radio communication, broadcasting, radar and radio navigation systems, communications satellites, wireless computer networks and many other applications. Different frequencies of radio waves have different propagation characteristics in the Earth’s atmosphere; long waves can diffract around obstacles like mountains and follow the contour of the earth (ground waves), shorter waves can reflect off the ionosphere and return to earth beyond the horizon (skywaves), while much shorter wavelengths bend or diffract very little and travel on a line of sight, so their propagation distances are limited to the visual horizon.

To prevent interference between different users, the artificial generation and use of radio waves is strictly regulated by law, coordinated by an international body called the International Telecommunications Union (ITU), which defines radio waves as “electromagnetic waves of frequencies arbitrarily lower than 3 000 GHz, propagated in space without artificial guide”. The radio spectrum is divided into a number of radio bands on the basis of frequency, allocated to different uses.

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Radioactive decay

Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles or photons. The weak force is the mechanism that is responsible for beta decay.

Radioactive decay is a stochastic (i.e. random) process at the level of single atoms. According to quantum theory, it is impossible to predict when a particular atom will decay, regardless of how long the atom has existed. However, for a significant number of identical atoms, the overall decay rate can be expressed as a decay constant or as half-life. The half-lives of radioactive atoms have a huge range; from nearly instantaneous to far longer than the age of the universe.

The decaying nucleus is called the parent radionuclide (or parent radioisotope), and the process produces at least one daughter nuclide. Except for gamma decay or internal conversion from a nuclear excited state, the decay is a nuclear transmutation resulting in a daughter containing a different number of protons or neutrons (or both). When the number of protons changes, an atom of a different chemical element is created.

  • Alpha decay occurs when the nucleus ejects an alpha particle (helium nucleus).
  • Beta decay occurs in two ways;
    • (i) beta-minus decay, when the nucleus emits an electron and an antineutrino in a process that changes a neutron to a proton.
    • (ii) beta-plus decay, when the nucleus emits a positron and a neutrino in a process that changes a proton to a neutron, this process is also known as positron emission.
  • In gamma decay a radioactive nucleus first decays by the emission of an alpha or beta particle. The daughter nucleus that results is usually left in an excited state and it can decay to a lower energy state by emitting a gamma ray photon.
  • In neutron emission, extremely neutron-rich nuclei, formed due to other types of decay or after many successive neutron captures, occasionally lose energy by way of neutron emission, resulting in a change from one isotope to another of the same element.
  • In electron capture, the nucleus may capture an orbiting electron, causing a proton to convert into a neutron in a process called electron capture. A neutrino and a gamma ray is subsequently emitted.
  • In cluster decay and nuclear fission, a nucleus heavier than an alpha particle is emitted

By contrast, there are radioactive decay processes that do not result in a nuclear transmutation. The energy of an excited nucleus may be emitted as a gamma ray in a process called gamma decay, or that energy may be lost when the nucleus interacts with an orbital electron causing its ejection from the atom, in a process called internal conversion. Another type of radioactive decay results in products that vary, appearing as two or more “fragments” of the original nucleus with a range of possible masses. This decay, called spontaneous fission, happens when a large unstable nucleus spontaneously splits into two (or occasionally three) smaller daughter nuclei, and generally leads to the emission of gamma rays, neutrons, or other particles from those products. In contrast, decay products from a nucleus with spin may be distributed non-isotropically with respect to that spin direction. Either because of an external influence such as an electromagnetic field, or because the nucleus was produced in a dynamic process that constrained the direction of its spin, the anisotropy may be detectable. Such a parent process could be a previous decay, or a nuclear reaction.

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Relativistic Heavy Ion Collider

The Relativistic Heavy Ion Collider (RHIC /ˈrɪk/) is the first and one of only two operating heavy-ion colliders, and the only spin-polarized proton collider ever built. Located at Brookhaven National Laboratory (BNL) in Upton, New York, and used by an international team of researchers, it is the only operating particle collider in the US. By using RHIC to collide ions traveling at relativistic speeds, physicists study the primordial form of matter that existed in the universe shortly after the Big Bang. By colliding spin-polarized protons, the spin structure of the proton is explored.

RHIC is as of 2019 the second-highest-energy heavy-ion collider in the world. As of November 7, 2010, the Large Hadron Collider (LHC) has collided heavy ions of lead at higher energies than RHIC. The LHC operating time for ions (lead-lead and lead-proton collisions) is limited to about one month per year.

In 2010, RHIC physicists published results of temperature measurements from earlier experiments which concluded that temperatures in excess of 345 MeV (4 terakelvins or 7 trillion degrees Fahrenheit) had been achieved in gold ion collisions, and that these collision temperatures resulted in the breakdown of “normal matter” and the creation of a liquid-like quark–gluon plasma.

In January 2020, the US Department of Energy Office of Science selected the eRHIC design for the future Electron–ion collider (EIC), building on the existing RHIC facility at BNL.

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Relativistic quantum mechanics

In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity.

Key features common to all RQMs include: the prediction of antimatter, spin magnetic moments of elementary spin 1/2
fermions, fine structure, and quantum dynamics of charged particles in electromagnetic fields. The key result is the Dirac equation, from which these predictions emerge automatically. By contrast, in non-relativistic quantum mechanics, terms have to be introduced artificially into the Hamiltonian operator to achieve agreement with experimental observations.

The most successful (and most widely used) RQM is relativistic quantum field theory (QFT), in which elementary particles are interpreted as field quanta. A unique consequence of QFT that has been tested against other RQMs is the failure of conservation of particle number, for example in matter creation and annihilation.

In this article, the equations are written in familiar 3D vector calculus notation and use hats for operators (not necessarily in the literature), and where space and time components can be collected, tensor index notation is shown also (frequently used in the literature), in addition the Einstein summation convention is used. SI units are used here; Gaussian units and natural units are common alternatives. All equations are in the position representation; for the momentum representation the equations have to be Fourier transformed – see position and momentum space.

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