$T\overline T$ deformation of Calogero-Sutherland model via dimensional reduction

We derive a general expression for the trace of the energy-momentum tensor $T\overline T$-deformed field theories using a dynamical change of coordinates. Then we perform a dimensional reduction of the bilinear $T\overline T$ operator and obtain a new $T\overline T$-like deformation of the quantum mechanics of free nonrelativistic fermions and the interacting Calogero-Sutherland system. The deformation leads to a change in the energy spectrum but does not affect the eigenfunctions. Furthermore, an expression for the deformed classical Lagrangian is obtained. We also study the correspondence between the two-dimensional Yang-Mills theory and the Calogero-Sutherland system in the presence of the deformation.