Unsharpness,Naimark Theorem and Informational Equivalence of Quantum Observables

For each commutative POV measure F there exists (Beneduci, J. Math. Phys. 47:062104-1, 2006; Int. J. Geom. Methods Mod. Phys. 3:1559, 2006) a PV measure E such that F can be interpreted as a random diffusion of E. In its turn, the self-adjoint operator A=∫ λ  dE _λ corresponding to E, can be interpreted (Beneduci, J. Math. Phys. 48:022102-1, 2007; Nuovo Cimento B 123:43–62, 2008) as the projection of a Naimark operator corresponding to the Naimark dilation E ⁺ of F. Moreover E can be algorithmically reconstructed by F. All that suggests that, in some sense, the observables represented by E and F should have the same informational content. We introduce an equivalence relation on the set of observables which we compare with other well known equivalence relations and prove that it is the only one for which E is always equivalent to F.     

Nature of conduction via impurities in uncompensated silicon

The static conductivity σ(E) and photoconductivity (PC) at radiation frequencies ħω=10 and 15 meV in Si doped with shallow impurities (density N=10¹⁶−6×10¹⁶ cm⁻³, ionization energy ε₁≃45 meV) with compensation K=10⁻⁴−10⁻⁵ in electric fields E=10–250 V/cm are measured at liquid-helium temperatures T. Special measures are taken to prevent the high-frequency part of the background radiation (ħω>16 meV) from striking the sample. It is found that the conductivity σ(E) is due to carrier motion along the D ⁻ band, which is filled with carriers under the influence of the field E. In fields E<E _q (E _q ≃100–200 V/cm) the carrier motion consists of hops along localized D ⁻ states in a 10–15 meV energy band below the bottom of the free band (energy ε=ε₁); for E>E _q carriers drift along localized D ⁻ states with energy ε∞ε₁−10 meV. An explanation is proposed for the threshold behavior of the field dependence of the photo-and static conductivities. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 232–236 (25 August 1997)     

On the Complete Classification of Unitary <Emphasis Type="Italic">N</Emphasis> = 2 Minimal Superconformal Field Theories

Aiming at a complete classification of unitary N = 2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate partition function of such a theory is indeed the partition function of a fully-fledged unitary N = 2 minimal model, subject to the assumptions that orbifolding is a ‘physical’ process and that the space-time supersymmetric A{\mathcal{A}} -D{\mathcal{D}} -E{\mathcal{E}} models are physical. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models then demonstrates that there exists a unitary N = 2 minimal model for every one of the allowed partition functions in the list obtained from Gannon’s work (Gannon in Nucl Phys B 491:659–688, 1997).     

Pure type I supergravity and DE 10

We establish a dynamical equivalence between the bosonic part of pure type I supergravity in D = 10 and a D = 1 non-linear σ-model on the Kac–Moody coset space DE ₁₀/K(DE ₁₀) if both theories are suitably truncated. To this end we make use of a decomposition of DE ₁₀ under its regular SO(9,9) subgroup. Our analysis also deals partly with the fermionic fields of the supergravity theory and we define corresponding representations of the generalised spatial Lorentz group K(DE ₁₀).     

Zeros of the Jones Polynomial for Multiple Crossing-Twisted Links

Let D be a general connected reduced alternating link diagram, C be the set of crossings of D and C′ be the nonempty subset of C. In this paper we first define a multiple crossing-twisted link family {D ⁿ (C′)|n=1,2,…} based on D and C′, which produces (2,2n+1)-torus knot family, the link family A _n defined in Chang and Shrock (Physica A 301:196–218, 2001) and the pretzel link family P(n,n,n) as special cases. Then by applying Beraha-Kahane-Weiss’s Theorem we prove that limits of zeros of Jones polynomials of {D ⁿ (C′)|n=1,2,…} are the unit circle |z|=1 (It is independent of the selections of D and C′) and several isolated limits, which can be determined by computing flow polynomials of subgraphs of G corresponding to D. Furthermore, we use the method of Brown and Hickman (Discrete Math. 242:17–30, 2002) to prove that, for any ε>0, all zeros of Jones polynomial of the link D ⁿ (C) lie inside the circle |z|=1+ε, provided that n is large enough. Our results extend results of F.Y. Wu, J. Wang, S.-C. Chang, R. Shrock and the present authors and refine partial result of A. Champanerkar and L. Kofman.     

