Open Quantum Random Walks with Decoherence on Coins with n Degrees of Freedom

In this paper we define a new type of decoherent quantum random walk with parameter 0≤p≤1, which becomes a unitary quantum random walk (UQRW) when p=0 and an open quantum random walk (OQRW) when p=1, respectively. We call this process a partially open quantum random walk (POQRW). We study the limiting distribution of a POQRW on Z ¹ subject to decoherence on coins with n degrees of freedom. The limiting distribution of the POQRW converges to a convex combination of normal distributions, under an eigenvalue condition. A Perron-Frobenius type of theorem is established to determine whether or not a POQRW satisfies the eigenvalue condition. Moreover, we explicitly compute the limiting distributions of characteristic equations of the position probability functions when n=2 and 3.     

Influence of differential stress on the galvanic interaction of pyrite–chalcopyrite

The effect of stress action on pyrite–chalcopyrite galvanic corrosion was investigated using polarization curves and electrochemical impedance spectroscopy (EIS) measurements. When stress increased from 0 to 4?×?10⁵ Pa, the corrosion current density of pyrite–chalcopyrite increased from 5.678 to 6.719 μA cm^?2, and the corrosion potential decreased from 281.634 to 270.187 mV, accompanied by a decrease in polarization resistance from 25.09 to 23.79 Ω·cm². EIS results show there have three time constants in the Nyquist diagrams, which indicated the presence of different steps during the corrosion process. Stress dramatically enhanced pyrite–chalcopyrite galvanic corrosion by affecting the Cu_1???x Fe_1???y S₂ film and the double layer, whereas had little impact on the adsorption species. When the stress changed from 0 to 4?×?10⁵ Pa, the pore resistance and capacitance of the Cu_1???x Fe_1???y S₂ film, R _p and Q _p, changed by 25.72 and 72.28 %, respectively. The adsorption species resistance, R _sl, and capacitance, Q _sl, only changed by 9.77 and 2.31 %, respectively.     

Region-Specific Susceptibilities to Cuprizone-Induced Demyelination of C57BL/6 Mouse: In vivo T2WI and DTI Studies at 7.0T

The cuprizone (CPZ) mouse model of demyelination was recognized and used to explore multiple sclerosis (MS)-like brain lesions. In this study, we assessed CPZ-treated mice using T₂-weighted imaging and diffusion tensor imaging (DTI). C57BL/6 mice treated with 2 weeks of 0.2 % CPZ-containing diet (n = 10) and regular chow diet (n = 10) were scanned with a 7.0 T MRI scanner (Agilent, USA), respectively, using fast spin-echo and fast spin-echo DTI sequences. The normalized T₂ signal intensity (normalized to the cerebrospinal fluid) was calculated and fractional anisotropy (FA value), mean diffusivity, axial diffusivity and radial diffusivity were measured in the brain region of the cerebral cortex (CTX), caudate putamen (CP), hippocampus (HP) and thalamus (TH). Compared with controls, increased normalized T₂ signal intensities and reduced FA values (p < 0.05) were observed in the CTX, HP and CP (p < 0.01), but not in TH in cuprizone-fed mice. In the regions of reduced FA values, an increase in mean diffusivity (p < 0.05) and radial diffusivity (p < 0.05) was also found. Significant decreased axial diffusivity was only observed in CTX (p < 0.05). DTI is sensitive to detecting cuprizone-induced demyelination of C57BL/6 mice. This study suggests that CTX, HP and CP are more susceptible to cuprizone-induced demyelination than TH. Our results also indicate that the decrease of FA value may be more likely due to increased radial diffusivity.     

Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States

We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in \({(\mathbb {C}^d)^{\otimes k}}\), where k and p/d ^k are fixed while d → ∞. When k = 1, the Mar?enko-Pastur law determines (up to small corrections) not only the largest eigenvalue (\({(1+\sqrt{p/d^k})^2}\)) but the smallest eigenvalue \({(\min(0,1-\sqrt{p/d^k})^2)}\) and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately \({(1+\sqrt{p/d^k})^2}\) and the spectral density approaches that of the Mar?enko-Pastur law, generalizing the random matrix theory result to the random tensor case. Our bound on the largest eigenvalue has implications both for sampling from a particular heavy-tailed distribution and for a recently proposed quantum data-hiding and correlation-locking scheme due to Leung and Winter.Since the matrices we consider have neither independent entries nor unitary invariance, we need to develop new techniques for their analysis. The main contribution of this paper is to give three different methods for analyzing mixtures of random product states: a diagrammatic approach based on Gaussian integrals, a combinatorial method that looks at the cycle decompositions of permutations and a recursive method that uses a variant of the Schwinger-Dyson equations.     

