Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Zeitschrift für angewandte Mathematik und Physik

New results for Heisenberg dynamics for nonself-adjoint Hamiltonians

Bagarello F.

Published Mar 23, 2026• 0 citations
Publisher

Abstract

Abstract In a previous paper, we began our analysis on the role of non-self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on dynamical systems, we continue this analysis focusing on what we believe is an unexplored (or, at least, not so explored! aspect of Heisenberg dynamics, related to the need for using vectors which are brute-force normalized . Our main interest is on conserved quantities and on conditions which guarantee that some observables of the system, or their mean values, do not evolve in time.

DOI
10.1007/s00033-026-02765-1

Related papers

New results for Heisenberg dynamics for non self-adjoint Hamiltonians

Fabio Bagarello

In a previous paper we began our analysis on the role of non self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on dynamical systems, we continue this analysis focusing on what we believe is an unexplored (or, at least, not so explored! aspect of Heisenberg dynamics, related to the need for using vectors which are {\em brute-force normalized}. Our main interest is on conserved quantities, and on conditions which guarantee that some observables of the system, or their mean values, do not evolve in time.

math-phCross-listedarXiv:2603.06419•Mar 9, 2026•0 citations

The dynamical problem for a non self-adjoint Hamiltonian

Fabio Bagarello, Miloslav Znojil

We review some recent results of the so-called quasi-hermitian quantum mechanics, with particular focus on the quantum dynamics both in the Schrödinger and in the Heisenberg representations. The role of Krein spaces is also discussed.

arXiv:1105.4716•May 24, 2011•0 citations

Generalized Heisenberg algebra and (non linear) pseudo-bosons

F Bagarello, Evaldo M. F. Curado, J P Gazeau

Abstract We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given physical system. We also discuss relations with nonlinear pseudo-bosons. Several examples are discussed.

arXiv:1802.03369•Journal of Physics A Mathematical and Theoretical•Feb 7, 2018•16 citations

New Results for Heisenberg Dynamics for Non-Self-Adjoint Hamiltonians

Ijaz Durrani

•Jan 1, 2026•0 citations

Damping and pseudo-fermions

Fabio Bagarello

After a short abstract introduction on the time evolution driven by non-self-adjoint Hamiltonians, we show how the recently introduced concept of pseudo-fermion can be used in the description of damping in finite dimensional quantum systems, and we compare the results deduced adopting the Schrödinger and the Heisenberg representations.

arXiv:1212.3663•Journal of Mathematical Physics•Feb 1, 2013•9 citations

A quantum-like model of political consensus via non self-adjoint Hamiltonians

Fabio Bagarello, Gloria Liarda

We discuss here how non self-adjoint Hamiltonians, and their related Heisenberg-like dynamics, can be used to model a political system consisting in a coalition $\C$ of different parties (forming a government) and by their (original) supporters $\Sc$. Our aim is to model how the opinion of these supporters changes depending on the efficiency, competence and coherence of the coalition $\C$, as these are perceived by $\Sc$ during their action while governing. After a rather general introduction we propose three specific models, and we describe and comment the dynamical behaviour of the { full} system, $\Sc\cup\C$. The role of the so-called {\em balanced Hamiltonians}, recently introduced by the authors in connection with integrals of motion, is discussed in details.

math-phCross-listedarXiv:2606.19014•Jun 18, 2026•0 citations
Abstract In a previous paper, we began our analysis on the role of non-self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on dynamical systems, we continue this analysis focusing on what we believe is an unexplored (or, at least, not so explored! aspect of Heisenberg dynamics, related to the need for using vectors which are brute-force normalized . Our main interest is on conserved quantities and on conditions which guarantee that some observables of the system, or their mean values, do not evolve in time.
In a previous paper we began our analysis on the role of non self-adjoint Hamiltonians in connection with the Heisenberg dynamics for quantum systems. Here, motivated by the growing interest on this topic and on some recent results on dynamical systems, we continue this analysis focusing on what we believe is an unexplored (or, at least, not so explored! aspect of Heisenberg dynamics, related to the need for using vectors which are {\em brute-force normalized}. Our main interest is on conserved quantities, and on conditions which guarantee that some observables of the system, or their mean values, do not evolve in time.
We discuss here how non self-adjoint Hamiltonians, and their related Heisenberg-like dynamics, can be used to model a political system consisting in a coalition $\C$ of different parties (forming a government) and by their (original) supporters $\Sc$. Our aim is to model how the opinion of these supporters changes depending on the efficiency, competence and coherence of the coalition $\C$, as these are perceived by $\Sc$ during their action while governing. After a rather general introduction we propose three specific models, and we describe and comment the dynamical behaviour of the { full} system, $\Sc\cup\C$. The role of the so-called {\em balanced Hamiltonians}, recently introduced by the authors in connection with integrals of motion, is discussed in details.