The many vacua of gauged extended supergravities

A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical data rather than analytic results, it overcomes the previous limitation of only being able to find vacua with large residual unbroken gauge symmetry groups. The effectiveness of this method is demonstrated by applying it to the technically most challenging D ≥ 3 scalar potential—that of SO(8) × SO(8) gauged Chern–Simons Supergravity in D = 3. Extensive data on the properties of 99 different vacua (92 of them new) of this model are given. Furthermore, techniques are briefly discussed which should allow using this numerical information as an input to the construction of semi-automatic stringent analytic proofs on the locations and properties of vacua. It hence is argued that these combined techniques presumably are powerful enough to systematically map all the nontrivial vacua of every supergravity model.     

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

The (D+1)-dimensional (β,β′)-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk (J. Phys., A Math. Gen. 39, 10909, 2006), leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′=2β up to first order over deformation parameter β. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for b < \frac18m²c²\beta<\frac{1}{8m^{2}c^{2}} which leads to an isotropic minimal length in the interval 10⁻¹⁷ m<(ΔX ⁱ )₀<10⁻¹⁵ m. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.     

On ‘light’ fermions and proton stability in ‘big divisor’ D3/D7 large volume compactifications

Building on our earlier work (Misra and Shukla, Nucl. Phys. B 827:112, 2010; Phys. Lett. B 685:347–352, 2010), we show the possibility of generating “light” fermion mass scales of MeV–GeV range (possibly related to the first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-brane restricted to (in principle) stacks of fluxed D7-branes wrapping the “big” divisor Σ _B . This part of the paper is an expanded version of the latter half of Sect. 3 of a published short invited review (Misra, Mod. Phys. Lett. A 26:1, 2011) written by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, and we estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10⁶¹ years. Based on GLSM calculations in (Misra and Shukla, Nucl. Phys. B 827:112, 2010) for obtaining the geometric K?hler potential for the “big divisor,” using further the Donaldson’s algorithm, we also briefly discuss in the first of the two appendices the metric for the Swiss-Cheese Calabi–Yau used, which we obtain and which becomes Ricci flat in the large-volume limit.     

Novel domain wall and Minkowski vacua of D=9 maximal SO(2) gauged supergravity

We show that a generalised reduction of D=10 IIB supergravity leads, in a certain limit, to a maximally extended SO(2) gauged supergravity in D=9. We show the scalar potential of this model allows both Minkowski and a new type of domain wall solution to the Bogomol'nyi equations. We relate these vacua to type IIB D-branes.     

Black holes with metric and fields of the same form

We present two rotating black hole solutions with axion ξ, dilaton f{\phi} and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and applying the “Newman–Janis complex coordinate trick” we get a rotating metric g _μν with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric Q _E and magnetic Q _M . Then we find a solution of the equations of motion having this g _μν as metric. Our solution is asymptotically flat and has angular momentum J = M a, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics, the vector fields and the quantity l = x+ie^-2f{\lambda=\xi+ie^{-2\phi}} of our solutions and the solution of: Sen for Q _E , Sen for Q _E and Q _M , Kerr–Newman for Q _E and Q _M , Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstr?m, Schwarzschild are the same function of a, and two functions ρ ² = r(r + b) + a ² cos² θ and Δ = r(r + b) − 2Mr + a ² + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most physically interesting and well known solutions, are listed in an “Appendix”.     

