Quantum decoherenceQuantum decoherence is the loss of quantum coherence, the process in which a system's behaviour changes from that which can be explained by quantum mechanics to that which can be explained by classical mechanics. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent.
Mixed boundary conditionIn mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary.
Vacuum expectation valueIn quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by One of the most widely used examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect. This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking.
Quantum harmonic oscillatorThe quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth 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.
Quantum vacuum stateIn quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. The term zero-point field is sometimes used as a synonym for the vacuum state of a quantized field which is completely individual. According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space".
Universal wavefunctionThe universal wavefunction (or wave function), introduced by Hugh Everett in his 1973 PhD thesis The Theory of the Universal Wave Function, informs a core concept in the relative state interpretation or many-worlds interpretation of quantum mechanics. It later received investigation from James Hartle and Stephen Hawking in which they derived a specific solution to the Wheeler–deWitt equation to explain the initial conditions of the Big Bang cosmology.
Density matrixIn quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states.
Phase spaceIn dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the direct product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.
Group schemeIn mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance.
Operator (computer programming)In computer programming, operators are constructs defined within programming languages which behave generally like functions, but which differ syntactically or semantically. Common simple examples include arithmetic (e.g. addition with +), comparison (e.g. "greater than" with >), and logical operations (e.g. AND, also written && in some languages). More involved examples include assignment (usually = or :=), field access in a record or object (usually .), and the scope resolution operator (often :: or .).
