Energy levels of the Fröhlich polaron in a spherical quantum dot

The one-phonon variational state is suitably applied to describe the ground state and excited states of the Fröhlich polaron bound to a quantum dot. A general analytical expression for the electronic energy spectra and the polaron binding energy for different electronic subband bound states in a quantum dot is presented and discussed with reference to the parameters of a real solid.     

Energy levels and states of parabolic cylindrical lens shaped quantum dots

The parabolic cylindrical lens shaped quantum dot is investigated theoretically. The Schrǒdinger equation for an electron confined in this structure is solved in the parabolic cylindrical coordinate system. The wavefunctions for the electron are presented in terms of confluent hypergeometric functions, and the electron energy spectra are also obtained.     

Inverse quantum mechanics problem for potentials with λx−2 singularities

Using a one-dimensional oscillator with a x^–2-singular potential as an example, a method of solving an inverse problem of quantum mechanics with the same singularity of the potential is given. A nontrivial form of corrections to the potential due to a change in the spectral parameters is found.Translated frpm Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 57–61, September, 1991.     

Energy levels of paired donor impurities in SixGe1−x alloys

The dependences on alloy compositionx of the bound and resonant deep energy levels of nearest-neighbor (P,P), (As, As), and (Sb, Sb) pairs in Si _x Ge_1–x alloys are predicted. Based on these predictions, it appears likely that (P, P) and (As, As) produce at least one deep level in the gap for allx, but that (Sb, Sb) does not for anyx.     

Energy levels of perturbed 6pnd J = 2 Rydberg states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6pnd J=2 Rydberg states of atomic lead are analyzed by the multichannel quantum defect theory (MQDT) with previous experimental energy levels. The 6pnd (6≤n ≤ 63) J=2 Rydberg energy levels are calculated and optimal MQDT parameters were obtained. Using these parameters, admixture coefficients for each level are calculated to designate the level denotations. The results show that strong channel mixings exist for the levels near the 6p6d (3/2)[5/2]2° and 6p6d (3/2)[3/2]2° pertubers. The five-channel model different from that in literature is used to predict 21 energy positions of 6pnd (1/2)[3/2]2° levels and to determine the denotations of all the 6pnd J=2 Rydberg states under 59788 cm-1 for Pb I.     

On the Mössbauer studies of harmonically bound quantum oscillators in Brownian motion

In many biological systems like whole cells, membranes or proteins and some of the polymeric systems, dynamics reveals itself in M?ssbauer spectra as a non Lorentzian behaviour above some particular temperature which is characteristic of the system. Moreover mean square displacement and line width show temperature dependence above the characteristic temperature. Brownian motion of harmonically bound oscillator has been able to explain the non-Lorentzian behaviour. In the present paper, a quantum picture of the above model is discussed and lineshape is expressed as the closed form for the extreme overdamping case. In addition to the non-Lorentzian behaviour, the present model also predicts a temperature dependence of mean square displacement and linewidth. Received 16 July 1997 and Received in final form 2 September 1998     

Energy–momentum tensor form factors of the nucleon in nuclear matter

The nucleon form factors of the energy–momentum tensor are studied in nuclear medium in the framework of the in-medium modified Skyrme model. We obtain a negative D  -term, in agreement with results from other approaches, and find that medium effects make the value of _d1$d_1$ more negative.     

Derivation of the Hamiltonian form of the Klein-Gordon equation from Schrödinger-Furth quantum diffusion theory: Comments

Stochastic formulations of the Klein-Gordon and Dirac equations existing in the literature are pointed out. A new derivation of the Schrödinger equation as an approximation to a deterministic field equation is discussed.     

Energy Spectra of the Local States in the Forbidden Gap of Monoclinic TlInS2xSe2(1?x) Crystals

Near IR properties of the mixed TlInS_2xSe_2(1–x) have been studied previously by the present authors. In this work the temperature and frequency dependence's of the conductivity and the current-voltage characteristics (in relatively weak electric field), have been investigated for monoclinic TlInS_2xSe_2(1–x) crystals, which are perspective materials for IR applications. From the temperature dependence's of conductivity in the direction perpendicular to c- axis the band gap E^g = 2.22 eV was determined for --TlInS₂ crystals. The impurity centres were determined located at 0.43, 0.73 eV and 0.35, 0.48, 1.12 eV for the direction of current i//c and i c, respectively. The concentration of the centres located at 0.48 and 1.12 eV were calculated to be N_A – N_D = 4.8 · 10⁹ cm^–3 and 1.9 · 10¹¹ cm^–3, respectively. It was found that in the solid solutions TlInS_2xSe_2(1–x) for 0.3 x 1, the conductivity follows the dependence (v) = ₀·^s in the temperature range between 100 to 600 K. In the temperature range of 80-400 K charge bounce plays an important role in the conductivity mechanism. Occurrence of the deep and low-levels impurity centres and a tail of the density of energy states in TlInS_2xSe_2(1–x) crystals make them perspective for practical applications: switching and memory effects, N-type current-voltage characteristics, induced conductivity etc.     

Manifestation of the composition inhomogeneity of Zn1 − x Mg x Te quantum wires in Raman spectra

The resonant Raman spectra of Zn_{1 − x} Mg _x Te quantum wires have been investigated. The dependences of the frequencies of longitudinal optical phonons of the ZnTe-like and MgTe-like modes (LO1 and LO2) on the photon energy have been found. The character of these dependences correlates with the variation in the frequencies of optical phonons of the Zn_{1 − x} Mg _x Te alloys on the composition (x). This gives grounds to assume that the quantum wires are inhomogeneous in the composition. This assumption is also confirmed by the fact that the intensity ratio of the LO2 and LO1 modes in the Raman spectra increases with increasing excitation energy.     

