Multipole expansionA multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, . Similarly to Taylor series, multipole expansions are useful because oftentimes only the first few terms are needed to provide a good approximation of the original function. The function being expanded may be real- or complex-valued and is defined either on , or less often on for some other .
Brownian motionBrownian motion is the random motion of particles suspended in a medium (a liquid or a gas). This motion pattern typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena).
Mean free pathIn physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a result of one or more successive collisions with other particles. Imagine a beam of particles being shot through a target, and consider an infinitesimally thin slab of the target (see the figure). The atoms (or particles) that might stop a beam particle are shown in red.
Charged particleIn physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, which are all believed to have the same charge (except antimatter). Another charged particle may be an atomic nucleus devoid of electrons, such as an alpha particle. A plasma is a collection of charged particles, atomic nuclei and separated electrons, but can also be a gas containing a significant proportion of charged particles.
Spin–statistics theoremIn quantum mechanics, the spin–statistics theorem relates the intrinsic spin of a particle (angular momentum not due to the orbital motion) to the particle statistics it obeys. In units of the reduced Planck constant ħ, all particles that move in 3 dimensions have either integer spin or half-integer spin. In a quantum system, a physical state is described by a state vector. A pair of distinct state vectors are physically equivalent if they differ only by an overall phase factor, ignoring other interactions.