arXiv subjects

F. Bagarello

Publications and source records attributed to F. Bagarello.

At least 19 recordsLinked to original sources

arXiv2023

Spreading of information on a network: a quantum view

This paper concerns the modeling of the spread of information through a complex, multi-layered network, where the information is transferred from an initial transmitter to a final receiver. The mathematical model is deduced within the framework of operatorial methods, according to the formal mathematical apparatus typical of quantum mechanics. Two different approaches are considered: one based on the ($H,\rho$)-induced dynamics and one on the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) equation. For each method, numerical results are presented.

quant-ph↗

arXiv2023

Dynamics for a quantum parliament

In this paper we propose a dynamical approach based on the Gorini-Kossakowski-Sudarshan-Lindblad equation for a problem of decision making. More specifically, we consider what was recently called a quantum parliament, asked to approve or not a certain law, and we propose a model of the connections between the various members of the parliament, proposing in particular some special form of the interactions giving rise to a {\em collaborative} or non collaborative behaviour.

quant-ph↗

arXiv2020

Modeling epidemics through ladder operators

We propose a simple model of spreading of some infection in an originally healthy population which is different from other models existing in the literature. In particular, we use an operator technique which allows us to describe in a natural way the possible interactions between healthy and un-healthy populations, and their transformation into recovered and to dead people. After a rather general discussion, we apply our method to the analysis of Chinese data for the SARS-2003 (Severe acute respiratory syndrome; SARS-CoV-1) and the Coronavirus COVID-19 (Corona Virus Disease; SARS-CoV-2 ) and we show that the model works very well in reproducing the long-time behaviour of the disease, and in particular in finding the number of affected and dead people in the limit of large time. Moreover, we show how the model can be easily modified to consider some lockdown measure, and we deduce that this procedure drastically reduces the asymptotic value of infected individuals, as expected, and observed in real life.

q-bio.PE↗

arXiv2020

Bicoherent-State Path Integral Quantization of a non-Hermitian Hamiltonian

We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from hermitian quantum physics. We do all this by working out a concrete example, namely, computation of the propagator of a certain quasi-hermitian variant of Swanson's model, which is not invariant under conventional $PT$-transformation. The resulting propagator coincides with that of the propagator of the standard harmonic oscillator, which is isospectral with the model under consideration by virtue of a similarity transformation relating the corresponding hamiltonians. We also compute the propagator of this model in position space by means of Feynman path integration and verify the consistency of the two results.

math-ph↗

arXiv2019

Reply to Comment on "A no-go result for the quantum damped harmonic oscillator"

In a recent paper, \cite{deguchi}, Deguchi and Fujiwara claim that our results in \cite{BGR} are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistake. We also consider a very simple example clarifying the core of the problem.

math-ph↗

arXiv2019

Tridiagonality, supersymmetry and non self-adjoint Hamiltonians

In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.

math-ph↗

arXiv2018

Quantum mechanical settings inspired by RLC circuits

In some recent papers several authors used electronic circuits to construct loss and gain systems. This is particularly interesting in the context of PT-quantum mechanics, where this kind of effects appears quite naturally. The electronic circuits used so far are simple, but not so much. Surprisingly enough, a rather trivial RLC circuit can be analyzed with the same perspective and it produces a variety of unexpected results, both from a mathematical and on a physical side. In this paper we show that this circuit produces two biorthogonal bases associated to the Liouville matrix $\Lc$ used in the treatment of its dynamics, with a biorthogonality which is linked to the value of the parameters of the circuit. We also show that the related loss RLC circuit is naturally associated to a gain RLC circuit, and that the relation between the two is rather naturally encoded in $\Lc$. We propose a pseudo-fermionic analysis of the circuit, and we introduce the notion of $m$-equivalence between electronic circuits.

math-ph↗

arXiv2018

Non-hermitian operator modelling of basic cancer cell dynamics

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.

q-bio.OT↗

arXiv2018

$(H,ρ)$--induced dynamics and large time behaviors

In some recent papers, the so called $(H,ρ)$-induced dynamics of a system $\mathcal{S}$ whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, $H$ is the Hamiltonian for $\mathcal{S}$, while $ρ$ is a certain rule applied periodically (or not) on $\mathcal{S}$. The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the $(H,ρ)$-induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of $\mathcal{S}$ may converge, for large $t$, to certain asymptotic values. This can not be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any Heisenberg dynamics implemented by a suitable hermitian operator $H$ can only give an oscillating behavior. We prove our claims both analytically and numerically for a simple system with two degrees of freedom, and then we apply our general scheme to a model describing a biological system of bacteria living in a two-dimensional lattice, where two different choices of the rule are considered.

physics.soc-ph↗

arXiv2017

Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment

This paper is devoted to justification of quantum-like models of the process of decision making based on the theory of open quantum systems, i.e. decision making is considered as decoherence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment ${\cal R}$ surrounding her. Such an interaction generates "dissipation of uncertainty" from Alice's belief-state $ρ(t)$ into ${\cal R}$ and asymptotic stabilization of $ρ(t)$ to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on ${\cal R}$ guaranteeing such stabilization. We found a partial solution of this problem (in the form of sufficient conditions). We present the corresponding decision making analysis for one class of mental environments, the so-called "almost homogeneous environments", with the illustrative examples: a) behavior of electorate interacting with the mass-media "reservoir", b) consumers' persuasion. We also comment on other classes of mental environments.