D2O‐catalyzed proton transfer selectivity of 4 different NH protons in the same molecule

When N‐benzyl‐N′‐methylacetamidinium hydrochloride (pKa=11.8) is dissolved in D₂O/DCl(1 M), an equilibrium of 2 54:46 stereoisomers in an ~2:1 =(R)N^δ+H(D) D/H ratio is formed. Therefore, 2 R =N‐benzyl (E and Z) and 2 R =N‐methyl (E and Z) groups attached to the corresponding H(D) (Z and E) for a total of 8 ¹H‐NMR signals are observed. Consequently, their rates of H and D transfer to D₂O can be measured by means of the ¹H‐NMR broadness (line shape) of the =(R )N^δ+H doublets and =(R )N^δ+D broad singlets. Acidity selectivity is observed for both processes. In fact, the relative proton and deuterium transfer rates follow the acidity order: =(PhCH₂)N^δ+‐H(E) > =(PhCH₂)N^δ+‐H(Z) > =(Me)N^δ+‐H(E) > =(Me)N^δ+‐H(Z). Proton transfer rates are in the range of 8 to 0.5 s^‐1 with α = .92. This tendency is independently supported by the observed experimental chemical shift deuterium isotopic perturbation. The rate‐limiting step for proton exchange is the breaking of the hydrogen bond due to the fast amidine reprotonation (~10¹¹ s). =(R)N^δ+D/=(R)N^δ+H equilibration is reached at ~80 s, and it can be measured by the relative =(R) N^δ+H versus =(R) N^δ+D signal integrations. The equilibrium of the 4 =(R)N^δ+H(D) centers is shifted toward deuterium, but they are further shifted in the more basic centers. Equilibrium is completely shifted toward D in the 4 centers when OD^? contributes with the exchange process at pD > 3.     

Ehrenfest’s Paradox and Radial Electric Field in Quasi-Neutral Tokamak Plasma

A relation between physical consequences of the so-called Ehrenfest’s Paradox and the radial electric field E _r (r) in the classical quasi-neutral tokamak plasma is shown. Basic author’s approach to the relativistic nature of the tokamak E _r (r) has been described in Romannikov (J. Exp. Theor. Phys. 108:340–348, 2009). The experiment which can resolve the Ehrenfest’s Paradox is presented.     

Thermo-optical properties of pure and Yb-doped monoclinic KY(WO4)2 crystals

The thermo-optic coefficients, dn/dT, were determined for pure and Yb(20 at.%)-doped monoclinic KY(WO₄)₂ crystals for light polarized along the optical indicatrix axes (N _p,N _m and N _g) in the wavelength range of 0.36–1.06 μm by a laser beam deviation method. The absolute values of thermo-optic coefficients satisfy the relation |dn _p/dT|>|dn _g/dT|>|dn _m/dT| and increase with the wavelength increasing. In the long-wavelength range, all the dn/dT values are negative: dn _p/dT=−14.6, dn _m/dT=−8.9, dn _g/dT=−12.4 [10⁻⁶ K⁻¹] for pure KY(WO₄)₂ at 1.06 μm. The dependency of thermo-optic coefficients on the wavelength was modeled using an approach that takes into account contribution of volumetric thermal expansion and change of electronic bandgap with temperature. Large volumetric expansion of KY(WO₄)₂ plays a key role in the observed negative dn/dT values. Electronic bandgap and its temperature coefficient were determined for KY(WO₄)₂ crystals from thermo-optic dispersion curves as E _g=4.8–5.0 eV and −dE _g/dT=0.7–1.1×10⁻⁴ eV/K. Athermal propagation directions were calculated for KY(WO₄)₂ crystals at the wavelength of 1.06 μm for light polarizations E∥N _m and N _p.     