The explicit form of the vertex operator fields in two-dimensional quantum SL(2, ℂ) field theory

The explicit form of the vertex operator fields in two-dimensional quantum sl(2, ) field theory is found.     

Transport properties and the anisotropy of Ba1 − x K x Fe2As2 single crystals in normal and superconducting states

The transport and superconducting properties of Ba_{1 ? x} K _x Fe₂As₂ single crystals with T _c ≈ 31 K were studied. Both in-plane and out-of-plane resistivity was measured by a modified Montgomery method. The in-plane resistivity is almost the same for all studied samples, unlike the out-of-plane resistivity, which differs considerably. We have found that the resistivity anisotropy γ = ρ _c /ρ _ab is almost independent of temperature and lies in the range 10–30 for the studied samples. This indicates the extrinsic nature of high out-of-plane resistivity, which may be due to the presence of flat defects along Fe-As layers in the samples. This statement is supported by comparatively small effective mass anisotropy, obtained from the upper critical field measurements, and from the observation of the so-called “Friedel transition,” which indicates the existence of some disorder in the samples in the c-direction.     

Solution of the Schrödinger equation for a particular form of Morse potential using the Laplace transform

In this paper, we have solved the Schrdinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the Laplace transform technique which reduces the second-order differential equation to a first-order.     

Magnetic properties of GdBa2Cu3O7−x in the normal and superconducting states

The magnetic properties of superconducting GdBa₂Cu₃O_7–x withT _c95 K are measured. In the normal state, its susceptibility closely follows the Curie law with an effective moment of 7.77 _B .H _c1 is determined to be 650 Oe. No superconducting fluctuation can be delineated. Flux pinning indicated behavior of type II superconductors. A 25–405 diamagnetic state indicating bulk superconductivity in GdBa₂Cu₃O_7–x .     

A new optical method for measuring the electron-phonon interaction parameter λ〈Ω2〉 using the spectral dependence of the relaxation rate

The spectral dependence of the electron-phonon relaxation rate γ_e−ph(ℏω) in metals is studied in pump-supercontinuum-probe (PSCP) experiments with femtosecond time resolution. Investigation of this spectral dependence, which exhibits a substantial slowing of the relaxation rate γ_e−ph(ℏω) near the Fermi level E _F , using the parametrization γ_e−ph(ℏω)∝λ〈Ω²〉 (ℏω−E _F )² makes it possible to determine directly the electron-phonon interaction parameter λ〈Ω²〉. The parameter λ〈Ω²〉 for YBa₂Cu₃O_7−δ is analyzed using this method. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 329–332 (10 September 1999)     

Determination of the Rydberg D and F° energy levels of Cs-like ions by the method of interpolation of relativistic quantum defects

Data are presented that allow one to determine the energy values of the Rydberg levels nD _3/2, nD _5/2, nF _5/2°, and nF _7/2° for ions of the cesium isoelectronic sequence by the method of interpolation of rela- tivistic quantum defects in the Dirac-Fock approximation. To improve agreement with the experimental data, it is proposed to use an empirical correction for the quantum defect. The obtained energy values are compared with the experimental data. The anomalous behavior of the quantum defects of the nf levels is discussed. The calculations are carried out for ten ions of the cesium isoelectronic sequence.     

Energy of the Kerr–Newman-AdS black hole by using approximate Lie symmetries

Using Lie approximate symmetry methods for differential equations second-order approximate symmetries of the geodesic equations for the Kerr–Newman-AdS (KN-AdS) spacetime are investigated. For this purpose the KN-AdS metric is considered as a second perturbation of the AdS metric. A rescaling of the arc length parameter for consistency of the trivial second-order approximate symmetries of the geodesic equations indicates that the energy in the KN-AdS spacetime has to be rescaled. There is an extra contribution to the energy of the KN-AdS spacetime due to the cosmological constant. This energy expression is compared with that for the Kerr–Newman (KN) spacetime.     

Energy average formula of photon gas rederived by using the generalised Hermann-Feynman theorem

By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.     

Two-dimensional quantum interference contributions to the magnetoresistance of Nd2−x CexCuO4−δ single crystals

Two-dimensional (2D) weak localization effects at low temperatures T=0.2–4.2 K are investigated in a nonsuperconducting sample Nd_1.88Ce_0.12CuO_4−δ and in the normal state of a superconducting sample Nd_1.82Ce_0.18CuO_4−δ for B>B _c2≃3 T. The phase coherence time τφ (≃5×10⁻¹¹ s at 1.9 K) and the effective thickness d of a conducting CuO₂ layer (≃1.5 Å) are estimated by fitting the expressions from the 2D weak localization theory to the magnetoresistivity data for the normal-to-plane and in-plane magnetic fields. The estimated value of the parameter d ensures the condition of strong carrier confinement and justifies a model of almost decoupled 2D metallic sheets for the Nd_2−x Ce_xCuO_4−δ single crystals. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 93–99 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Determination of the transport lifetime limiting scattering rate in InSb/AlxIn1−x Sb quantum wells using optical surface microscopy

We report magnetotransport measurements of InSb/Al_1−xIn_xSb quantum well structures at low temperature (3 K), with evidence for 3 characteristic regimes of electron carrier density and mobility. We observe characteristic surface structure using differential interference contrast DIC (Nomarski) optical imaging, and through use of image analysis techniques, we are able to extract a representative average grain feature size for this surface structure. From this we deduce a limiting low temperature scattering mechanism not previously incorporated in transport lifetime modelling of this system, with this improved model giving strong agreement with standard low temperature Hall measurements. We have demonstrated that the mobility in such a material is critically limited by quality from the buffer layer growth, as opposed to fundamental material scattering mechanisms. This suggests that the material has immense potential for mobility improvement over that reported to date.