Search results for: F. Bagarello

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article

Dynamics for a quantum parliament

F. Bagarello, F. Gargano

Studies in Applied Mathematics > 150 > 4 > 1182 - 1200

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...

article

A concise review of pseudobosons, pseudofermions, and their relatives

F. Bagarello

Theoretical and Mathematical Physics > 2017 > 193 > 2 > 1680-1693

We review some basic definitions and a few facts recently established for D-pseudobosons and pseudofermions. We also discuss an extended version of pseudofermions based on biorthogonal bases in a finitedimensional Hilbert space and describe some examples in detail.

article

Modeling interactions between political parties and electors

F. Bagarello, F. Gargano

Physica A: Statistical Mechanics and its Applications > 2017 > 481 > C > 243-264

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 decision functions, i.e. the attitude of each party to form or not an alliance. In the first model the interactions...

article

kq-Representation for pseudo-bosons, and completeness of bi-coherent states

F. Bagarello

Journal of Mathematical Analysis and Applications > 2017 > 450 > 1 > 631-646

We show how the Zak kq-representation can be adapted to deal with pseudo-bosons, and under which conditions. Then we use this representation to prove completeness of a discrete set of bi-coherent states constructed by means of pseudo-bosonic operators. The case of Riesz bi-coherent states is analyzed in detail.

article

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

F. Bagarello, R. Di Salvo, F. Gargano, F. Oliveri

Applied Mathematical Modelling > 2017 > 43 > C > 15-32

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 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...

article

First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

F. Bagarello, E. Haven

Physica A: Statistical Mechanics and its Applications > 2016 > 444 > Complete > 403-414

We discuss a non linear extension of a model of alliances in politics, recently proposed by one of us. The model is constructed in terms of operators, describing the interest of three parties to form, or not, some political alliance with the other parties. The time evolution of what we call the decision functions is deduced by introducing a suitable Hamiltonian, which describes the main effects of...

article

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

F. Bagarello

Annals of Physics > 2015 > 362 > C > 424-435

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper...

chapter

Introduction

F. Bagarello, J.P. Gazeau, F. Szafraniec, M. Znojil

Non‐Selfadjoint Operators in Quantum Physics > 1 - 6

article

Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians

F. Bagarello

Annals of Physics > 2015 > 356 > Complete > 171-184

We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered...

article

A Quantum-Like View to a Generalized Two Players Game

F. Bagarello

International Journal of Theoretical Physics > 2015 > 54 > 10 > 3612-3627

This paper consider the possibility of using some quantum tools in decision making strategies. In particular, we consider here a dynamical open quantum system helping two players, G 1 $\mathcal {G}_{1}$ and G 2 $\mathcal {G}_{2}$ , to take their decisions in a specific context. We see that, within our approach, the final choices of the players do not depend in general on their...

article

Some invariant biorthogonal sets with an application to coherent states

F. Bagarello, S. Triolo

Journal of Mathematical Analysis and Applications > 2014 > 415 > 1 > 462-476

We show how to construct, out of a certain basis invariant under the action of one or more unitary operators, a second biorthogonal set with similar properties. In particular, we discuss conditions for this new set to be also a basis of the Hilbert space, and we apply the procedure to coherent states. We conclude the paper considering a simple application of our construction to pseudo-Hermitian quantum...

article

The role of information in a two-traders market

F. Bagarello, E. Haven

Physica A: Statistical Mechanics and its Applications > 2014 > 404 > Complete > 224-233

In a very simple stock market, made by only two 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 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...

article

Matrix Computations for the Dynamics of Fermionic Systems

F. Bagarello

International Journal of Theoretical Physics > 2014 > 53 > 2 > 555-565

In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and lowering operators play a relevant role in this analysis. The technical problem of our approach stands in the difficulty of solving the equations of motion, which...

