In classical dynamics, to the leading order, the effective interaction potential in phase space is the time-averaged real space interaction in one driving period U i j = 1 T ∫ ∫ 0 T V [ x i ( t ) − − x j ( t ) ] . Here, x i ( t ) represents the trajectory of i -th particle in the absence of driving field. For the model power-law interaction potential V ( x i − − x j ) = ϵ ϵ 2 n / | x i − − x j | 2 n with integers and half-integers n ≥ ≥ 1 / 2 , the direct integral given by the above time-average formula is divergent, i.e., U i j = ∞ ∞ . A renormalisation procedure was introduced to remove the divergence and the correct phase space interaction is a function of phase space distance R i j in the ( X i , P i ) plane. For the Coulomb potential n = 1 / 2 , the result U ( R i j ) = 2 π π − − 1 ϵ ϵ ~ ~ / R i j still keeps the form of Coulomb's law up to a logarithmic renormalised "charge" ϵ ϵ ~ ~ = ϵ ϵ ln ⁡ ⁡ ( ϵ ϵ − − 1 e 2 R i j 3 / 2 ) , where e = 2.71828 ⋯ ⋯ is the Euler's number. For n = 1 , 3 / 2 , 2 , 5 / 2 , ⋯ ⋯ , the renormalised phase space interaction potential is U i j = U ( R i j ) = 2 ϵ ϵ γ γ 2 n − − 1 4 1 2 n − − 1 π π ( 2 n − − 1 ) R i j 1 − − 1 n , where γ γ = ( 4 n − − 1 ) 1 2 n − − 1 is the collision factor. For the special case of n = 1 , there is no effective interaction in phase space since U ( R i j ) = 3 ϵ ϵ π π − − 1 is a constant with respect to phase space distance. In general for the case of n > 1 , phase space interaction U ( R i j ) grows with the phase space distance R i j . For the hard-sphere interaction ( n → → ∞ ∞ ), phase space interaction U ( R i j ) = ϵ ϵ π π − − 1 R i j behaves like the confinement interaction between quarks in Quantum chromodynamics (QCD). The above phase space interaction is indeed invariant under the discrete rotational or translational operations in phase space. Combined with the phase space lattice potential from driving, there exist a stable regime where the particles arrange themselves periodically in phase space giving rise to many-body phase space crystals.