Comment on ‘Supersymmetry, PT-symmetry and spectral bifurcation’

We demonstrate that the recent paper by Abhinav and Panigrahi entitled ‘Supersymmetry, PT-symmetry and spectral bifurcation’ [K. Abhinav, P.K. Panigrahi, Ann. Phys. 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex sl(2) potential algebra.     

Supersymmetry, PT-symmetry and spectral bifurcation

We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real and shape-invariant, leading to translational shift in a suitable parameter by real units. The case of two different superpotentials, leading to same potential, yields broken PT-symmetry, the energy spectra in the two phases being separated by a bifurcation. Interestingly, these two superpotentials generate the two disjoint sectors of the Hilbert space. In the broken case, shape invariance produces complex parametric shifts.     

Periodic Square-Well Potential and Spontaneous Breakdown of PT-symmetry

A particle moving on a circle in a purely imaginary one-step potential is studied in both the exact and broken PT-symmetric regime.     

Phenomenology of the minimal<Emphasis Type="Italic">SO</Emphasis>(10) SUSY model

In this talk I define what I call the minimalSO(10) SUSY model. I then discuss the phenomenological consequences of this theory, vis-a-vis gauge and Yukawa coupling unification, Higgs and super-particle masses, the anomalous magnetic moment of the muon, the decayB _s → μ⁺ itμ⁻ and dark matter. On leave of absence at the Institute for Advanced Study, Princeton, NJ, USA     

Studies of spectral and coloristic properties of ultradispersive hematite particles

B. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, 70 F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 6, pp. 157–165, November–December, 1995.     

Erratum to “The extended Higgs system in R-symmetric supersymmetry theories” [Phys. Lett. B 697 (2011) 215]

We correct Fig. 1(right) of S.Y. Choi et al. (2011) [1] illustrating the neutralino masses in the R-symmetric model.     

<Emphasis Type="Italic">SL(2; R)</Emphasis> Duality of the Noncommutative DBI Lagrangian

We study the action of the SL(2; R) group on the noncommutative DBI Lagrangian. The symmetry conditions of this theory under the above group will be obtained. These conditions determine the extra U(1) gauge field. By introducing some consistent relations we observe that the noncommutative (or ordinary) DBI Lagrangian and its SL(2; R) dual theory are dual of each other. Therefore, we find some SL(2; R) invariant equations. In this case the noncommutativity parameter, its T -dual and its SL(2; R) dual versions are expressed in terms of each other. Furthermore, we show that on the effective variables, T -duality and SL(2; R) duality do not commute. We also study the effects of the SL(2; R) group on the noncommutative Chern–Simons action.     

Effect ofγ-radiation on the spectral luminescence characteristics of impure cadmium tungstate crystals

Results of a study of the effect of γ-radiation on the spectral luminescence properties of cadmium tungstate crystals doped with silver, bismuth, and molybdenum cations are presented. Spectral characteristics of the nondnnnoped crystals are briefly described. Absorption and photo and X-ray luminescence spectra of the crystals taken before and after exposure to γ-radiation (5.5·10⁴ Gy) are compared. It is found that the spectral characteristics of the crystals doped with silver, bismuth, and molybdenum cations do not change markedly after the exposure. The relation between the type of impurity-induced defects, individual characteristics of the impurity cations, and the character of the effect of γ-radiation on the spectral luminescence properties of impure crystals is analyzed (preliminarily). Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 55–60, January–February, 1997.     

Influence of the sample orientation in Sn<Subscript>2</Subscript>P<Subscript>2</Subscript>S<Subscript>6</Subscript> crystals on the hydrostatic piezoelectric coefficients

The influence of the sample orientation on the effective value of the hydrostatic piezoelectric coefficients d _h ⁽ⁱ⁾ of Sn₂P₂S₆ crystals has been studied. The hydrostatic piezoelectric coefficients d _h ⁽¹⁾ and d′ _h ⁽³⁾ , were measured, d _h ⁽¹⁾ =(244±3) pC/N and d′ _h ⁽³⁾ =(92±1) pC/N. The hydrostatic piezoelectric coefficient d _h ⁽³⁾ for orthogonal axis system was calculated to be d _h ⁽³⁾ =(87±2) pC/N. The, optimal orientation of the sample has been found as (Xy l)−20°-cut. Maximal value of the effective hydrostatic piezoelectric coefficient d _h ⁽¹⁾ equals 260 pC/N. Double rotated samples were also studied. The orientation of the samples insensitive to the pressure has been found. The theoretical mean value of hydrostatic piezoelectric coefficient (d _h ) _mean corresponding to randomly oriented Sn₂P₂S₆ grains in a poled composite has been calculated to be (d _h ) _mean =136 pC/N.     

