The paper considers the problem of collective decision-making as a second order phase-transition, which occurs in heterogeneous information-oriented communities possessing frequent information exchange between individuals. We examine the quantum-like model of simplified two-level cognitive systems (TLCS) interacting with a socially important (contextual) information field. The model exploits approaches to the modern social cohesion framework. We refer to some target network community, which is in close interaction (e.g. message exchange) with “reservour” (large network community) possessing infinite degree of freedom. We introduce a new approach for valence and arousal variables, used in cognitive sciences for the description of collective emotion states. We express them via collective polarization and population imbalance respectively. The model predicts a super-radiant phase transition for target network community leading to coherent polarization establishment in the socium. The valence and arousal parameters can be evaluated from actrors behaviour in social network communities as a result of immediate response (decision-making) to some notable news. We introduce Gaussian and Levy distribution functions to reveal the influence of social community inhomogeneity on decision-making features. We show that a critical (social) temperature is determined by the population imbalance (valence), detuning, field coupling strength parameter and relay to conditions of social polarization establishment. We predict coherent social energy release in a community without inversion due to its specific properties close to the superfluid paradigm in quantum physics, or social cohesion in sociology. We establish a connection of our model to the recently presented quantum-like model of the social laser to describe the waves of social protests as the result of collective decision-making process in the system with inversion of population in mental states. Finally, we compare our model with existing social impact models, a.k.a. cellular automata models, in the limit when social community perceives information field in the state induced by large information reservoir (mass-media). Notably, eliminating quantized field we lose important information how collective emotions (arousal) form in social community.

Considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition state and maximally path entangled N00N-state. We examine these macroscopic states by Mach-Zehnder interferometer in the context of parity measurements, which has been done to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio of two-body scattering length to intra-well hopping parameter can be measured with the scaling beyond this limit by using nonlinear phase shift with interacting quantum solitons.

The recent years were characterized by increasing interest to applications of the quantum formalism outside physics, e.g., in psychology, decision-making, socio-political studies. To distinguish such approach from quantum physics, it is called quantum-like. It is applied to modeling socio-political processes on the basis of the social laser model describing stimulated amplification of social actions. The main aim of this paper is establishing the socio-psychological interpretations of the quantum notions playing the basic role in lasing modeling. By using the Copenhagen interpretation and the operational approach to the quantum formalism, we analyze the notion of the social energy. Quantum formalizations of such notions as a social atom, s-atom, and an information field are presented. The operational approach based on the creation and annihilation operators is used. We also introduce the notion of the social color of information excitations representing characteristics linked to lasing coherence of the type of collimation. The Bose–Einstein statistics of excitations is coupled with the bandwagon effect, one of the basic effects of social psychology. By using the operational interpretation of the social energy, we present the thermodynamical derivation of this quantum statistics. The crucial role of information overload generated by the modern mass-media is emphasized. In physics laser’s resonator, the optical cavity, plays the crucial role in amplification. We model the functioning of social laser’s resonator by “distilling” the physical scheme from connection with optics. As the mathematical basis, we use the master equation for the density operator for the quantum information field.

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