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V. E. Bunakov

Publications and source records attributed to V. E. Bunakov.

3 recordsLinked to original sources
arXiv2001

The critical perturbation parameter estimate for the transition from regularity to chaos in quantum systems

In this paper we continue to develop our approach to the chaoticity properties of the quantum Hamiltonian systems. Our earlier suggested chaoticity criterion characterizes the initial symmetry breaking and the destruction of the corresponding integrals of motion in a perturbed system, which causes the system's chaotisation. Transition from regularity to chaos in quantum systems occurs at a certain critical value of the perturbation parameter. In our previous papers we had to diagonalize the perturbed system's Hamiltonian matrix in order to estimate this parameter. In the present paper we demonstrate that the critical perturbation parameter for the transition from regularity to chaos can be estimated in the framework of the first order perturbation theory. The values of thus obtained critical parameter are in good agreement with the results of our previous precise calculations for Hennon-Heiles Hamiltonian and diamagnetic Kepler problem.

quant-ph↗
arXiv2001

Approximate integrals of motion and the quantum chaoticity problem

The problem of existence and constructing of integrals of motion in stationary quantum mechanics and its connection with quantum chaoticity is discussed. It is shown that the earlier suggested quantum chaoticity criterion characterizes destruction of initial symmetry of regular system and of basis quantum numbers under influence of perturbation. The convergent procedure allowing to construct approximate integrals of motion in the form of non-trivial combinations depending on operators $(q,p)$ is suggested. Properties of the obtained integrals with complicated structure and the consequences of their existence for system's dynamics are discussed. The method is used for explicit construction and investigation of the approximate integrals in Henon-Heiles problem.

quant-ph↗