InstantonAn instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime. In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action.
Path integral formulationThe path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.
Reaction rate constantIn chemical kinetics, a reaction rate constant or reaction rate coefficient (k) is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants. For a reaction between reactants A and B to form a product C, where A and B are reactants C is a product a, b, and c are stoichiometric coefficients, the reaction rate is often found to have the form: Here k is the reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution.
Quantum field theoryIn theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.
Reaction rateThe reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second.
Rate equationIn chemistry, the rate law or rate equation for a chemical reaction is a mathematical equation that links the rate of forward reaction with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as where [\mathrm{A}] and [\mathrm{B}] express the concentration of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M).
QuantumIn physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation).
Rate-determining stepIn chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS or RD-step or r/d step) or rate-limiting step. For a given reaction mechanism, the prediction of the corresponding rate equation (for comparison with the experimental rate law) is often simplified by using this approximation of the rate-determining step. In principle, the time evolution of the reactant and product concentrations can be determined from the set of simultaneous rate equations for the individual steps of the mechanism, one for each step.
WKB approximationIn mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be changing slowly. The name is an initialism for Wentzel–Kramers–Brillouin. It is also known as the LG or Liouville–Green method.
Quantum computingA quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.
Quantum mechanicsQuantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.
Quantum gravityQuantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars as well as in the early stages of the universe moments after the Big Bang Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction, the strong force, and the weak force; this leaves gravity as the only interaction that has not been fully accommodated.
Quantum geometryIn theoretical physics, quantum geometry is the set of mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at distance scales comparable to the Planck length. At these distances, quantum mechanics has a profound effect on physical phenomena. quantum gravity Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion.
Equilibrium constantThe equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture.
Semiclassical physicsIn physics, semiclassical refers to a theory in which one part of a system is described quantum mechanically, whereas the other is treated classically. For example, external fields will be constant, or when changing will be classically described. In general, it incorporates a development in powers of Planck's constant, resulting in the classical physics of power 0, and the first nontrivial approximation to the power of (−1).
Quantum networkQuantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum processors. A quantum processor is a small quantum computer being able to perform quantum logic gates on a certain number of qubits. Quantum networks work in a similar way to classical networks. The main difference is that quantum networking, like quantum computing, is better at solving certain problems, such as modeling quantum systems.
Gauge theoryIn physics, a gauge theory is a field theory in which the Lagrangian is invariant under local transformations according to certain smooth families of operations (Lie groups). The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators.
Quantum programmingQuantum programming is the process of designing or assembling sequences of instructions, called quantum circuits, using gates, switches, and operators to manipulate a quantum system for a desired outcome or results of a given experiment. Quantum circuit algorithms can be implemented on integrated circuits, conducted with instrumentation, or written in a programming language for use with a quantum computer or a quantum processor. With quantum processor based systems, quantum programming languages help express quantum algorithms using high-level constructs.
Round-off errorIn computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error.
Approximation errorThe approximation error in a data value is the discrepancy between an exact value and some approximation to it. This error can be expressed as an absolute error (the numerical amount of the discrepancy) or as a relative error (the absolute error divided by the data value). An approximation error can occur for a variety of reasons, among them a computing machine precision or measurement error (e.g. the length of a piece of paper is 4.53 cm but the ruler only allows you to estimate it to the nearest 0.
