Dynamic equivalence of a two-dimensional quantum electron gas and a classical harmonic oscillator chain with an impurity mass

There is an exact equivalence in the time-dependent behaviour of a zero-temperature two-dimensional interacting electron gas at long wavelengths and a classical harmonic oscillator chain with one impurity mass. The mass difference m-m 0 , where m 0 is the impurity mass, acts as the electron-electron interaction. Time evolution is asymmetric in m-m 0 about m=m 0 .