An interaction that occurs between two individual particles or ions.A pairwise interaction is a fundamental interaction that occurs between exactly two individual particles, such as two electrons, two ions, or an electron and a photon. This concept is the building block of many-body physics, where the complex behavior of large systems is often understood as a sum of these two-body interactions. In quantum mechanics, pairwise interactions are described by potentials that depend on the relative positions and properties of the two particles involved.
The concept of pairwise interactions has roots in Newton's law of gravitation and Coulomb's law of electrostatics, both formulated in the 18th century. The modern quantum treatment of pairwise interactions was developed in the early 20th century with the advent of quantum mechanics.
In a system of many particles, the total energy is often approximated as the sum of pairwise interaction energies. For example, in a crystal lattice, the interaction between any two ions can be described by a Coulomb potential. When particles are close together, quantum effects like exchange interaction (due to the Pauli exclusion principle) also come into play. In more exotic systems, such as ultracold atomic gases, pairwise interactions can be tuned using magnetic fields (Feshbach resonances) to create strongly correlated states.
Pairwise interactions are used in molecular dynamics simulations to model protein folding, in the design of quantum gates where two qubits interact, and in understanding the behavior of ions in traps for quantum computing.
In a gas of ultracold atoms, the pairwise interaction can be made so strong that atoms pair up into molecules, even though the gas is extremely dilute—this is the basis of the BEC-BCS crossover in superfluidity.





