Technical Physics Letters

Bifurcations in the trajectory problem as a cause of internal-time singularities and the onset of quantum (wave)chaos

А. В. Богданов, Ashot S. Gevorkyan, A. G. Grigoryan

Published Aug 1, 1999• 2 citations

Abstract

A new theory is proposed for quantum-mechanical multichannel scattering in a collinear three-body system. This simple problem is used to show that the principle of quantum determinism is generally violated and we are dealing with microirreversible quantum mechanics. Fundamental calculations of quantum (wave) chaos are presented for the first time for the elementary reaction Li+(FH)→(LiFH)*→LiF+H.

DOI: 10.1134/1.1262582

Related papers

INTERNAL TIME PECULIARITIES AS A CAUSE OF BIFURCATIONS ARISING IN CLASSICAL TRAJECTORY PROBLEM AND QUANTUM CHAOS CREATION IN THREE-BODY SYSTEM

А. В. Богданов, Ashot S. Gevorkyan, A. G. Grigoryan +1 more

A new formulation of the theory of quantum mechanical multichannel scattering for three body collinear systems is proposed. It is shown that for this simple case, the principle of quantum determinism in the general case breaks down, and we have a micro-irreversible quantum mechanics. The first principle calculations of the quantum chaos (wave chaos) were pursued on the example of an elementary chemical reaction Li+(FH)→(LiFH)*→(LiF)+ H.

arXiv:quant-ph/9810005International Journal of Bifurcation and ChaosNov 1, 19997 citations

Regular and Chaotic Quantum Dynamic in Atom-Diatom Reactive Collisions

Ashot S. Gevorkyan, А. В. Богданов, Gunnar Nyman

A new micro-irreversible 3D theory of quantum multichannel scattering in the three-body system is developed. The quantum approach is constructed on the generating trajectory tubes which allow taking into account influence of classical non-integrability on the dynamical quantum system. It was shown that when the volume of classical chaos in phase space is larger than quantum sell in the main object of quantum system the wavefunction generates chaos (quantum chaos). The probability of quantum transitions is constructed for this case. On the example of collinear collision of Li+(FH) -> (LiF)+H system is carried out the numerical calculation and was shown that in the system is generated quantum (wave) chaos.

arXiv:quant-ph/0610128Oct 16, 20060 citations

Three Body Multichannel Scattering as a Model of Irreversible Quantum Mechanics

А. В. Богданов, Ashot S. Gevorkyan

The new formulation of the theory of multichannel scattering on the example of collinear model is proposed. It is shown, that in the closed three-body scattering system the principle of quantum determinism in general case breaks down and we have a micro- irreversible quantum mechanics.

arXiv:quant-ph/9712022Dec 10, 19977 citations

Numerical Investigation of Quantum Chaos in the Problem of Multichannel Scattering in Three Body System

А. В. Богданов, Ashot S. Gevorkyan, A. A. Udalov

Lecture notes in computer scienceJan 1, 20011 citation

Chaos in Bohmian Quantum Mechanics: A Short Review

George Contopoulos, Athanasios C. Tzemos

This is a short review of the theory of chaos in Bohmian quantum mechanics based on our series of works in this field. Our first result is the development of a generic theoretical mechanism responsible for the generation of chaos in an arbitrary Bohmian system (in 2 and 3 dimensions). This mechanism allows us to explore the effect of chaos on Bohmian trajectories and study in detail (both analytically and numerically) the different kinds of Bohmian trajectories where, in general, chaos and order coexist. Finally, we explore the effect of quantum entanglement on the evolution of the Bohmian trajectories and study chaos and ergodicity in qubit systems which are of great theoretical and practical interest. We find that the chaotic trajectories are also ergodic, i. e., they give the same final distribution of their points after a long time regardless of their initial conditions. In the case of strong entanglement most trajectories are chaotic and ergodic and an arbitrary initial distribution of particles will tend to Born’s rule over the course of time. On the other hand, in the case of weak entanglement the distribution of Born’s rule is dominated by ordered trajectories and consequently an arbitrary initial configuration of particles will not tend, in general, to Born’s rule unless it is initially satisfied. Our results shed light on a fundamental problem in Bohmian mechanics, namely, whether there is a dynamical approximation of Born’s rule by an arbitrary initial distribution of Bohmian particles.

arXiv:2009.05867Regular and Chaotic DynamicsSep 1, 202020 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, 19930 citations