Figure 1
From: Dynamics of entangled networks of the quantum Internet
The stability function \(\Psi _{{{\mathscr {F}}}_{N} } \left( \phi \left( F\left( {{\mathscr {F}}}_{N} \right) \right) \right)\) and the stable \({{\mathscr {S}}}^{*} \left( N\right)\) equilibrium states of the entangled quantum network N at \(\Delta \left( {{\mathscr {F}}}_{N} \right) =0\), in function of \(\phi \left( F\left( {{\mathscr {F}}}_{N} \right) \right) \in \left[ -F\left( {{\mathscr {F}}}_{N} \right) ,F\left( {{\mathscr {F}}}_{N} \right) \right]\) and \(f \left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right)\). (a) The stable \({{\mathscr {S}}}^{*} \left( N\right)\) equilibrium state of the entangled structure for \(f\left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right) =0,1\) (depicted by green-line empty dot), and the stable \({{\mathscr {S}}}^{*} \left( N\right)\) equilibrium states of the entangled structure for \(f\left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right) =2\) (depicted by red dots). As \(f \left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right) \le 1\), the entangled structure has one stable equilibrium state (green), while as \(f\left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right) >1\), the entangled structure has two stable equilibrium states (red dots). (b) The stable \({{\mathscr {S}}}^{*} \left( N\right)\) equilibrium states of the entangled structure for \(f\left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right) =3,4,5\) (depicted by red dots). Since \(f\left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right) >1\), the entangled structure has two stable equilibrium states (red dots) for a given \(f\left( B_{F} \left( {{\mathscr {F}}}_{N} \right) \right)\).
