# On Interpretational Questions for Quantum-Like Modeling of Social Lasing

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## Abstract

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## 1. Introduction

#### 1.1. Quantum versus Quantum-Like Models

#### 1.2. Quantum-Like Modeling of the Process of Decision-Making

#### 1.3. Operational Formalism: Creation and Annihilation Operators

#### 1.4. Social Laser as a Fruit of the Quantum Information Revolution

#### 1.5. Powerful Information Flows as the Basic Condition of Social Laser Functioning

#### 1.6. Resonators of Physical and Social Lasers

## 2. Physical Laser: Schematic Presentation

#### 2.1. Spontaneous and Stimulated Emission

- An atom in the excited state can spontaneously emit a photon. This process is irreducibly random, i.e., even for a single atom, it is impossible to predict neither the instance of time nor the direction of emitted photon.
- Atoms in the ground state can absorb from this field only photons having the resonance energy ${E}_{A}={E}_{2}-{E}_{1}.$
- An excited atom interacting with photons with energy ${E}_{A}$ emits a photon of the same energy
- This output flow of photons is coherent. All photons produced from the “seed-photon” have the same features: direction of flow, polarization, and energy.

#### 2.2. Population Inversion

## 3. Social Energy

#### 3.1. Energy of s-Atoms

#### 3.2. Energy of the Quantum Information Field

## 4. Social Laser

#### 4.1. Quantum Field Representation of Information Flow Generated by Mass-Media

#### 4.2. Coloring Information Excitations

#### 4.3. Indistinguishability from Information Overload and Complexity

#### 4.4. From Statistical Mechanics to Thermodynamics of Indistinguishable Systems

- ${m}_{s}=0,1,2,\dots .$ (Bose–Einstein statistics),
- ${m}_{s}=0,\dots ,q,$ where $q\ge 1$ is a natural number (parastatistics).

#### 4.5. Coloring Role: Pumping versus Emission

## 5. Comparing Stimulated Emission in Quantum Physics and Bandwagon Effect in Psychology and Social Science

## 6. Social Lasing Schematically

## 7. Resonators of Physical Lasers

## 8. Resonators of Social Lasers

#### 8.1. Structure and Functioning of Social Resonator

#### Output Beam from Echo Chamber

#### 8.2. Stimulated Initiation of Social Lasing

- spontaneous emission and filtering photons with momentum vectors deviating from the x-axis by using the optical cavity;
- stimulated emission generated by a coherently injected ensemble of photons with the x-momentum vector.

## 9. Dynamics the Quantum Information Field in Social Laser’s Resonator

#### 9.1. Creation-Annihilation Algebras for s-Atoms and Quantum Information Field

#### 9.2. Dynamics of the Compound System s-Atom-Field

#### 9.3. Gorini–Kossakowski–Sudarshan–Lindblad Equation for the State of the Quantum Information Field

#### 9.4. Social Interpretation of Assumptions for Derivation of Quantum Master Equation

**Assumption**

**1.**

**Assumption**

**2.**

#### 9.5. Probabilistic Consequences of the Quantum Markov Dynamics

- If $A/C<1,$ then the solution of Equation (42) can be approximately represented in the form $p(n)\approx (1-A/C){(A/C)}^{n}.$ Thus, for this region of variation of the parameter $A/C,$ the field is characterized by a small number of excitations: the probability that, in the resonator of the social laser, there can be found n excitations decreases exponentially, $p(n)\sim {e}^{-(\mathrm{ln}C-\mathrm{ln}A)}.$
- If $A/C\approx 1,$ then the solution has no simple analytical representation. This range of variation of parameter $A/C$ is characterized by large fluctuations of number n of field’s excitations.
- If $A/C>>1,$ then $p(n)$ can be approximated by the Poission distribution:$$p(n)\approx {e}^{-\overline{n}}\frac{{\overline{n}}^{n}}{n!},$$

## 10. Conclusions

- A gain medium is characterized by the long lifetime of the excited state and the big gap between the states of relaxation and excitation.
- The social energy carried by excitations of the information field has to match the resonance energy of s-atoms in the gain medium.
- The interrelation of the magnitudes of the excitation and absorption rates ${r}_{2},{r}_{1}$ and the lifetimes of the corresponding levels ${T}_{2},{T}_{1}$ has to imply inequality $A>C,$ where A and C are gain and loss coefficients, respectively.
- The nonlinear character of interactions between excitations in a social laser resonator (encoded in the B-coefficient) plays the crucial role in initiation of stable social lasing.
- The quantum-like regime of lasing is characterized by the threshold value of the pump parameter.

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Khrennikov, A.; Alodjants, A.; Trofimova, A.; Tsarev, D.
On Interpretational Questions for Quantum-Like Modeling of Social Lasing. *Entropy* **2018**, *20*, 921.
https://doi.org/10.3390/e20120921

**AMA Style**

Khrennikov A, Alodjants A, Trofimova A, Tsarev D.
On Interpretational Questions for Quantum-Like Modeling of Social Lasing. *Entropy*. 2018; 20(12):921.
https://doi.org/10.3390/e20120921

**Chicago/Turabian Style**

Khrennikov, Andrei, Alexander Alodjants, Anastasiia Trofimova, and Dmitry Tsarev.
2018. "On Interpretational Questions for Quantum-Like Modeling of Social Lasing" *Entropy* 20, no. 12: 921.
https://doi.org/10.3390/e20120921