Multilayer optics for XUV spectral region: technology fabrication and applications

We present research investigations in the field of multilayer optics in X-ray and extreme ultra-violet ranges (XUV), aimed at the development of optical elements for applications in experiments in physics and in scientific instrumentation. We discuss normal incidence multilayer optics in the spectral region of “water window”, multilayer optics for collimation and focusing of hard X-ray, multilayer dispersing elements for X-ray spectroscopy of high-temperature plasma, multilayer dispersing elements for analysis of low Z-elements. Our research pays special attention to optimization of multilayer optics for projection EUV-lithography (ψ-13nm) and short period multilayer optics.     

Reflection spectra of narcotic-containing plants and choice of spectral ranges for their detection

Journal of Applied Spectroscopy -     

Density functional theory study on the structural and electronic properties of Ag-adsorbed (MgO)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters

Equilibrium geometries, charge distributions, stabilities and electronic properties of the Ag-adsorbed (MgO) _n (n = 1–8) clusters have been investigated by density functional theory (DFT) with generalized gradient approximation (GGA) for exchange-correlation functional. The results show that hollow site is energetically preferred for n⩾4, and the incoming Ag atoms tend to cluster on the existing Ag cluster. The Mulliken populations indicate that the interaction between the Ag atom and Magnesia clusters is mainly induced by a weak atomic polarization. The adsorbed Ag atom only causes charge redistributions of the atoms near itself. The effect of the adsorbed Ag atom on the bonding natures and structural features of Magnesia clusters is minor. Furthermore, the investigations on the first energy difference, fragmentation energies and electron affinities show that the Ag(MgO)₄ and Ag(MgO)₆ are the most stable among studied clusters. Supported by the Startup Fund of High-level Personal for Shihezi University (Grant No. RCZX200747)     

<Emphasis Type="Italic">O</Emphasis>(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits withO(12) algebra which breakF spin but preserves theF _z quantum numberM _F. The generators ofO(12) are derived and the quantum numberU ofO(12) for a given boson numberN is determined by identifying the corresponding quasi-spin algebra. TheO(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With theO(12) algebra identified, complete classification of pnIBM symmetry limits with goodM _F is established.     

Charge fluctuation,charge ordering,and zero-gap state in organic conductors

We have carried out a series of measurements of angular dependence of solid-state NMR spectrum using single crystal samples on various organic molecular conductors, in order to investigate the natures of the electronic states at low temperatures. We confirmed a charge ordered insulating state in α-(BEDT-TTF)₂I₃ and large charge disproportionation in the metallic state of this salt. In another charge ordered system, θ-(BEDT-TTF)₂RbZn(SCN)₄, we observed unusual NMR line broadening, proportional to resonance shift, in the metallic state above the transition. We found that this broadening is due to charge disproportionation, or more correctly, due to the inhomogeneity of local susceptibility at nuclear sites and analyzed its dynamics. We observed similar broadening in various organic molecular conductors as well, such as θ-(BEDT-TTF)₂CsZn(SCN)₄, an exotic Bechgaad salt, (TMTSF)₂FSO₃, and λ-type BETS salts, λ-(BETS)₂(Fe,Ga)Cl₄. We found the mechanism of CD in each system is different, respectively.     

A comparative study on geometries,stabilities, and electronic properties between bimetallic AgnX（X=Au,Cu;n=1-8）and pure silver clusters

Using the meta-generalized gradient approximation (meta-GGA) exchange correlation TPSS functional, the geo- metric structures, the relative stabilities, and the electronic properties of bimetallic Ag n X (X=Au, Cu; n=1–8) clusters are systematically investigated and compared with those of pure silver clusters. The optimized structures show that the transition point from preferentially planar to three-dimensional structure occurs at n = 6 for the Ag n Au clusters, and at n = 5 for Ag n Cu clusters. For different-sized Ag n X clusters, one X (X=Au or Cu) atom substituted Ag n+1 structure is a dominant growth pattern. The calculated fragmentation energies, second-order differences in energies, and the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps show interesting odd–even oscillation behaviours, indicating that Ag 2,4,6,8 and Ag 1,3,5,7 X (X=Au, Cu) clusters keep high stabilities in comparison with their neighbouring clusters. The natural population analysis reveals that the charges transfer from the Ag n host to the impurity atom except for the Ag 2 Cu cluster. Moreover, vertical ionization potential (VIP), vertical electronic affinity (VEA), and chemical hardness (η) are discussed and compared in depth. The same odd–even oscillations are found for the VIP and η of the Ag n X (X=Au, Cu; n=1–8) clusters.     

Influence of ion dynamics on the shape of neutral-atom spectral lines

Reported at the 1st Yugoslavian Conference on Spectral Line Broadening, September 11–14, 1995, Belgrade.