The Geometric Phases and Quasienergy Spectral Series of a Hartree-Type Equation with a Quadratic Potential

Based on the ideology of the complex WKB–Maslov method, the general construction of quasiclassically concentrated solutions is given for Hartree-type equations with a quadratic potential and periodic coefficients. Exact expressions are constructed for the quasienergies and associated quasienergy states. In the construction of solutions, an important role is played by the Hamilton–Ehrenfest system of equations obtained in this work. Explicit expressions are found for the geometric phase of Aharonov–Anandan quasienergy states.     

Vacuum polarization for atomic quasienergy states

Vacuum polarization for an atomic system in the laser field is considered in the representation of quasienergy states as a radiation correction to the quasienergy. It is shown that laser effects are absent in the polarization fermion loop in case of resonant mixing of atomic levels. Perspectivity of investigation of laser effects in vacuum polarization of muonic atoms is discussed.     

Two-level system in the field of two intense waves

The problem of a two-level system in the field of two intense monochromatic waves is reduced to the problem of a two-level system in the field of a nonmonochromatic but periodic (in time) wave, which makes it possible to introduce quasienergy states. An investigation is made by the method proposed in [1, 2]. For the quasienergy an analytic expression is obtained that is valid in the complete range of variation of the frequencies at all values of one of the intensity parameters and moderate values of the other. The quasienergy is also calculated in the case of asymptotically large values of the parameters of both intensities when one of the frequencies of the external field is equal to the resonance frequency. The Fourier components of the density matrix at the frequencies of the external field are also calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 23–25, August, 1980.We thank M. L. Ter-Mikaelyan for interest in the work.     

The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.     

A modified Jaynes-Cummings model for an atom interacting with a classical multifrequency field

An open quantum system, which consists of a “dressed” two-level atom, i.e., an atom interacting with a classical multifrequency field, and a single quantized mode of an electromagnetic field, is examined. It is shown that when the frequency of the quantized mode coincides with one of the transition frequencies between the quasienergy levels, two interaction mechanisms, which differ in the dynamics of the populations of the quasienergy states, can be realized. Zh. éksp. Teor. Fiz. 112, 818–827 (September 1997)     

The influence of intense electromagnetic field on the energy-gap between spin branches in ferromagnetic semiconductors

The influence of an intense laser field on the intraband motion of a charge carrier in the localized moment potential of a ferromagnetic semiconductor is discussed. The quasienergy spectrum of a free carrier is calculated and it is shown that for very large fields the energy-gap between the spin branches decreases with increasing laser amplitude.     

Removal of interminiband interactions in dynamic Wannier-Stark ladder by means of a pulse train with periodic repetition

A quasienergy structure of a dynamic Wannier-Stark ladder (DWSL) that is driven by a pulse train with periodic repetition is analyzed. Here, novel properties on coherent control realized by means of tuning a combination of laser parameters are revealed. In particular, we report a striking property that interminiband interactions due to both static and dynamic Zener tunnelings are completely removed from the DWSL by utilizing the periodic pulse train with either square or full-cycle saw-toothed unit-pulse-shape in a temporal domain, regardless of magnitude of Dc- and Ac-electric fields exerted on the original superlattices.     

Floquet spectrum for two-level systems in quasiperiodic time-dependent fields

We study the time evolution ofN-level quantum systems under quasiperiodic time-dependent perturbations. The problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged Hilbert space, or equivalently of a generalized Floquet operator. We discuss criteria for the appearance of pure point as well as continuous spectrum, corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior. We discuss two types of mechanisms that lead to instability. The first one is due to near resonances, while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation. We treat explicitly an example of this type. The stability of the pure point spectrum under small perturbations is proven using KAM techniques.     

Quantum instability for a wave packet kicked periodically by a quadratic potential

The quantal behaviour of wave packet periodically kicked by a quadratic potential has been investigated using Floquet theory. The wave function of the particle afterN kicks has been determined. This wave function has been utilized to obtain the packet width, energy and loss of memory as a function of the number of kicks. It has also been shown that the free particle wave packet quasienergy spectrum makes a transition from discrete to absolutely continuous atɛ T=2. The behaviour forɛT>2 is quantum mechanically irregular.     

