Searcharxiv⌕ Search

arXiv subjects

I. B. Ivanov

Publications and source records attributed to I. B. Ivanov.

6 recordsLinked to original sources
arXiv2016

The reconstruction of sound speed in the Marmousi model by the boundary control method

We present the results on numerical testing of the Boundary Control Method in the sound speed determination for the acoustic equation on semiplane. This method for solving multidimensional inverse problems requires no a priory information about the parameters under reconstruction. The application to the realistic Marmousi model demonstrates that the boundary control method is workable in the case of complicated and irregular field of acoustic rays. By the use of the chosen boundary controls, an `averaged' profile of the sound speed is recovered (the relative error is about $10-15\%$). Such a profile can be further utilized as a starting approximation for high resolution iterative reconstruction methods.

physics.geo-ph↗
arXiv2015

Numerical testing in determination of sound speed from a part of boundary by the BC-method

We present the results of numerical testing on determination of the sound speed $c$ in the acoustic equation $u_{tt}-c^2Δu=0$ by the ${\it boundary}$ ${control}$ ${method}$. The inverse data is a response operator (a hyperbolic Dirichlet-to-Neumann map) given on controls, which are supported on ${\it a part}$ of the boundary. The speed is determined in the subdomain covered by acoustic rays, which are emanated from the points of this part orthogonally to the boundary. The determination is ${\it time-optimal}$: the longer is the observation time, the larger is the subdomain, in which $c$ is recovered. The numerical results are preceded with brief exposition of the relevant variant of the BC-method.

math.OC↗
arXiv2002

Unpredictability of wave function's evolution in nonintegrable quantum systems

It is shown that evolution of wave functions in nonintegrable quantum systems is unpredictable for a long time T because of rapid growth of number of elementary computational operations $\mathcal O(T)\sim T^α$. On the other hand, the evolution of wave functions in integrable systems can be predicted by the fast algorithms $\mathcal O(T)\sim (log_2 T)^β$ for logarithmically short time and thus there is an algorithmic "compressibility" of their dynamics. The difference between integrable and nonintegrable systems in our approach looks identically for classical and quantum systems. Therefore the minimal number of bit operations $\mathcal O(T)$ needed to predict a state of system for time interval T can be used as universal sign of chaos.

quant-ph↗
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↗