High-resolution infrared study of the 2ν3 (A1, E) and ν1 + ν3 (E) bands of NF3

The 2ν₃ overtone (A₁, E) and the ν₁ + ν₃ (E) combination bands of the oblate symmetric top ¹⁴NF₃ were studied by FTIR spectroscopy with a resolution of 2.5 × 10⁻³ cm⁻¹. Nearly 500 lines up to K_max/J_max = 30/43 were observed for the weak A₁ component reaching the v₃ = 2⁰ substate (1803.1302 cm⁻¹), the majority of which corresponded to reinforced K = 3p-type transitions. For the strong E component reaching the v₃ = 2^±2 substate (1810.4239 cm⁻¹), about 3550 transitions were assigned up to K_max/J_max = 65/69, favoring a clear observation of the ℓ(4, −2) and ℓ(4, 4) splittings within the kℓ = −2 and +4 sublevels, respectively. The two v₃ = 2 substates are linked by the ℓ(2, 2)- and ℓ(2, −1)-type interactions, providing severe crossings, respectively, at K′ = 6 and near K′ = 24 on the v₃ = 2⁺² side. A model working in the D-reduction and including all these ℓ-type interactions could reproduce together 3695 nonzero weighted experimental data (NZW) through 33 free parameters with a standard deviation of σ = 0.357 × 10⁻³  cm⁻¹. As for the ν₁ + ν₃ (E) combination band, about 3690 lines were assigned up to K_max/J_max = 45/55. Its v₁ = v₃ = 1 upper state (1931.577 5 cm⁻¹) was treated using the same model recently applied to the v₃ = 1 (E, 907.5413 cm⁻¹) state. It yielded 21 free parameters through 3282 NZW experimental data, adjusted with σ = 0.344 × 10⁻³  cm⁻¹ in the D-reduction. For the two excited states, the small and unobserved ℓ(0, 6) interaction was tested as useless. To confirm the adequacy of the vibrationally isolated models used, some other reductions of the Hamiltonian were tried. For the v₃ = 2 state, the D-, L-, and LD-reductions led to similar σ’s, while the Q one was not successful. For the v₁ = v₃ = 1 state, the D- and Q-reductions gave comparable σ’s, while the QD-reduction was not as good. The corresponding unitary equivalence relations are generally more nicely fulfilled for the v₃ = 2 state than for the v₁ = v₃ = 1 state. The three derivable anharmonicity constants in cm⁻¹ are x₃₃ = −4.1528, g₃₃ = +1.8235 and x₁₃ = −7.9652.     

Stability of a Model of Relativistic Quantum Electrodynamics

The relativistic “no pair” model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A– in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges ≤Z. If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground state energy E=−∞) if one uses the customary D(0) to define the electron space, but is stable (E > − const.(N+K)) if one uses D(A) itself (provided the fine structure constant α and Z are not too large). This result is extended to quantized fields here, and stability is proved for α= 1/137 and Z≤ 42. This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons. Received: 8 September 2001 / Accepted: 18 March 2002     

Structural properties of silver nanoparticle agglomerates based on transmission electron microscopy: relationship to particle mobility analysis

In this work, the structural properties of silver nanoparticle agglomerates generated using condensation and evaporation method in an electric tube furnace followed by a coagulation process are analyzed using Transmission Electron Microscopy (TEM). Agglomerates with mobility diameters of 80, 120, and 150 nm are sampled using the electrostatic method and then imaged by TEM. The primary particle diameter of silver agglomerates was 13.8 nm with a standard deviation of 2.5 nm. We obtained the relationship between the projected area equivalent diameter (d _pa) and the mobility diameter (d _m), i.e., d _pa = 0.92 ± 0.03 d _m for particles from 80 to 150 nm. We obtained fractal dimensions of silver agglomerates using three different methods: (1) D _f = 1.84 ± 0.03, 1.75 ± 0.06, and 1.74 ± 0.03 for d _m = 80, 120, and 150 nm, respectively from projected TEM images using a box counting algorithm; (2) fractal dimension (D _fL) = 1.47 based on maximum projected length from projected TEM images using an empirical equation proposed by Koylu et al. (1995) Combust Flame 100:621–633; and (3) mass fractal-like dimension (D _fm) = 1.71 theoretically derived from the mobility analysis proposed by Lall and Friedlander (2006) J Aerosol Sci 37:260–271. We also compared the number of primary particles in agglomerate and found that the number of primary particles obtained from the projected surface area using an empirical equation proposed by Koylu et al. (1995) Combust Flame 100:621–633 is larger than that from using the relationship, d _pa = 0.92 ± 0.03 d _m or from using the mobility analysis.     

