Inverse scattering problem in the relativistic quasiclassical approximation

We apply the quasipotential approach of quantum field theory to solve the inverse scattering problem in the relativistic quasiclassical approximation. We obtain expressions for reconstructing the quasipotential from the phase shifts and consider both nonrelativistic and ultrarelativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No-5, pp. 11–17, May, 1987.The authors are deeply grateful to Yu. S. Vernov and N. B. Skachkov for their interest and helpful discussion of the results.     

Continuous quantization procedure in quasiclassical scattering: Application to atom-Morse oscillator collisions

The recently developed method of continuous quantization is applied to the atom-Morse oscillator collinear collision problem. This geometrical formulation of the classical scattering process allows for the extraction of transition probabilities for classically forbidden processes with reasonable accuracy. The accuracy of this method over the simple (histogram) quasi-classical procedure is demonstrated for two-model systems.     

Tracking quasiclassical chaos in ultracold boson gases

We study the dynamics of an ultracold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from Kolmogorov-Arnold-Moser arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.     

Converse spectral problem in the relativistic quasiclassical approximation

The problem of quasipotential reconstruction from a given two-particle composite system energy spectrum is solved in the relativistic quasiclassical approximation. The nonrelativistic and ultrarelativistic asymptotes of the expressions obtained are studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 63–68, April, 1984.The authors thank Yu. S. Vernov, V. G. Kadyshevskii, and N. B. Skachkov for their interest in the study and valuable discussion of the results obtained.     

Quantum duality classical and quasiclassical limits

Quantum duality principle is applied to a study of classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized Lie-bialgebras are proved to be two-parametric varieties with two classical limits called dual. When considered from the point of view of quantized symmetries, such varieties can have boundaries that are noncommutative and noncocommutative. In this case the quantum duality and dual limits still exist while instead of Lie bialgebra one has a pair of tangent vector fields.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.I am heartily grateful to Prof. J. Lukierski for fruitful discussions and to all the scientists of the Institute of Theoretical Physics of Wroclaw University for their warm hospitality.The work is supported in part by the International Sci. Foundation, Grant N U9J000, and by the Russian Foundation for Fundamental Research, Grant No 95-01-00569a.     

Three-dimensional quasiclassical van Horn wave functions

A rigorous mathematical basis is given for the general equation for the three-dimensional quasiclassical wave functions recently proposed by Van Horn.     

Vacuum degeneration in the quasiclassical approximation in non-Abelian quantum theory

In this paper we construct quasiclassical wave packets for a non-Abelian particle in an external chromomagnetic field and field-averaged coordinates and color vector. In this case the average color vector is found not to satisfy the quasiclassical Wong equations and vacuum degeneration is noted in such a field. The choice of the vacuum leads to spontaneous breakdown of the initial symmetry of the Hamiltonian.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 106–111, January, 1990.     

Quantum and quasiclassical types of superfluid turbulence

By injecting negative ions in superfluid 4He in the zero-temperature limit (T0.7 K, a jet of ions generates quasiclassical tangles identical to those produced by mechanical means.     

Theory of interband optical absorption in a quasiclassical random field

Green's functions are used to study interband transitions in a quasiclassical (i.e. slowly varying in space) irregular field. It is assumed that the irregular field is random, i.e., the mean square of the fluctuation of the potential energy of an electron in such a field is much less than the width of the forbidden band. Explicit expressions are obtained for the coefficient of interband optical absorption for the case of an anisotropic irregular field and for the case when the irregular fields that act on electrons in the conduction and the valence band are different. As examples, we consider a fluctuation random field in ferroelectrics and a random field produced by long-wave acoustic lattice vibrations. The behavior of the tail of the optical absorption coefficient in ferroelectrics in the region of a phase transition is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 121–130, April, 1972.I am most grateful to V. L. Bonch-Bruevich for suggesting the subject and for his constant interest.