Collisional-radiative model for non-Maxwellian inductively coupled argon plasmas using detailed fine-structure relativistic distorted-wave cross sections

Our recently developed collisional-radiative model which included fine-structure cross sections calculated with a fully relativistic distorted-wave method [R.K. Gangwar, L. Sharma, R. Srivastava, A.D. Stauffer, J. Appl. Phys. 111, 053307 (2012)] has been extended to study non-Maxwellian inductively coupled argon plasmas. We have added more processes to our earlier collisional-radiative model by further incorporating relativistic distorted-wave electron impact cross sections from the 3p ⁵4sJ = 0, 2 metastable states, (1s ₃, 1s ₅ in Paschen’s notation) to the 3p ⁵5p (3p _i ) excited states. The population of various excited levels at different pressures in the range of 1–25 mTorr for an inductively coupled argon plasma have been calculated and compared with the recent optical absorption spectroscopy measurements as well as emission model results of Boffard et al. [Plasma Sources Sci. Technol. 19, 065001 (2010)]. We have also calculated the intensities of two emission lines, 420.1 nm (3p ₉ → 1s ₅) and 419.8 nm (3p ₅ → 1s ₄) and compared with measured intensities reported by Boffard et al. [J. Phys. D 45, 045201 (2012)]. Our results are in good agreement with the measurements.     

Variational calculations on the energy levels of graphene quantum antidots

The critical properties of the two-dimensional Ising and Blume-Capel model on directedsmall-world lattices with quenched connectivity disorder are investigated. The disordered system is simulated by applying the Monte Carlo method with heat bath update algorithm and histogram re-weighting techniques. The critical temperature, as well as the critical exponents are obtained. For both models the critical parameters have been obtained for several values of the rewiring probability p. It is found that these disorder systems do not belong to the same universality class as two-dimensional ferromagnetic model on regular lattices. In particular, the Blume-Capel model, with zero crystal field interaction, on a directedsmall-world lattice presents a second-order phase transition for p < p _c , and a first-order phase transition for p > p _c , where p _c  ≈ 0.25. The critical exponents for p < p _c are different from those of the same model on a regular lattice, but are identical to the exponents of the Ising model on directedsmall-world lattice.     

Single intermediate-band solar cells of InGaN/InN quantum dot supracrystals

We measured the elemental mappings in dental enamel of Gigantopithecus blacki (n=3) using synchrotron radiation X-ray fluorescence (SRXRF) to understand the dietary variation during the time of tooth eruption. In order to account for the effects of diagenesis on the variation of elements in these fossil teeth, we compared the Fe and Mn elemental distribution and levels in dental enamel of G. blacki with that of a single modern pig tooth and found no differences. The observation of the variations of Sr, Ca and RE (rare earth elements) distribution in the incremental lines reveals that the plant foods utilized by G. blacki from the early Pleistocene or the middle Pleistocene had varied during the formation of dental enamel, possibly caused by the change of living environment or food resources. The variations of elemental distribution in different incremental lines are very promising to understand the nutritional and physical stress of G. blacki during the tooth eruption and environmental adaptations.     

Three-Body Treatment of the pep Reaction in the Sun

The experimental result of the neutrino flux produced by the p + p + e → d + ν _e reaction (pep) in the Sun at 1 AU was announced for the first time in 2012 by the Borexino collaboration. We use the three-body model for the proton–proton–electron system in the initial state for the calculation of the rate of the pep reaction with various types of nucleon–nucleon potentials.     

Forming metastable carbon-rich anions in planetary atmospheres: the case of diacetylene

Alignment of the L ₃ ? (J = 3 / 2) subshell vacancy states in the Au, Bi, Th and U elements following photoinisation have been investigated through angular distribution measurements of subsequently emitted L ₃ subshell X-rays. The 59.54 keV unpolarised γ-rays from the ²⁴¹Am radioactive point-source were used to ionize the target and the subsequently emitted L X-rays were measured using an HPGe detector. The improved experimental procedure along with correct evaluation scheme permits straight-forward method for investigating anisotropy in photo-excited L X-ray emission. The efficiency of the detector and the absorption correction for the emitted L X-rays in the target remain fairly constant as the target-detector assemblage remains undisturbed in the present measurements at various angles. Isotropically emitted L ₁ subshell (J = 1 / 2) X-rays measured simultaneously were used to normalize the L X-ray spectra taken at different emission angles. The present measurements clearly support small theoretical predicted values of the alignment parameter; however, it is difficult to infer regarding the predicted anisotropic trends. The angular distribution measurements for the L ₃ subshell X-ray emission were also performed by placing the target in magnetic field  ～ 0.6 T. The earlier reported large anisotropy in angular distribution of the emitted L ₃ subshell X-rays and significant effect of external magnetic field on the angular distribution are ruled out.     

