paritydependent

Paritydependent is an adjective used to describe phenomena whose outcome or properties depend on the parity (evenness or oddness) of a quantity, typically an integer such as a quantum number, site index, or particle count. In physics, parity refers to the behavior of a system under spatial inversion. A parity-dependent effect changes according to whether the relevant quantity is even or odd, and may alter the magnitude or sign of a quantity.

In atomic and molecular physics, parity-dependent rules influence transitions and selection rules. For example, electric dipole transitions require a change in parity between initial and final states, making certain transitions allowed or forbidden based on parity. In nuclear and particle physics, matrix elements and amplitudes can carry parity-dependent factors, and processes that violate parity (parity violation) reveal asymmetries between mirror-related configurations, a hallmark of the weak interaction.

In condensed matter and solid-state physics, parity of wavefunctions in crystals with inversion symmetry can constrain band structure and optical responses. Parity indicators at high-symmetry points can help classify topological phases or predict response properties.

In mathematics and computer science, parity-dependence appears in problems where evenness or oddness drives behavior. Examples include recursive sequences that differ by parity, parity-check algorithms in data transmission, and parity games in automata theory, where the winner is determined by the parity of a parameter.

Parallels to the broader concept of symmetry and the notion of parity are common across disciplines, with paritydependent models highlighting how simple binary properties can influence complex outcomes.