Nonlinear Chaotic Dynamics of Quantum Systems

Хаотична Динаміка Двоатомних Молекулв Електромагнітному Полі

“…Below we briefly consider a quantum dynamical approach to studying a regular and chaotic dynamics of diatomic molecules in a resonant electromagnetic field [11]. It is based on the numerical solution of the time-dependent Schrödinger equation and realistic Simons-Parr-Finlan model for the diatomic molecule potential U (x).…”

“…The corresponding energy of interaction with the field is much higher than anharmonicity constant . It is obvious that a spectrum in this case become more complicated [7][8][9][10][11][12].…”

“…The theoretical foundations of the universal approach to analysis of chaotic dynamics of the quantum systems in an electromagnetic field have been presented earlier (see, c.g., [11,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]). Here we are limited only by the key moments.…”

“…Theoretical and experimental studying regular and chaotic dynamics of nonlinear processes in the different classes of quantum systems (in particular, atomic and molecular systems in an external electromagnetic field) attracts a great interest that is of a significant importance for multiple scientific and technical applications etc . Some of the beauty of quantum chaos is that it has developed a set of tools which have found applications in a large variety of different physical contexts, ranging from atomic, molecular and nuclear physics (Chirijov, 1979, Delande-Gay 1986, Wintgen-Friedrich 1986, Wintgen 1987, Zaslavsky, Berman, Kolovsky, 1988, 1992, Meredith et al, 1988, Chelkowski et al, 1991, Delande et al 1991, Zhang, Katsouleas, Joshi, 1993, Cassati et al 1994, Glushkov et al 1993, 1997 Glushkov et al, -2007) and others (see review [11]). New field of investigations of the quantum and other systems has been provided by the known progress in a development of a nonlinear analysis and chaos theory methods [1][2][3][4][5][6][7][8][9][10][11][12][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

“…In Refs. [11,[27][28][29][30][31][32][33] the authors applied different approaches to quantitative studying regular and chaotic dynamics of atomic and molecular systems interacting with a strong electromagnetic field and laser systems. The most popular approach includes the combined using the advanced nonlinear analysis and a chaos theory methods such as the autocorrelation function method, multifractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, Lyapunov exponent's analysis, surrogate data method, stochastic propagators method, memory and Green's functions approaches etc (see details in Refs.…”