Einstein Supergravity and New Twistor String Theories

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. The theories include one with the spectrum of N = 8 supergravity, another with the spectrum of N = 4 supergravity coupled to N = 4 super-Yang-Mills, and a family with N ≥ 0 supersymmetries with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills. The non-supersymmetric string with N = 0 gives self-dual gravity coupled to self-dual Yang-Mills and a scalar. A three-graviton amplitude is calculated for the N = 8 and N = 4 theories and shown to give a result consistent with the cubic interaction of Einstein supergravity.     

Optical properties of glasses in the Li2O–MoO3–P2O5 system

Glasses xLi₂O–(50-x)(MoO₃)₂–50P₂O₅ with x = 10, 20, 30, and 40 mol% were prepared and their optical and electrical properties were investigated. Analysis of the IR spectra revealed that the Li⁺ ions act as a glass modifier that enter the glass network by breaking up other linkages and creating non-bridging oxygens in the network. The optical absorption edge of the glasses was measured for specimens in the form of thin blown films and the optical absorption spectra of those were recorded in the range 200–800 nm. From the optical absorption edges studies, the optical band gap (E _opt) and the Urbach energy (E _e) values have been evaluated by following the available semi-empirical theories. The linear variation of (αhν)^1/2 with hν, is taken as evidence of indirect interband transitions. The E _opt values were found to decrease with increasing Li₂O content by causing increase in the number of non-bridging oxygens in network. The Urbach tail analysis gives the width of localized states between 0.48 and 0.74 eV.     

Integral energy spectrum of primary cosmic rays at high energies

The integral energy spectrum of primary cosmic rays has been obtained. In the energy range (2.4×10³−1.1×10⁵ GeV), the spectrum of all nuclei is consistent with a power law of indexγ=1.55±0.06 and the flux of all nuclei is:N(⩾E ₀)⋍(5.1±1.8)×10⁻¹×E ₀ ^−1.55 particles/cm² sterad. sec., whereE ₀ is in GeV. The spectrum of primaryα-particles in the energy range (4.4×10³−4.8×10⁴) GeV is also consistent with a power law of indexγ=1.71±0.12 and the flux is:N(⩾E ₀)=(4.2±1.4)×10⁻¹×E ₀ ^−1.71 , particles per cm² sterad. sec, whereE ₀ is in GeV.     

Mobility–diffusivity relationship for heavily doped organic semiconductors

The relationship between the diffusivity D _n and the mobility μ _n of chemically doped organic n-type semiconductors exhibiting a disordered band structure is presented. These semiconductors have a Gaussian-type density of states. So, calculations have been performed to elucidate the dependence of D _n /μ _n on the various parameters of this Gaussian density of states. Y. Roichman and N. Tessler (Appl. Phys. Lett. 80:1948, 2002), and subsequently Peng et al. (Appl. Phys. A 86:225, 2007), conducted numerical simulations to study this diffusivity–mobility relationship in organic semiconductors. However, almost all other previous studies of the diffusivity–mobility relationship for inorganic semiconductors are based on Fermi–Dirac integrals. An analytical formulation has therefore been developed for the diffusivity/mobility relationship for organic semiconductors based on Fermi–Dirac integrals. The D _n /μ _n relationship is general enough to be applicable to both non-degenerate and degenerate organic semiconductors. It may be an important tool to study electrical transport in these semiconductors.