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Quantum cosmology

Quantum cosmology is the attempt in theoretical physics to develop a quantum theory of the Universe. This approach attempts to answer open questions of classical cosmology, particularly those related to the first phases of the universe. The classical cosmology is based on Albert Einstein's General Theory of Relativity (GTR). It describes the evolution of the universe very well, as long as you do not approach the Big Bang. It is the gravitational singularity and the Planck time where relativity theory fails to provide what must be demanded of a final theory of space and time. Therefore, a theory is needed that integrates relativity theory and quantum theory. Such an approach is attempted for instance with the loop quantum gravity, another approach with the string theory. More details Android, Windows

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Bose–Einstein condensate

"Super atom" redirects here. For clusters of atoms that seem to exhibit some of the properties of elemental atoms, see Superatom. Play media Schematic Bose-Einstein Condensation versus temperature and the energy diagram A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero (that is, very near 5000000000000000000♠0 K or 5000000000000000000♠−273.15 °C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point macroscopic quantum phenomena become apparent. It is formed by cooling a gas of extremely low density, about one-hundred-thousandth the density of normal air, to ultra-low temperatures. This state was first predicted, generally, in 1924–25 by Satyendra Nath Bose and Albert Einstein. More details Android, Windows

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Compton wavelength

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons (a process known as Compton scattering). The Compton wavelength of a particle is equivalent to the wavelength of a photon whose energy is the same as the rest-mass energy of the particle. The standard Compton wavelength, λ, of a particle is given by λ = h m c ,   {\displaystyle \lambda ={\frac {h}{mc}},\ } where h is the Planck constant, m is the particle's rest mass, and c is the speed of light. The significance of this formula is shown in the derivation of the Compton shift formula. The CODATA 2010 value for the Compton wavelength of the electron is 6988242631023890000♠2.4263102389(16)×10−12 m. Other particles have different Compton wavelengths. More details Android, Windows

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Commutator

This article is about the mathematical concept. For the relation between canonical conjugate entities, see Canonical commutation relation. For other uses, see Commutation. In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. More details Android, Windows

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Quantum mysticism

Quantum mysticism is a set of metaphysical beliefs and associated practices that seek to relate consciousness, intelligence, spirituality, or mystical world-views to the ideas of quantum mechanics and its interpretations. Quantum mysticism is considered by most scientists and philosophers to be pseudoscience or "quackery". More details Android, Windows

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Quantum discord

In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement. The notion of quantum discord was introduced by Harold Ollivier and Wojciech H. Zurek and, independently by L. Henderson and Vlatko Vedral. Olliver and Zurek referred to it also as a measure of quantumness of correlations. From the work of these two research groups it follows that quantum correlations can be present in certain mixed separable states; In other words, separability alone does not imply the absence of quantum effects. The notion of quantum discord thus goes beyond the distinction which had been made earlier between entangled versus separable (non-entangled) quantum states. More details Android, Windows

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Quantum gyroscope

A quantum gyroscope is a very sensitive device to measure angular rotation based on quantum mechanical principles. The first of these has been built by Richard Packard and his colleagues at the University of California, Berkeley. The extreme sensitivity means that theoretically a larger version could detect effects like minute changes in the rotational rate of the Earth. More details Android, Windows

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Quantum harmonic oscillator

"QHO" redirects here. It is also the IATA airport code for all airports in the Houston area. Some trajectories of a harmonic oscillator according to Newton's laws of classical mechanics (A–B), and according to the Schrödinger equation of quantum mechanics (C–H). In A–B, the particle (represented as a ball attached to a spring) oscillates back and forth. In C–H, some solutions to the Schrödinger Equation are shown, where the horizontal axis is position, and the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. C, D, E, F, but not G, H, are energy eigenstates. H is a coherent state—a quantum state that approximates the classical trajectory. The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known. More details Android, Windows