article

D pseudo-bosons in quantum models

F. Bagarello, M. Lattuca

Physics Letters A > 2013 > 377 > 44 > 3199-3204

•We consider some examples of non-self-adjoint Hamiltonians having real eigenvalues.•We show that D-pseudo-bosons provide an unifying settings for those Hamiltonians.•We conclude that for Hamiltonians with linear real eigenvalues, D-pseudo-bosons provide the natural description.

article

Pseudo-bosons for the D2 type quantum Calogero model

F. Bagarello

Journal of Mathematical Analysis and Applications > 2013 > 407 > 1 > 90-96

In the first part of this paper we show how a simple system, a 2-dimensional quantum harmonic oscillator, can be described in terms of pseudo-bosonic variables. This apparently strange choice is useful when the natural Hilbert space of the system, L2(R2) in this case, is, for some reason, not the most appropriate. This is exactly what happens for the D2 type quantum Calogero model considered in the...

article

Quantizations from reproducing kernel spaces

S. Twareque Ali, F. Bagarello, Jean Pierre Gazeau

Annals of Physics > 2013 > 332 > Complete > 127-142

The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L2(C,d2z/π) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s. We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite...

article

Pseudo-fermions in an Electronic Loss-Gain Circuit

F. Bagarello, G. Pantano

International Journal of Theoretical Physics > 2013 > 52 > 12 > 4507-4518

In some recent papers a loss-gain electronic circuit has been introduced and analyzed within the context of PT-quantum mechanics. In this paper we show that this circuit can be analyzed using the formalism of the so-called pseudo-fermions. In particular we discuss the time behavior of the circuit, and we construct two biorthogonal bases associated to the Liouville matrix $\mathcal {L}$ used in...

article

Induced and reduced unbounded operator algebras

F. Bagarello, A. Inoue, C. Trapani

Annali di Matematica Pura ed Applicata ( 01923 -) > 2012 > 191 > 2 > 285-292

The induction and reduction precesses of an O*-vector space $${{\mathfrak M}}$$ obtained by means of a projection taken, respectively, in $${{\mathfrak M}}$$ itself or in its weak bounded commutant $${{\mathfrak M}^\prime_{\rm w}}$$ are studied. In the case where $${{\mathfrak M}}$$ is a partial GW*-algebra, sufficient conditions are given for the induced and the reduced spaces...

article

Few Simple Rules to Fix the Dynamics of Classical Systems Using Operators

F. Bagarello

International Journal of Theoretical Physics > 2012 > 51 > 7 > 2077-2085

We show how to use operators in the description of exchanging processes often taking place in (complex) classical systems. In particular, we propose a set of rules giving rise to an Hamiltonian operator for such a system ${\mathcal{S}}$ , which can be used to deduce the dynamics of ${\mathcal{S}}$ .

article

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

F. Bagarello

Physics Letters A > 2011 > 376 > 2 > 70-74

We have recently proposed a strategy to produce, starting from a given Hamiltonian h1 and a certain operator x for which [h1,xx†]=0 and x†x is invertible, a second Hamiltonian h2 with the same eigenvalues as h1 and whose eigenvectors are related to those of h1 by x†. Here we extend this procedure to build up a second Hamiltonian, whose eigenvalues are different from those of h1, and whose eigenvectors...

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INFONA - science communication portal

Search results for: F. Bagarello

Dynamics for a quantum parliament

A concise review of pseudobosons, pseudofermions, and their relatives

Modeling interactions between political parties and electors

kq-Representation for pseudo-bosons, and completeness of bi-coherent states

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

First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

Introduction

Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians

A Quantum-Like View to a Generalized Two Players Game

Some invariant biorthogonal sets with an application to coherent states

The role of information in a two-traders market

Matrix Computations for the Dynamics of Fermionic Systems

D pseudo-bosons in quantum models

Pseudo-bosons for the D2 type quantum Calogero model

Quantizations from reproducing kernel spaces

Pseudo-fermions in an Electronic Loss-Gain Circuit

Induced and reduced unbounded operator algebras

Few Simple Rules to Fix the Dynamics of Classical Systems Using Operators

Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity

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