On Quantum-Classical Transition of a Single Particle

We discuss the issue of quantum-classical transition in a system of a single particle with and without external potential. This is done by elaborating the notion of self-trapped wave function recently developed by the author. For a free particle, we show that there is a subset of self-trapped wave functions which is particle-like. Namely, the spatially localized wave packet is moving uniformly with undistorted shape as if the whole wave packet is indeed a classical free particle. The length of the spatial support of the wave packet is given by the Compton wavelength so that the wave packet is more localized for particle with larger mass. Whereas for a particle of mass m in a macroscopic external potential, we show that the time needed by the corresponding self-trapped wave function to depart from a classical trajectory is of the order ∼m ² c/ℏ. We argue that it is the Compton wavelength that matters and not the de Broglie wavelength as in conventional semiclassical approach.     

Effect of γ irradiation on the low-temperature electrical conductivity and dielectric properties of TlGaSe2 crystals

Electrical conductivity and dielectric properties of single-crystal TlGaSe₂ have been studied as a function of γ irradiation dose in the 100–280 K range including the existence of an incommensurate phase. Anomalies in the form of maxima have been observed in the σ=f(T), tan δ=f(T), and ɛ=f(T) curves at the points of transition from the paraphase to incommensurate (IC) phase, T _i, and from the IC to commensurate phase, T _c. The increase in the quantities σ, tan δ, and ɛ observed initially with increasing irradiation dose is followed by their strong decrease and disappearance of the anomalies. It has been established that γ irradiation does not affect the phase transition temperatures T _i and T _c. Fiz. Tverd. Tela (St. Petersburg) 40, 1328–1331 (July 1998)     

Synthesis, structure, and dielectric properties of KH2PO4 fractal aggregates

Macroscopic fractal aggregates of KH₂PH₄ (KDP) measuring up to 500 μm have been obtained. The fractal structure forms as a result of the precipitation of KDP particles from a supersaturated aqueous solution in the presence of a temperature gradient followed by a diffusioncontrolled mechanism of aggregation. The electron-microscopic analysis performed has shown that the fractals are formed predominantly from crystallites of the tetragonal modification measuring ∼1 μm. The dielectric constant (ɛ) of fractal KH₂PO₄ has been measured in the temperature range 80–300 K. A characteristic anomaly has been discovered on the ɛ(T) curve in the vicinity of 122 K, which attests to a ferroelectric phase transition. The absolute value of ɛ is significantly smaller than the components ɛ ₁₁ and ɛ ₃₃ for KH₂PO₄. Fiz. Tverd. Tela (St. Petersburg) 41, 2059–2061 (November 1999)     

Stability range for a flat graphene sheet subjected to in-plane deformation

The effects of the elastic deformation on the mechanical and physical properties of graphene are a subject of intensive current studies. Nevertheless, the stability range for a flat graphene sheet subjected to in-plane deformation is still unknown. Here, this problem is solved by atomistic simulations. In the three-dimensional space corresponding to the ɛ _xx , ɛ _yy , and ɛ _xy components of the planar strain tensor, the surface bounding the stability range for a flat graphene sheet has been constructed disregarding the thermal vibrations and the effects of boundary conditions. For the points of this surface, force components T _x , T _y , and T _xy have been calculated. It is shown that graphene is structurally stable up to strains on the order of 0.3–0.4, but it is unstable with respect to the shear in the absence of stretching forces. In addition, graphene cannot preserve its flat shape under the effect of a compressive force since it has zero flexural stiffness.     

Effect of a bias field on the dielectric properties of NaNbO3 solid solutions in the range of the giant temperature hysteresis of a phase transition

The effect of a bias field E on the value and temperature dependence of permittivity ɛ of ceramic samples of solid solutions 0.6NaNbO₃-0.4 NaTaO₃ (I), and 0.97[0.9NaNbO₃-0.1Na_0.5Bi_0.5TiO₃]-0.03LiNbO₃ (II) possessing an anomalously large temperature hysteresis of ɛ(T) dependence is studied. The character of the dependences of both the height and the temperature of the ɛ(T) maximum on the field show that composition (I) has antiferroelectric properties, while composition (II) has ferroelectric properties. It is found that up to 8 kV/cm, the strength of the bias field has actually no effect on the width of the ɛ(T) temperature hysteresis of the compositions under study.     

