Vol 127, No 3 (2018)

Optical tomogram of a quantum state can serve as an alternative to its density matrix since it contains all the information on this state. In this paper we use the explicit expression of the intermediate state |q, f, g〉(that is, an eigenvector of the coordinate and momentum operator fQ + gP) and the Radon transform between the Wigner operator Δ(p, q) and the pure-state density operator |q, f, g〉〈q, f, g| to calculate the specific tomograms for multiple-photon-added coherent states (MPACSs), thermal states (MPATSs) and displaced thermal states (MPADTSs). Their analytical tomograms are actually the finite-summation representations related to single-variable Hermite polynomials. Besides, the numerical results indicate that the larger photon-addition number can lead to the multi-peak tomographic distributions for these three states, and the measurable tomograms of MPACSs and MPADTSs exhibit π-periodic features but MPATSs can’t.

We consider the relationship between the unitary quantization scheme and the para-Fermi statistics of order 2. We propose an appropriate generalization of Green’s ansatz, which has made it possible to transform bilinear and trilinear commutation relations for the creation and annihilation operators for two different para-Fermi fields φ_a and φ_b into identities. We also propose a method for incorporating para-Grassmann numbers ξ_k into the general unitary quantization scheme. For the parastatistics of order 2, a new fact has been revealed: the trilinear relations containing both para-Grassmann variables ξ_k and field operators ak and bm are transformed under a certain reversible mapping into unitary equivalent relations in which commutators are replaced by anticommutators, and vice versa. It is shown that this leads to the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green’s components of operators a_k and b_m is constructed in explicit form, which enabled us to reduce the initial commutation rules for the components to the normal commutation relations for ordinary Fermi fields. We have analyzed a nontrivial relationship between the trilinear commutation relations of the unitary quantization scheme and the so-called Lie supertriple system. The possibility of incorporating the Duffin–Kemmer–Petiau theory into the unitary quantization scheme is discussed briefly.

When describing the dynamics of quantum systems interacting with a coherent external electromagnetic field, the instant at which the exciting (measuring) field begins to act is traditionally taken as zero time in the laboratory frame. Using the concept of coherence sudden death in an observed quantum system, we introduce the definition of local, completely incoherent subensembles of the quantum system in which it is found with a certain probability at each instant of time in the process of a continuous observation (measurement). For such subensembles an arbitrary instant of time in the laboratory frame is the initial time of the interaction with the external (measuring) field. As a result, the dynamics of an open quantum system is represented by a superposition of the dynamics of local subsystems with a continuous distribution of the times at which the interaction with the external field begins. We have derived an expression for the dynamical “multitime” contribution to the stationary solution of the Bloch equations, which clearly demonstrates the meaning of time relativity in the dynamics of two-level quantum systems in the semiclassical approximation. This dynamical multitime contribution is shown to explain the emergence of quantum beats at zero frequency (the Hanle effect, the level crossing) in EPR.

The formation of excitons in a helical molecular nanochain is considered. The model equations are derived with allowance for a spatial dispersion of the polarization of optical transitions treated in the approximation of nearest-neighbor interaction and constant dipole moment of molecules. Models of the medium are formulated, which determine the formation of polarization domains. Some examples are considered, which show that a helical medium admits the formation of stable localized structures (solitons) due to the curvature of the molecular chain. These features of the nanosystem can produce a critical influence on the luminescent properties of the chiral medium.

The problem of elastic scattering of particles has been considered by the potential quantization method. The properties of the eigenfunctions ϕ_ν⁽⁺⁾(r) and eigenvalues α_ν⁽⁺⁾ of this method for states with positive energies (continuous spectrum) have been studied. Under the assumption of the completeness of the set {ϕ_ν⁽⁺⁾(r)}, the problem has been solved by expanding the desired wavefunction in this set. The proposed approach reproduces known results in all considered limiting cases. At the same time, it gives a more detailed description of the scattering amplitude than the standard phase theory.