q-bio.NC↗

arXiv2017

Coordinate representation for non Hermitian position and momentum operators

In this paper we undertake an analysis of the eigenstates of two non self-adjoint operators $\hat q$ and $\hat p$ similar, in a suitable sense, to the self-adjoint position and momentum operators $\hat q_0$ and $\hat p_0$ usually adopted in ordinary quantum mechanics. In particular we discuss conditions for these eigenstates to be {\em biorthogonal distributions}, and we discuss few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with $\hat q$ and $\hat p$, based on the so-called {\em quasi *-algebras}.

math-ph↗

arXiv2017

A model of adaptive decision making from representation of information environment by quantum fields

We present the mathematical model of decision making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioral, and geo-political factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are of the purely informational nature. The QFT-model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism (QBism). We demonstrate the quantum-like interference effect in DM which is exhibited as a violation of the formula of total probability and hence the classical Bayesian inference scheme.

math-ph↗

arXiv2017

Modeling interactions between political parties and electors

In this paper we extend some recent results on an operatorial approach to the description of alliances between political parties interacting among themselves and with a basin of electors. In particular, we propose and compare three different models, deducing the dynamics of their related {\em decision functions}, i.e. the attitude of each party to form or not an alliance. In the first model the interactions between each party and their electors are considered. We show that these interactions drive the decision functions towards certain asymptotic values depending on the electors only: this is the {\em perfect party}, which behaves following the electors' suggestions. The second model is an extension of the first one in which we include a $rule$ which modifies the status of the electors, and of the decision functions as a consequence, at some specific time step. In the third model we neglect the interactions with the electors while we consider cubic and quartic interactions between the parties and we show that we get (slightly oscillating) asymptotic values for the decision functions, close to their initial values. This is the {\em real party}, which does not listen to the electors. Several explicit situations are considered in details and numerical results are also shown.

physics.soc-ph↗

arXiv2016

$(H,ρ)$-induced dynamics and the quantum game of life

We propose an extended version of quantum dynamics for a certain system S, whose evolution is ruled by a Hamiltonian $H$, its initial conditions, and a suitable set $ρ$ of {\em rules}, acting repeatedly on S. The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of $H$, $ρ$ as well as on the initial conditions. After a general discussion on this $(H,ρ)$-{\em induced dynamics}, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension.

quant-ph↗

arXiv2014

${\cal D}$-deformed harmonic oscillators

We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint hamiltonians whose eigenvalues and eigenvectors can be found adopting the quite general framework of the so-called $\cal{D}$-pseudo bosons. In particular, we show that several models previously introduced in the literature perfectly fit into this scheme.

math-ph↗

arXiv2014

Towards a formalization of a two traders market with information exchange

This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here {models a two traders system with information exchange with the help of four fundamental operators: cash and share operators; a portfolio operator and an operator reflecting the loss of information. An information Hamiltonian is considered and an additional Hamiltonian is presented which reflects the dynamics of selling/buying shares between traders. An important result of the paper is that when the information Hamiltonian is zero, portfolio operators commute with the Hamiltonian and this suggests that the dynamics are really due to the information. Under the assumption that the interaction and information terms in the Hamiltonian have similar strength, a perturbation scheme is considered on the interaction parameter. Contrary to intuition, the paper shows that up to a second order in the interaction parameter, a key factor in the computation of the portfolios of traders will be the initial values of the loss of information (rather than the initial conditions on the cash and shares). Finally, the paper shows that a natural outcome from the inequality of the variation of the portfolio of trader one versus the variation of the portfolio of trader two, begs for the introduction of `good' and `bad' information. It is shown that `good' information is related to the reservoirs (where an infinite set of bosonic operators are used) which model rumors/news and external facts, whilst `bad' information is associated with a set of two modes bosonic operators.

q-fin.MF↗

arXiv2014

Dynamics of closed ecosystems described by operators

We adopt the so--called \emph{occupation number representation}, originally used in quantum mechanics and recently adopted in the description of several classical systems, in the analysis of the dynamics of some models of closed ecosystems. In particular, we discuss two linear models, for which the solution can be found analytically, and a nonlinear system, for which we produce numerical results. We also discuss how a damping effect could be {\em effectively} implemented in the model.

physics.bio-ph↗

arXiv2014

The role of information in a two-traders market

In a very simple stock market, made by only two \emph{initially equivalent} traders, we discuss how the information can affect the performance of the traders. More in detail, we first consider how the portfolios of the traders evolve in time when the market is \emph{closed}. After that, we discuss two models in which an interaction with the outer world is allowed. We show that, in this case, the two traders behave differently, depending on \textbf{i)} the amount of information which they receive from outside; and \textbf{ii)}the quality of this information.

q-fin.CP↗