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

Effect of ionizing radiation on the dielectric characteristics of TlInSe<Subscript>2</Subscript> and TlGaTe<Subscript>2</Subscript> single crystals

The temperature dependences of the electrical conductivity and the permittivity of TlInSe₂ and TlGaTe₂ crystals unirradiated and irradiated with 4-MeV electrons at a doze of 10¹⁶ cm⁻² have been investigated. It has been established that electron irradiation leads to a decrease in the electrical conductivity σ and the permittivity ɛ over the entire temperature range under study (90–320 K). It has been revealed that the TlInSe₂ and TlGaTe₂ single crystals undergo a sequence of phase transitions characteristic of crystals of this type, which manifest themselves as anomalies in the temperature dependences σ = f(T) and ɛ = f(T). Electron irradiation at a doze of 10¹⁶ cm⁻² does not affect the phase transition temperatures of the crystals under investigation.     

Dielectric properties and phase transitions in crystals of TlInS x Se2 − x solid solutions

This paper reports on a study of the dielectric permittivity and electrical conductivity of single-crystal TlInS _x Se_{2 − x} solid solutions as functions of temperature and composition. It has been found that the dielectric permittivity ɛ and electrical conductivity σ decrease with increasing x and increase with growing temperature. The temperature dependences ɛ = f(T) and σ = f(T) for TlInS _x Se_{2 − x} crystals have been demonstrated to reveal anomalies in the form of maxima, which suggests that these crystals undergo phase transitions. The temperatures of the phase transitions increase with increasing x.     

Colossal magnetodielectric effect in SmFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The colossal (more than threefold) decrease in the dielectric constant ɛ in the easy-plane SmFe₃(BO₃)₄ ferroborate in a magnetic field of ∼5 kOe applied in the basal ab plane of the crystal has been found. A close relation of this effect to anomalies in the field dependence of the electric polarization has been established. It has been shown that this magnetodielectric effect is due to the contribution to ɛ from the electric susceptibility, which is related to the rotation of spins in the ab plane, arises in the region of the antiferromagnetic ordering T < T _N = 33 K, and is suppressed by the magnetic field. A theoretical model describing the main features of the behavior of ɛ and electric polarization in the magnetic field has been proposed, taking into account the additional anisotropy in the basal plane induced by the magnetoelastic stresses.     

Effect of γ irradiation on the hysteresis phenomena at the incommensurate-commensurate phase transition in Rb2ZnBr4

The effect of γ irradiation on the temperature hysteresis in dielectric permittivity ɛ and loss tangent tan δ of crystalline Rb₂ZnBr₄ has been studied in the vicinity of the incommensurate-commensurate phase transition. The ɛ(T) and tan δ(T) curves were found to exhibit anomalies in the form of maxima. Hysteresis was observed in the measured properties, including the transition temperature T _c (ΔT=T _c ^h −T _c ^c ), in both unirradiated and irradiated samples. It is shown that, as the radiation dose increases the extent of the hysteresis ΔT increases, the values of ɛ _max and tan δ _max at the transition point decrease, and the anomalies wash out. Fiz. Tverd. Tela (St. Petersburg) 40, 1911–1914 (October 1998)     

Tunnelling time of a gaussian wave packet through two potential barriers

The resonant and non-resonant dynamies of a Gaussian quantum wave packet travelling through a double barrier system is studied as a function of the initial characteristics of the spectrum and of the parameters of the potential. The behaviour of the tunnelling time shows that there are situations where the Hartman effect occurs, while, when the resonances are dominant, and in particular for b>π/Δk (b being the inter-barrier distance and Δk the spectrum width), the tunnelling time becomes very large and the Hartman effect does not take place.     

