Random Lasers as Social Processes Simulators

Abstract

In this work, we suggest a quantum-like simulator concept to study social processes related to the solution of NP-hard problems. The simulator is based on the solaser model recently proposed by us in the framework of information cascade growth and echo chamber formation in social network communities. The simulator is connected with the random laser approach that we examine in the A and D-class (superradiant) laser limits. Novel network-enforced cooperativity parameters of decision-making agents, which may be measured as a result of the solaser simulation, are introduced and justified for social systems. The innovation diffusion in complex networks is discussed as one of the possible impacts of our proposal.

Keywords: complex networks; decision-making agents; innovation diffusion; quantum-like simulators; random lasers; superradiance.

Figure 1

(a) Complete and PLDD graphs with $N=50$ and $N=200$ nodes, respectively, for (b) $\eta =2.3$ and (c) $\eta =4$. (d) PLDDs in a logarithmic scale for the networks given in (b,c). The dependence of $\langle k\rangle$ on power degree $\eta$ is shown in the inset; $k_{min}=3$.

Figure 2

(a) Diffusive and (b) localized (Anderson) regimes of light scattering in random lasers that possess two-level (spin) systems. In random lasers, the angle between incident and outgoing light beams (not shown here) is small enough.

Figure 3

Sketch of the solaser simulator that represents an ensemble of two-level (spin) systems located within a complex network. In general, the network edges may represent projections of photon-guiding channels in the plane. All the system occupies an area of linear size $L\le \lambda$ in the presence of a classical pump beam (pink cylinder).

Figure 4

Dependence of the decimal logarithm of normalized NEC parameter $C_{\mathrm{\Gamma }}/4C_0$ on the number of TLSs (equal to the number of nodes) N for the complete graph and various PLDD networks with $k_{min}=3$.

Figure 5

Mean-field dependence of normalized field amplitude $\left|\mathrm{\Psi }\right|$ (the solid lines), TLS polarization $|J_{-}|$ (the dashed lines), and population imbalance D (the dotted lines) on dimensionless time t for (a) A-class and (b) D-class (superradiant) lasers, respectively. The control field is normalized as $r^{\prime }\equiv r/\kappa$, ${\Delta }_i=0,D_0=1$. The other parameters are $\kappa /({\gamma }_P+{\gamma }_D)=0.5$; $\kappa /\mathrm{\Gamma }=0.1$ for (a) and $\gamma =10$; ${\gamma }_D/\kappa =0.01$; $r^{\prime }=0$ for (b). Dependence of $|J_{-}|$ vs. ${\gamma }_{D}t$ below the threshold is shown in the insert to (b).