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Quantum state

In quantum physics, quantum state refers to the state of an isolated quantum system. A quantum state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, all other states are called mixed quantum states. Mathematically, a pure quantum state can be represented by a ray in a Hilbert space over the complex numbers. The ray is a set of nonzero vectors differing by just a complex scalar factor; any of them can be chosen as a state vector to represent the ray and thus the state. A unit vector is usually picked, but its phase factor can be chosen freely anyway. Nevertheless, such factors are important when state vectors are added together to form a superposition. Hilbert space is a generalization of the ordinary Euclidean space:93–96 and it contains all possible pure quantum states of the given system. If this Hilbert space, by choice of representation (essentially a choice of basis corresponding to a complete set of observables), is exhibited as a function space, a Hilbert space in its own right, then the representatives are called wave functions. For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vectors are identified by the principal quantum number n, the angular momentum quantum number l, the magnetic quantum number m, and the spin z-component sz. A more complicated case is given (in bra–ket notation) by the spin part of a state vector | ψ ⟩ = 1 2 ( | ↑↓ ⟩ − | ↓↑ ⟩ ) , {\displaystyle \left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\bigg (}\left|\uparrow \downarrow \right\rangle -\left|\downarrow \uparrow \right\rangle {\bigg )},} which involves superposition of joint spin states for two particles with spin  1⁄2. A mixed quantum state corresponds to a probabilistic mixture of pure states; however, different distributions of pure states can generate equivalent (i.e., physically indistinguishable) mixed states. Mixed states are described by so-called density matrices. A pure state can also be recast as a density matrix; in this way, pure states can be represented as a subset of the more general mixed states. For example, if the spin of an electron is measured in any direction, e.g. with a Stern–Gerlach experiment, there are two possible results: up or down. The Hilbert space for the electron's spin is therefore two-dimensional. A pure state here is represented by a two-dimensional complex vector ( α , β ) {\displaystyle (\alpha ,\beta )} , with a length of one; that is, with | α | 2 + | β | 2 = 1 , {\displaystyle |\alpha |^{2}+|\beta |^{2}=1,} where | α | {\displaystyle |\alpha |} and | β | {\displaystyle |\beta |} are the absolute values of α {\displaystyle \alpha } and β {\displaystyle \beta } . A mixed state, in this case, is a 2 × 2 {\displaystyle 2\times 2} matrix that is Hermitian, positive-definite, and has trace 1. Before a particular measurement is performed on a quantum system, the theory usually gives only a probability distribution for the outcome, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. These probability distributions arise for both mixed states and pure states: it is impossible in quantum mechanics (unlike classical mechanics) to prepare a state in which all properties of the system are fixed and certain. This is exemplified by the uncertainty principle, and reflects a core difference between classical and quantum physics. Even in quantum theory, however, for every observable there are some states that have an exact and determined value for that observable.:4–5 More details Android, Windows

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Quantum-confined Stark effect

The quantum-confined Stark effect (QCSE) describes the effect of an external electric field upon the light absorption spectrum or emission spectrum of a quantum well (QW). In the absence of an external electric field, electrons and holes within the quantum well may only occupy states within a discrete set of energy subbands. only a discrete set of frequencies of light may be absorbed or emitted by the system. When an external electric field is applied, the electron states shift to lower energies, while the hole states shift to higher energies. This reduces the permitted light absorption or emission frequencies. Additionally, the external electric field shifts electrons and holes to opposite sides of the well, decreasing the overlap integral, which in turn reduces the recombination efficiency (i.e. fluorescence quantum yield) of the system. The spatial separation between the electrons and holes is limited by the presence of the potential barriers around the quantum well, meaning that excitons are able to exist in the system even under the influence of an electric field. The quantum-confined Stark effect is used in QCSE optical modulators, which allow optical communications signals to be switched on and off rapidly. Even if Quantum Objects (Wells, Dots or Discs, for instance) emit and absorb light generally with higher energies than the band gap of the material, the QCSE may shift the energy to values lower than the gap. This was evidenced recently in the study of quantum discs embedded in a nanowire. More details Android, Windows

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Quantum tomography

Quantum tomography or quantum state tomography is the process of reconstructing the quantum state (density matrix) for a source of quantum systems by measurements on the systems coming from the source. The source may be any device or system which prepares quantum states either consistently into quantum pure states or otherwise into general mixed states. To be able to uniquely identify the state, the measurements must be tomographically complete. That is, the measured operators must form an operator basis on the Hilbert space of the system, providing all the information about the state. Such a set of observations is sometimes called a quorum. Figure 1: One harmonic oscillator represented in the phase space by its momentum and position Figure 2: Many identical oscillators represented in the phase space by their momentum and position In quantum process tomography on the other hand, known quantum states are used to probe a quantum process to find out how the process can be described. Similarly, quantum measurement tomography works to find out what measurement is being performed. The general principle behind quantum state tomography is that by repeatedly performing many different measurements on quantum systems described by identical density matrices, frequency counts can be used to infer probabilities, and these probabilities are combined with Born's rule to determine a density matrix which fits the best with the observations. This can be easily understood by making a classical analogy. Let us consider a harmonic oscillator (e.g. a pendulum). The position and momentum of the oscillator at any given point can be measured and therefore the motion can be completely described by the phase space. This is shown in figure 1. By performing this measurement for a large number of identical oscillators we get a possibility distribution in the phase space (figure 2). This distribution can be normalized (the oscillator at a given time has to be somewhere) and the distribution must be non-negative. So we have retrieved a function W(x,p) which gives a description of the chance of finding the particle at a given point with a given momentum. For quantum mechanical particles the same can be done. The only difference is that the Heisenberg’s uncertainty principle mustn’t be violated, meaning that we cannot measure the particle’s momentum and position at the same time. The particle’s momentum and its position are called quadratures (see Optical phase space for more information) in quantum related states. By measuring one of the quadratures of a large number of identical quantum states will give us a probability density corresponding to that particular quadrature. This is called the marginal distribution, pr(X) or pr(P) (see figure 3). In the following text we will see that this probability density is needed to characterize the particle’s quantum state, which is the whole point of quantum tomography. Figure 3: Marginal Distribution More details Android, Windows

