Mean-field theory of superradiant phase transition in complex networks

Bazhenov, A. Yu.; Tsarev, D. V.; Alodjants, A. P.

doi:10.1103/physreve.103.062309

Cited by 10 publications

(5 citation statements)

References 49 publications

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“…In this sense, the problem of non-equilibrium phase transition is of primary interest, as it may appear in laser-like systems possessing Ising-like Hamiltonians, cf. 18 , 69 . Such models become crucial for feature modelling of distributed intelligence systems, which presume artificial and natural intelligence agents of DM behaviour and their interaction capacity in the framework of a socially oriented network 70 .…”

Section: Introductionmentioning

confidence: 99%

Mean-field theory of social laser

Alodjants

Bazhenov

Khrennikov

et al. 2022

Sci Rep

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In this work we suggest a novel paradigm of social laser (solaser), which can explain such Internet inspired social phenomena as echo chambers, reinforcement and growth of information cascades, enhancement of social actions under strong mass media operation. The solaser is based on a well-known in quantum physics laser model of coherent amplification of the optical field. Social networks are at the core of the solaser model; we define them by means of a network model possessing power–law degree distribution. In the solaser the network environment plays the same role as the gain medium has in a physical laser device. We consider social atoms as decision making agents (humans or even chat bots), which possess two (mental) states and occupy the nodes of a network. The solaser establishes communication between the agents as absorption and spontaneous or stimulated emission of socially actual information within echo chambers, which mimic an optical resonator of a convenient (physical) laser. We have demonstrated that social lasing represents the second order nonequilibrium phase transition, which evokes the release of coherent socially stimulated information field represented with the order parameter. The solaser implies the formation of macroscopic social polarization and results in a huge social impact, which is realized by viral information cascades occurring in the presence of population imbalance (social bias). We have shown that decision making agents follow an adiabatically time dependent mass media pump, which acts in the network community reproducing various reliable scenarios for information cascade evolution. We have also shown that in contrast to physical lasers, due to node degree peculiarities, the coupling strength of decision making agents with the network may be enhanced $$\sqrt{\langle k\rangle }$$ ⟨ k ⟩ times. It leads to a large increase of speed, at which a viral message spreads through a social media. In this case, the mass media pump supports additional reinforcement and acceleration of cascade growth. We have revealed that the solaser model in some approximations possesses clear links with familiar Ising and SIS (susceptible-infected-susceptible) models typically used for evaluating a social impact and information growth, respectively. However, the solaser paradigm can serve as a new platform for modelling temporal social events, which originate from “microscopic” (quantum-like) processes occurring in the society. Our findings open new perspectives for interdisciplinary studies of distributed intelligence agents behavior associated with information exchange and social impact.

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Section: Introductionmentioning

confidence: 99%

Mean-field theory of social laser

Alodjants

Bazhenov

Khrennikov

et al. 2022

Sci Rep

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“…Even though the models considered here were characterized by a single order parameter, our results are valid, in general, for any multi-order parameter systems with any global symmetry, e.g. open and/or dissipative extensions of thermal Z 2 -symmetric systems with light-matter interactions [79,80].…”

Section: Discussionmentioning

confidence: 69%

Continuous dissipative phase transitions with or without symmetry breaking

et al. 2021

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The paradigm of second-order phase transitions (PTs) induced by spontaneous symmetry breaking (SSB) in thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems. Dissipative phase transitions (DPTs) of second order are often connected with SSB, in close analogy with well-known thermal second-order PTs in closed quantum and classical systems. That is, a second-order DPT should disappear by preventing the occurrence of SSB. Here, we prove this statement to be wrong, showing that, surprisingly, SSB is not a necessary condition for the occurrence of second-order DPTs in \textit{out-of-equilibrium open quantum systems}. We analytically prove this result using the Liouvillian theory of dissipative phase transitions, and demonstrate this anomalous transition in two exemplary models: a paradigmatic laser model, where we can arbitrarily remove SSB while retaining criticality, and a $Z_2$-symmetric model of a two-photon Kerr resonator.

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“…Revealing a link, if any, with extensions of topological theories for DPTs is one of our future objectives [43,44]. Even though the models considered here were characterized by a single order parameter, our results are valid, in general, for any multi-order parameter systems with any global symmetry, e.g., open and/or dissipative extensions of thermal Z 2 -symmetric systems with light-matter interactions [68,69].…”

Section: Discussionmentioning

confidence: 80%

Continuous Dissipative Phase Transitions without Symmetry Breaking

Minganti,

Arkhipov,

Miranowicz

et al. 2021

Preprint

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The paradigm of second-order phase transitions (PTs) induced by spontaneous symmetry breaking (SSB) in thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems. Dissipative phase transitions (DPTs) of second order are often connected with SSB, in close analogy with well-known thermal second-order PTs in closed quantum and classical systems. That is, a second-order DPT should disappear by preventing the occurrence of SSB. Here, we prove this statement to be wrong, showing that, surprisingly, SSB is not a necessary condition for the occurrence of second-order DPTs in out-of-equilibrium open quantum systems. We analytically prove this result using the Liouvillian theory of dissipative phase transitions, and demonstrate this anomalous transition in a paradigmatic laser model, where we can arbitrarily remove SSB while retaining criticality, and on a Z2-symmetric model of a two-photon Kerr resonator. This new type of a phase transition cannot be interpreted as a "semiclassical" bifurcation, because, after the DPT, the system steady state remains unique.

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Mean-field theory of superradiant phase transition in complex networks

Cited by 10 publications

References 49 publications

Mean-field theory of social laser

Mean-field theory of social laser

Continuous dissipative phase transitions with or without symmetry breaking

Continuous Dissipative Phase Transitions without Symmetry Breaking

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