The results of the experiments, where the intense generation of alpha particles with an energy of about 8.6 MeV was observed at the interaction of 400–600-eV slow protons with a thin lithium foil or lithium vapors, have been analyzed. It has been shown that the high efficiency of these reactions at such a low energy cannot be explained within standard models of accelerator nuclear fusion. A model has been proposed and considered for the initiation of these reactions by correlated coherent states of protons, which are formed at the electrostatic interaction of these moving particles with the fields of surface lithium atoms in a solid target, as well as with atoms in molecules of lithium vapor. It has been shown that the formation of such states is accompanied by a sharp increase in short-term fluctuations of the energy of protons, which are due to the Schrödinger–Robertson uncertainty relation, to an amplitude of 30–80 keV. The calculation has shown that the optimal energy of the initial motion of protons, at which these processes occur and the probability of the (Li, p) reactions involving these protons is large, is near 500 eV in complete agreement with the experimental data.

The conditions for the formation of amplitude instabilities in two-dimensional Yukawa systems consisting of seven charged particles have been investigated. An analytical approach to searching for a criterion of the development of such instabilities based on the determination of the inflection point of a system’s potential energy when the particles deviate from their equilibrium positions is considered. The results obtained are compared with the melting criteria for extended two-dimensional systems.

We have studied the Nb(70 nm)/Ni_0.65Cu_0.35(6.5 nm)/Si layered structure in the temperature range T = 1.5–10 K using polarized neutron reflectometry. The correlation of the states of magnetic structures is observed at temperature T = 9 K, which is slightly higher than the superconducting transition temperature T_c = 8.5 K of the structure. At temperature T = 4 K, which is lower than T_c, the effect of reflexivity of magnetic states existing at T = 9 K was observed.

Conditions and mechanisms of controlled variation of the magnetic anisotropy of GaMnSb films containing magnetic MnSb nanoinclusions by means of heat treatment have been determined. For this purpose, the temperature and magnetic-field dependences of the magnetic moments of samples before and after thermal annealing were measured using a SQUID magnetometer. It is established that the heat treatment of GaMnSb films leads to a significant increase in the values of characteristics determined by the magnetic anisotropy, including the growth of blocking temperature (from 95 to 390 K) and the magnetic anisotropy field (from 330 to 630 Oe). Results of transmission electron microscopy investigation indicate that a change in the magnetic anisotropy of GaMnSb films as a result of their thermal annealing can be related to a transition of the crystalline structure of magnetic MnSb nanoinclusions from hexagonal (space group P6₂/mmc) to cubic (space group F-43m).

We have studied the dependence of the compression and burning of a spherical direct-drive fusion target on the nonuniformity of its heating caused by the asynchronous arrival of laser beams under conditions of irradiation by a modern laser system with a total energy of 2 MJ intended for the fuel ignition and fusion energy evolution equal to the absorbed laser energy. The investigation is performed by numerical simulation based on 2D hydrodynamic codes. It is established that the limiting permissible spread of the moments of laser pulse action on the target for ignition significantly exceeds the level that can be ensured using modern methods of controlled temporal synchronization of laser beams.

The forced phase locking in a system of the oscillating electroconvective rolls that form in a nematic liquid crystal layer in a dc electric field is studied. As a result of the action of an additive ac electric field with a small amplitude, the system of oscillators is found to be divided into clusters, where oscillations are fully phase locked. The electroconvective rolls in neighboring clusters oscillate in antiphase and the clusters are separated by Ising walls. The phase locking is shown to be maximal at the forcing frequency that is close to the double frequency of the natural oscillations of rolls. A model is proposed to describe spatially distributed phase oscillators, and it takes into account the symmetries of a system of electroconvective rolls and external forcing. The results of numerical simulations agree well with the experimental data.

The dynamics of torus vortex configurations V_{n, p, q} in a superfluid liquid at zero temperature (n is the number of quantum vortices, p is the number of turns of each filament around the symmetry axis of the torus, and q is the number of turns of the filament around its central circle; radii R₀ and r₀ of the torus at the initial instant are much larger than vortex core width ξ) has been simulated numerically based on the regularized Biot–Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter B₀ = r₀/R₀ for various values of parameter Λ = ln(R₀/ξ). It turns out that for certain values of n, p, and q, there exist quasi-stability regions in the plane of parameters (B₀, Λ), in which the vortices remain almost invariable during dozens and even hundreds of characteristic lengths.