In this paper we will analyse a group of agents and their attitude to follow, or not, some rules. The model is based on some quantum-like ideas, and in particular on an Hamiltonian operator H describing the dynamics of the agents, assuming they are driven by some mutual interactions and that they are subjected to an external source of “information” used by the agents to decide whether to obey or not these rules. We will discuss how the relative strengths of the parameters of H determine this attitude and we will discuss in particular the role of the external information. We will also apply our general idea to a specific situation, involving drivers and pedestrians trying to cross a road.
BaaquieB. E. (2004). Quantum finance, path integrals and Hamiltonians for options and interest rates. Cambridge University Press.
2.
BagarelloF. (1989). Thermodynamical limit and boundary effects in long range spin models. Master thesis. SISSA.
3.
BagarelloF. (2012). Quantum dynamics for classical systems: With applications of the number operator. John Wiley & Sons.
4.
BagarelloF. (2019). Quantum concepts in the social, ecological and biological sciences. Cambridge University Press.
5.
BagarelloF. (2023). Phase transitions, KMS-condition and decision making. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, 381(2256), Article 20220377. https://doi.org/10.1098/rsta.2022.0377
6.
BagarelloF.GarganoF.OliveriF. (2023). Quantum tools for macroscopic systems. Springer, Synthesis Lectures on Mathematics & Statistics.
7.
BagarelloF.MorchioG. (1992). Dynamics of mean field spin models from basic results in abstract differential equations. Journal of Statistical Physics, 66(3-4), 849–866. https://doi.org/10.1007/bf01055705
8.
BratteliO.Robinsone D. W. (1979). Operator algebras and quantum statistical mechanics (vol 1). Springer.
9.
BratteliO.Robinsone D. W. (1981). Operator algebras and quantum statistical mechanics (vol 2). Springer.
10.
BusemeyerJ. R.BruzaP. D. (2012). Quantum models of cognition and decision. Cambridge University Press.
11.
BusemeyerJ. R.WangZ.TownsendJ. T. (2006). Quantum dynamics of human decision making. Journal of Mathematical Psychology, 50(3), 220–241. https://doi.org/10.1016/j.jmp.2006.01.003
12.
HavenE.KhrennikovA. (2013). Quantum social science. Cambridge University Press.
13.
KhrennikovA. (2010). Ubiquitous quantum structure: From psychology to finance. Springer.
14.
KhrennikovA. (2020). Social laser. Jenny Stanford Publ.
ReedM.SimonB. (1972). Methods of modern mathematical physics I, functional analysis. Academic Press.
18.
RuelleD. (1999). Statistical mechanics. Rigorous resultsReprint of the 1989 edition, World Scientific Publishing Co., Inc., River Edge, NJ. Imperial College Press.
19.
SewellG. L. (1989). Quantum theory of collective phenomena. Oxford University Press.
20.
SewellG. L. (2002). Quantum mechanics and its emergent macrophysics. Princeton University Press.
