Figure 1

(a–c) Snapshots of the velocity field in the stationary state of the two phases. We exclude the first five (really hot) sites near the boundaries to have a more clear view of the field. Each panel shows the vectors in linear scale and the moduli in log scale in order to better appreciate the phenomenology of the system. Orange and blue bars discriminate the two directions. We note that a great cluster of particles with same direction and similar modulus is found in the NHHP only, signaling that in terms of correlations the key parameter is \(\gamma _a\) rather than \(T_a\). (d) Autocorrelation times for each site defined as the time \(\tau _i\) for which \(\Gamma _i(\tau _i)=0.4\). The autocorrelation function is defined as \(\Gamma (t')=\lim _{t\rightarrow \infty } \langle v_i(t)v_i(t+t') \rangle /\langle v_i^2 (t)\rangle\) where the brackets refer to a time average on the stationary state. We note that in the NHHP the dynamics is far slower than in the HHP also when \(T_a=0\). The snapshots are obtained by numerical integration of Eq. (1) with \(L=50\), \(\gamma =5\), \(\gamma _b=10\), \(\gamma _a=\{3,0\}\), \(T_1=T_L=0.002\), \(T_a=\{0.002,0\}\) after a time \(t_M=10^8/\gamma\) and with a temporal step \(dt=0.05/\gamma\).