Dielectric properties of single-crystal deuterated triglycine sulfate (DTGS) in ultra-weak low-and infra-low-frequency electric fields

The complex permittivity ɛ* is studied with separate readings for ɛ′ and ɛ″ at low and infralow frequencies and ultraweak fields. The effective conductivity λ is determined. An Arrhenius dependence is observed for ln ɛ′(1/T), ln ɛ″(1/T), and ln λ(1/T), both in the paraphase and in the polar phase. It is proposed that the conductivity of crystalline DTGS in the paraphase is an ion jump conductivity. Fiz. Tverd. Tela (St. Petersburg) 41, 1073–1075 (June 1999)     

Energy and critical ionic-bond parameter of a 3D large-radius bipolaron

A theory of a strong-coupling large-radius bipolaron has been developed. The possibility of the formation of 3D bipolarons in high-temperature superconductors is discussed. For the bipolaron energy, the lowest variational estimate has been obtained at α > 8, where α is the electron-phonon coupling constant. The critical ionic-bond parameter η _c = ɛ_∞/ɛ₀, where ɛ_∞ and ɛ₀ are the high-frequency and static dielectric constants, has been found to be η _c = 0.2496.     

Effect of infrared radiation on the plasticity of solid hydrogen

This paper reports on the first results obtained from the investigation of the effect of IR radiation on the low-temperature (1.8 ≤ T ≤ 4.2 K) plasticity of solid hydrogen. It has been found that, when the samples are exposed to IR radiation, a drastic increment Δɛ_IR of the elongation per unit length ɛ (which was preliminarily achieved under a continuously applied mechanical stress σ = const) occurs without an increase in the temperature of the samples. It has been revealed that the effect observed both in the case of normal hydrogen (n-H₂, 75% o-H₂) and in the case of parahydrogen (p-H₂, ∼0.2% o-H₂) only for a sufficiently high power of the IR radiation source has a threshold character. The reverse deformation of solid hydrogen is observed after the irradiation with a flux of IR photons is completed: the quantity ɛ rapidly decreases to values provided only by the applied load. The appearance of jumps in the increment of deformation Δɛ_IR ⁱ is interpreted as a consequence of the existence of the fundamental IR absorption band for solid hydrogens. It has been established that, depending on the time t of exposure of the samples to IR radiation, the change in the quantity Δɛ_IR ⁱ (t) obeys the logarithmic law, which is characteristic of the dislocation creep and observed in the case of unirradiated hydrogen. It has also been found that, under multiple relatively long-term exposure to IR radiation, the constant α of the logarithmic creep of n-H₂ abruptly decreases, whereas the strength of both the n-H₂ and p-H₂ samples increases significantly, which indicates their explicit hardening (instead of the expected “superplastic” behavior due to the exposure to IR irradiation).     

Thermal conductivity of nonlinear waves in disordered chains

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity κ(T). We find indications for an asymptotic low-temperature κ ∼ T ⁴ and intermediate temperature κ ∼ T ² laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).     

Remarks to the standard scheme (theory) of neutrino oscillations. Corrected scheme of neutrino oscillations

In the standard theory of neutrino oscillations, it is supposed that physically observed neutrino states ν _e , ν_μ, ν_τ, have no definite masses, that they are initially produced as a mixture of the ν₁, ν₂, ν₃ neutrino states (i.e., they are produced as a wave packet), and that neutrino oscillations are the real ones. Then, this wave packet must decompose at a definite distance into constituent parts and neutrino oscillations must disappear. It was shown that these suppositions lead to violation of the law of energy and momentum conservation. An alternative scheme of neutrino oscillations obtained within the framework of particle physics has been considered, where the above mentioned shortcomings are absent, the oscillations of neutrinos with equal masses are the real ones, and the oscillations of neutrinos with different masses are the virtual ones. Expressions for probabilities of neutrino transitions (oscillations) in the alternative (corrected) scheme are given. The text was submitted by the author in English.     

