Transition of the uniform statistical field anyon state to the nonuniform one ar low particle densities

Using results of our exact description of the spinless fermion motion in a nonhomogeneous magnetic field \( {\bf B} = B( 0, 0, 1/cosh^{2}( \frac{x-x_{0}}{ \delta })) \) we study a gas of these particles moving in this field. For lower densities \( \nu < \nu_{c}(B, \delta ) \) the corresponding total energy is lower than that of the uniform field state. Thus when the density of anyons decreases a transition from the uniform statistical field state to the nonhomogeneous field state is predicted.