Tonks–Girardeau gas

In physics, a Tonks–Girardeau gas is a Bose gas in which the repulsive interactions between bosonic particles confined to one dimension dominate the system's physics. It is named after physicists Lewi Tonks, who developed a classical model in 1936, and Marvin D. Girardeau who generalized it to the quantum regime. It is not a Bose–Einstein condensate as it does not demonstrate any of the necessary characteristics, such as off-diagonal long-range order or a unitary two-body correlation function, even in a thermodynamic limit and as such cannot be described by a macroscopically occupied orbital (order parameter) in the Gross–Pitaevskii formulation.

The Tonks–Girardeau gas is a particular case of the Lieb–Liniger model.