Dielectric properties of Sn2P2S6 crystals as a function of their growth conditions

The behavior of the permittivity near a phase transition in Sn₂P₂S₆ crystals of different technological quality is studied. It is established that, in high-resistance crystals, where an internal electric field is formed by the screening of spontaneous polarization in the polar phase, long-time relaxation of ɛ is observed in a temperature range ∼2 K above T _max. This relaxation and change in the form of the maximum of ɛ′(T) at a phase transition are attributed to an internal electric field induced by the volume space charge formed in regions near the surface. It is established that the existing differences in the properties of Sn₂P₂S₆ crystals are due to deviations from stoichiometry, arising during growth and synthesis of the crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1456–1461 (August 1999)     

Energy Transfer in Spectra of the d-Dimensional Past Grid Turbulence

Free decay theory of the homogeneous and isotropic developed turbulence isconsidered in the d-dimensional case. The basic quantities under our consideration are the kinetic energy spectrum E(k,t) and energy transfer spectrum T(k,t) as functions of wave number k and decay time t. Starting point for studying E and T represents their adaptation from the stationary model which predicts the Kolmogorov spectrum which is multiplicatively dependent on an unknown scaling function F. In order to study the spectra of decaying turbulence both parameters l and εɛ are supposed to be dependent on t. Formerly derived basic integro–differential equation for F (by Adzhemyan, et al., 1998) has been here solved numerically in the dimension interval d∈(2, 3) for two cases of the Saffman invariant and the Loitsyansky integral fixing an arbitrary theor parameter α (α ⩵ 2 and 4, correspondingly). The energy transfer spectrum T(k) has been analyzed for several dimensions d≤3 showing the presence of integration regions in the wavenumber space where an inverse energy cascade can occur. PACS numbers: 47.27.ef, 47.11.-j, 47.27.er     

Spin-orbit coupling,spin-lattice relaxation,and spin-memory studies ofF-center-molecular-ion pairs in alkali halides

Summary The spin-orbit parameter Δ, spin-lattice relaxation timeT ₁, and spin-mixing parameter ɛ ofF _H(OH⁻) andF _H(CN⁻) centers in several alkali halides have been studied with magnetic circular dichroism at ∼2 K. A close comparison of the experimental results before and after optically induced association of theF center with the molecular ion has been made. In crystals of NaCl structure the negative spin-orbit parameter Δ changes little betweenF andF _H centers in the same host. For CsCl and CsBr two values of Δ have been derived forF _H(CN⁻) centers with axis parallel or perpendicular to the magnetic field. In all studied systems, the spin-lattice relaxation timeT ₁ is already shorter before aggregation compared toF formation. The spin-mixing parameter ɛ decreases slightly forF _H(OH⁻) compared toF centers, while it increases drastically forF _H(CN⁻) defects and reaches its maximum possible value ɛ=0.5 in cesium halides. First attempts to interpret these magneto-optical results will be presented. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Convergent-beam electron diffraction analysis of GaSe crystals grown from the melt by different doping elements

Summary A systematic investigation of the structural modifications of GaSe crystals, grown from the melt by different doping elements, has been performed by convergent-beam electron diffraction technique, in order to analyse the dependence of the structure on the doping atoms. Iodine-doped crystals have shown the ɛ-2H hexagonal and γ-3R rhombohedral polytypes. The structure of crystals doped either by silver, or copper, or cadmium, or zinc, or arsenic has been proved a mixture of the ɛ-2H hexagonal and of γ, 9 R, 12 R, 15 R rhombohedral phases. Ingots doped either by zinc or arsenic have shown the ɛ polytype prevailing in some zones and the γ structure in the other ones. The ɛ modification is dominant in ingots doped by the remaining atoms.