A phenomenological operator description of dynamics of crowds: Escape strategies

Abstract

We adopt an operatorial method, based on creation, annihilation and number operators, to describe one or two populations mutually interacting and moving in a two-dimensional region. In particular, we discuss how the two populations, contained in a certain two-dimensional region with a non-trivial topology, react when some alarm occurs. We consider the cases of both low and high densities of the populations, and discuss what is changing as the strength of the interaction increases. We also analyze what happens when the region has either a single exit or two ways out.

Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics

“…In the past few years several macroscopic dynamical systems have been discussed using quantum tools. This approach has been considered by many authors and the range of its applications is wide, and has been successfully applied to various fields of sociology and decision making processes [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ], biology [ 14 , 15 ], ecology [ 16 , 17 , 18 ] economics [ 19 , 20 , 21 ], population and crowd dynamics [ 22 , 23 , 24 , 25 , 26 ], etc. More applications of quantum ideas outside a standard quantum realm can be found, for instance, in the monographs [ 27 , 28 , 29 , 30 , 31 , 32 ], and in many of the references cited there.…”

An operatorial model for complex political system dynamics

“…In this paper, another approach, based on operator algebras, typical of quantum theory , is considered to model the dynamics of a political system affected by a ‘turncoat‐like’ behavior of part of their members. As shown in , the description of the dynamics of macroscopic complex systems may be profitably carried out by using raising and lowering operators and the number representation; in fact, this method has been used in several recent papers to analyze the dynamical aspects in rather different areas, for example, stock markets and the role of information exchange in stock markets , love affairs , population migration phenomena , ecological models , escape strategies of crowds , desertification processes , and bacterial populations in a closed environment . Moreover, operatorial techniques have been used to set up dynamical models describing alliances in politics with specific reference to Italian political parties.…”

Modeling interactions between political parties and electors

“…Among all the strategies adopted during the years to build up models of some specific phenomenon, in recent years many researchers started to use methods typically connected with quantum mechanics, even when dealing with macroscopic systems. This has been done in decision-making processes, [22,21,12,1,2,3], in population dynamics, [6,20], in ecological processes, [4,9,15], and, recently, in the analysis of political systems, [23,24,5,7,8]. In these latter papers, the general operatorial settings analyzed in details in [3] have been used in the description of a political system consisting of three parties interacting among them and with a basin of electors and of undecided voters.…”