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

Chinese Journal of Physics

Nonlinear classical dynamics described by a density matrix in the classical limit

Gaspar Gonzalez, Angel Ricardo Plastino, Andrés M. Kowaslki

Published Mar 10, 2026• 0 citations
Publisher
DOI
10.1016/j.cjph.2026.03.006

Related papers

Chaotic density matrix in the classical limit

A.M. Kowalski, Angelo Plastino

Physics Letters A•Apr 6, 2020•4 citations

Using density matrices in classical dynamical systems

M. Fannes

Banach Center Publications•Jan 1, 1998•0 citations

Nonlinear Classical Dynamics described by a Density Matrix in the Classical Limit

Gaspar Gonzalez, Angelo Plastino, Andrés Kowalski

We examine the classical limit of a fairly general nonlinear semiclassical hybrid system within a MaxEnt framework. The consistency of the hybrid dynamics requires algebraic constraints on quantum operators and smoothness conditions for the classical variables. Analytically, we demonstrate that the classical limit is characterized by a pure density matrix representing a single state, which reproduces the dynamics of its classical analogue. To illustrate the methodology, we revisit and synthesize two previously studied examples.

quant-pharXiv:2512.05423•Dec 8, 2025•0 citations

We discuss the solutions of quantum problems which are nonlinear in the classical limit. It is shown that in this case it is necessary to solve the corresponding nonlinear classical problem and study its bifurcation properties.

K. N. Yugai

Dynamical chaos in quantum systems (quantum chaos) has been studied by a large number of physicists [1-7]. It has been shown that quantum chaos is possible only in the quasiclassical region, for example in the case of quantum states near the dissociation limit in molecules or near the ionization limit in atoms and molecules. However, the quantum equations of motion are linear and hence they cannot contain dynamical chaos. In the present paper we discuss the solution of quantum problems which are nonlinear in the classical limit. It will be show that in solving the quantum problem in this case it is necessary to use the solution of the nonlinear classical problem forming the classical limit of the quantum problem. i. We note first that here we are not interested in the usual field nonlinearities considered, for example, in quantum optics. This is because field nonlinearities cannot determine the bifurcation properties of the quantum equations of motion since the latter are linear in the wave function ~ or density matrix p. In other words, dynamical chaos, which is intimately connected with the bifurcation properties of the corresponding equations, is not determined by nonlinearities in the fields in quantum equations of motion linear in ~ or 0o

•Jan 1, 1993•0 citations

Quantum Simulation of Nonlinear Classical Dynamics

Ilon Joseph, Alessandro R. Castelli, Jonathan L. DuBois +6 more

Bulletin of the American Physical Society•Mar 3, 2020•0 citations

Bifurcation and chaos in nonlinear Lindblad equations

Bernd Fernengel, Barbara Drossel

The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the density matrix is obtained from a mean field theory of interacting quantum systems or from a top-down control by a changing classical environment, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example of a two-level system. By using techniques developed for classical dynamical systems we show that various types of bifurcations and even chaotic dynamics can occur. We also discuss experimental situations for which our results could be relevant.

arXiv:1907.09349•Jul 22, 2019•0 citations
We examine the classical limit of a fairly general nonlinear semiclassical hybrid system within a MaxEnt framework. The consistency of the hybrid dynamics requires algebraic constraints on quantum operators and smoothness conditions for the classical variables. Analytically, we demonstrate that the classical limit is characterized by a pure density matrix representing a single state, which reproduces the dynamics of its classical analogue. To illustrate the methodology, we revisit and synthesize two previously studied examples.
Dynamical chaos in quantum systems (quantum chaos) has been studied by a large number of physicists [1-7]. It has been shown that quantum chaos is possible only in the quasiclassical region, for example in the case of quantum states near the dissociation limit in molecules or near the ionization limit in atoms and molecules. However, the quantum equations of motion are linear and hence they cannot contain dynamical chaos. In the present paper we discuss the solution of quantum problems which are nonlinear in the classical limit. It will be show that in solving the quantum problem in this case it is necessary to use the solution of the nonlinear classical problem forming the classical limit of the quantum problem. i. We note first that here we are not interested in the usual field nonlinearities considered, for example, in quantum optics. This is because field nonlinearities cannot determine the bifurcation properties of the quantum equations of motion since the latter are linear in the wave function ~ or density matrix p. In other words, dynamical chaos, which is intimately connected with the bifurcation properties of the corresponding equations, is not determined by nonlinearities in the fields in quantum equations of motion linear in ~ or 0o
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time evolution to be linear. However, when the density matrix is obtained from a mean field theory of interacting quantum systems or from a top-down control by a changing classical environment, the ensemble interpretation is inappropriate and nonlinear dynamics arise naturally. We therefore study the dynamical behavior of nonlinear Lindblad equations using the example of a two-level system. By using techniques developed for classical dynamical systems we show that various types of bifurcations and even chaotic dynamics can occur. We also discuss experimental situations for which our results could be relevant.