Two-level electron dynamics in a strong variable external field

This paper studies the quantum dynamics of an electron in a double-well potential subject to a strong time-periodic nonharmonic external field. The quasienergy spectrum of the system is calculated and an expression for the electron density distribution is derived. It is found that under certain conditions imposed on the shape of the excitation, the electron wave packet gets locked, into one potential well, as it were, and is unable to tunnel through the potential barrier. Zh. éksp. Teor. Fiz. 112, 1209–1225 (October 1997)     

Quasienergy band structure of solids

The problem of the band structure of solids under the influence of intense laser fields is addressed via the concept of quasienergy bands. The difficulties in evaluation of the quasienergy spectrum in the general case are stated, and a simple effective mass nearly free electron model is treated qualitatively and quantitatively, yielding some useful results.     

Models of Two-Level Atoms in Quasiperiodic External Fields

We prove that the spectrum of the generalized quasienergy operator of a plane-polarized two-level atom in a strong external quasiperiodic electromagnetic field with nonzero constant Fourier component is pure point, under Diophantine conditions on the frequency ratio, and excluding a small subset of resonant values. The widespread belief that there may be only pure point spectrum in such models is briefly discussed in Section 2 and the circularly polarized case—a well-known soluble model—is revisited from the point of view of the quasienergy operator..     

Multiphoton excitation of molecules and the quasienergy spectrum of the anharmonic oscillator

The quasienergy levels of an anharmonic oscillator in a strong external alternating field form two families, transitions between which are forbidden because of the large value of the quasiclassicality parameter of the forced oscillations caused by the external field. This makes it possible to explain the results of a number of experiments on the multiphoton excitation of molecules by infrared radiation. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 13–18 (10 July 1996)     

Principles of statistical mechanics: The energy duality

We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces. We show general theorems and their implications and apply the approach to the particle confinement in fields of rotational symmetry. Misleading associations with the theories of quasienergy and generalized thermodynamic potential are exposed.     

Localization and fluctuations in quantum kicked rotors

We address the issue of fluctuations, about an exponential line shape, in a pair of one-dimensional kicked quantum systems exhibiting dynamical localization. An exact renormalization scheme establishes the fractal character of the fluctuations and provides a method to compute the localization length in terms of the fluctuations. In the case of a linear rotor, the fluctuations are independent of the kicking parameter k and exhibit self-similarity for certain values of the quasienergy. For given k, the asymptotic localization length is a good characteristic of the localized line shapes for all quasienergies. This is in stark contrast to the quadratic rotor, where the fluctuations depend upon the strength of the kicking and exhibit local "resonances." These resonances result in strong deviations of the localization length from the asymptotic value. The consequences are particularly pronounced when considering the time evolution of a packet made up of several quasienergy states.     

Dynamic chaos in highly excited states of an anharmonic oscillator in an external electric field

The behavior of an anharmonic quantum oscillator in a harmonic external electric field is examined. The quasienergy is calculated numerically as a function of the field parameters (intensity and frequency) for highly excited states. It depends in complex fashion on frequency and field intensity near resonance. Quasi-intersection of levels is observed in a broad range of quantum numbers. These effects are manifestations of dynamic chaos in highly excited states of an anharmonic oscillator in an external field. Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 11–18, February, 1998.     

Zeldovich's regularization method in the theory of quasistationary states

The complex quasienergy, including the level width Γ, is calculated for a loosely bound atomic state in an intense monochromatic laser field of circular polarization. The method proposed by Zeldovich for regularizing divergent integrals that involve the Gamow wave function is employed in this calculation. The convergence of the method is demonstrated, and the conditions of its applicability are indicated.     

Quasienergy pseudopotential method in the theory of interaction of a coherent electromagnetic field with matter

We formulate the quasienergy pseudopotential methods, allowing us to study the behavior of the electronic structure of a material in a coherent electromagnetic field. We show that after canonical transformation, we can look for the solution to the nonsteady-state Schrödinger equation in a basis of wave functions from extended Hubert space, substituting the quasienergy pseudopotential for the true nonsteady-state electronic potential. We prove that the familiar compensation theorem remains valid even in this case.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 33–37, February, 1992.