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Quantum statistical mechanics

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic. More details Android, Windows

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Observable

This article is about the use in physics. For the use in statistics, see Observable variable. For the use in control theory, see Observability. In physics, particularly in quantum physics, a system observable is a measurable operator, or gauge, where the property of the system state can be determined by some sequence of physical operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states. Physically meaningful observables must also satisfy transformation laws which relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations which preserve some mathematical property. More details Android, Windows

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Quantum information science

Quantum information science is an area of study based on the idea that information science depends on quantum effects in physics. It includes theoretical issues in computational models as well as more experimental topics in quantum physics including what can and cannot be done with quantum information. The term quantum information theory is sometimes used, but it fails to encompass experimental research in the area. Subfields include: Quantum computing, which deals on the one hand with the question how and whether one can build a quantum computer and on the other hand, algorithms that harness its power (see quantum algorithm) Quantum complexity theory Quantum cryptography and its generalization, quantum communication Quantum error correction Quantum communication complexity Quantum entanglement, as seen from an information-theoretic point of view Quantum dense coding Quantum teleportation is a well-known quantum information processing operation, which can be used to move any arbitrary quantum state from one particle (at one location) to another. More details Android, Windows

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Quantum entanglement

Spontaneous parametric down-conversion process can split photons into type II photon pairs with mutually perpendicular polarization. Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently of the others, even when the particles are separated by a large distance – instead, a quantum state must be described for the system as a whole. Measurements of physical properties such as position, momentum, spin, and polarization, performed on entangled particles are found to be appropriately correlated. For example, if a pair of particles are generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, the spin of the other particle, measured on the same axis, will be found to be counterclockwise, as to be expected due to their entanglement. However, this behavior gives rise to paradoxical effects: any measurement of a property of a particle can be seen as acting on that particle (e.g., by collapsing a number of superposed states) and will change the original quantum property by some unknown amount; and in the case of entangled particles, such a measurement will be on the entangled system as a whole. It thus appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances. Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrödinger shortly thereafter, describing what came to be known as the EPR paradox. Einstein and others considered such behavior to be impossible, as it violated the local realist view of causality (Einstein referring to it as "spooky action at a distance") and argued that the accepted formulation of quantum mechanics must therefore be incomplete. Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally. Experiments have been performed involving measuring the polarization or spin of entangled particles in different directions, which – by producing violations of Bell's inequality – demonstrate statistically that the local realist view cannot be correct. This has been shown to occur even when the measurements are performed more quickly than light could travel between the sites of measurement: there is no lightspeed or slower influence that can pass between the entangled particles. Recent experiments have measured entangled particles within less than one hundredth of a percent of the travel time of light between them. According to the formalism of quantum theory, the effect of measurement happens instantly. It is not possible, however, to use this effect to transmit classical information at faster-than-light speeds (see Faster-than-light § Quantum mechanics). Quantum entanglement is an area of extremely active research by the physics community, and its effects have been demonstrated experimentally with photons, neutrinos, electrons, molecules the size of buckyballs, and even small diamonds. Research is also focused on the utilization of entanglement effects in communication and computation. More details Android, Windows

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Quantum fluid

A quantum fluid refers to any system that exhibits quantum mechanical effects at the macroscopic level such as superfluids, superconductors, ultra cold gases, etc. Most matter is either solid or gaseous (at low densities) near absolute zero. However, for the cases of helium-4 and its isotope helium-3, there is a pressure range where they can remain liquid down to absolute zero because the amplitude of the quantum fluctuations experienced by the helium atoms is larger than the inter-atomic distances. In the case of solid quantum fluids, it is only a fraction of its electrons or protons that behave like a “fluid”. One prominent example is that of superconductivity where quasi-particles made up of pairs of electrons and a phonon act as bosons which are then capable of collapsing into the ground state to establish a supercurrent with a resistivity near zero. More details Android, Windows

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Quantum capacitance

Quantum capacitance, also called chemical capacitance is a quantity first introduced by Serge Luryi (1988). In the simplest example, if you make a parallel-plate capacitor where one or both of the plates has a low density of states, then the capacitance is not given by the normal formula for parallel-plate capacitors. Instead, the capacitance is lower, as if there was another capacitor in series. This second capacitance, related to the density of states of the plates, is the quantum capacitance. Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene. More details Android, Windows