Study of the Three-Nucleon Force Effects in the 2H(p, n) Breakup Reaction at 170 MeV

For the study of three nucleon force (3NF) effects in the intermediate energy region, the differential cross sections and the vector analyzing power A _y were measured for the ²H(p, n) inclusive breakup reaction at 170 MeV. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD₂) target and the energy of scattered neutrons were deduce by TOF method. The data was compared with the results of the Faddeev calculations with and without 3NFs. Concerning about the differential cross sections, we can see large discrepancies between the data and the calculations in the region where the energies of scattered neutrons are low, which are similar to the results of the ²H(p, p) inclusive breakup reaction at 250 MeV.     

Correlation between Hepatic Fat Content Using 3-Echo 3-D Dixon Method and Intravoxel Incoherent Motion (IVIM) Perfusion MR Imaging

Fat accumulates as droplets in the hepatocyte swelling, distortion of microcirculatory anatomy and compression of sinus. This study aims to investigate the correlation between the T2*-corrected fat fraction (FF) value acquired via gradient echo with a low flip angle and parenchymal pseudorandom blood perfusion (P _fraction), microcirculation (D _fast), and slow component of diffusion (D _slow), acquired via intravoxel incoherent motion (IVIM), and to investigate the blood microcirculation and diffusion components of liver parenchyma, according to fat deposition. A total of 126 patients underwent 3-T magnetic resonance imaging, including a 3-echo three-dimensional (3-D) gradient echo sequence with T2*-corrected Dixon reconstruction and IVIM sequence. Pearson’s correlation analysis was conducted to investigate the correlation of the FF obtained via the Dixon method with the apparent diffusion coefficient (ADC), D _slow, P _fraction, and D _fast obtained via IVIM. Correlation analysis was also conducted for the IVIM mapping images. A confidence level of p < 0.05 was set. A negative correlation was found between the T2*-corrected FF acquired using the 3-echo 3-D Dixon method and D _slow acquired via IVIM (r = ?0.181, p < 0.05). It was likely due to the increased extracellular collagen deposition and increased intracellular fat droplets during the progression of liver fibrosis.     

Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0

This paper investigates infinite-time spreading and finite-time blow-up for the Keller-Segel system. For 0 < m ≤  2 ? 2 / d, the L ^p space for both dynamic and steady solutions are detected with ${p:=\frac{d(2-m)}{2} }$ p : = d ( 2 - m ) 2 . Firstly, the global existence of the weak solution is proved for small initial data in L ^p . Moreover, when m > 1 ? 2 / d, the weak solution preserves mass and satisfies the hyper-contractive estimates in L ^q for any p < q < ∞. Furthermore, for slow diffusion 1 < m ≤  2 ? 2/d, this weak solution is also a weak entropy solution which blows up at finite time provided by the initial negative free energy. For m > 2 ? 2/d, the hyper-contractive estimates are also obtained. Finally, we focus on the L ^p norm of the steady solutions, it is shown that the energy critical exponent m = 2d/(d + 2) is the critical exponent separating finite L ^p norm and infinite L ^p norm for the steady state solutions.     

Effectiveness Evaluation of the Fat Percentage Determination in Multi-Echo T2-Corrected Single-Voxel Spectroscopy by Comparing the 3-Point Dixon and the 6-Point Interference Dixon Techniques

This study compared fat percentage in the HISTO method and chemical-shift imaging method, a 3-echo 3D gradient echo sequence with a T2*-corrected Dixon (3-point Dixon) and 6-echo interference Dixon magnetic resonance (MR) imaging (6-point Dixon) method, to evaluate clinical significance of fatty liver quantification by multi-echo T2*-corrected single-voxel spectroscopy Histo (HISTO). A total of 21 liver donors underwent MR imaging examination. The 3-T MR system (Siemens Healthcare Tim Verio, Erlangen, Germany) was used for all studies. For fat percentage evaluations, a 3-echo 3D gradient echo sequence with T2*-corrected Dixon (3-point Dixon) and 6-Echo Interference Dixon (6-point Dixon) pulse sequences, including HISTO, were applied in sequence. Using fat percentages obtained from each pulse sequence, levels of fatty liver were classified as: non-fatty liver, <5 %; mild fatty liver, >5 but <31 %; and severe fatty liver, >31 %. The correlation between methods was calculated with a correlation coefficient (R ²): HISTO and 3-point Dixon, 0.936 (p < 0.001); HISTO and 6-point Dixon, 0.944 (p < 0.001); and 3-point Dixon and 6-point Dixon, 0.984 (p < 0.001). The HISTO, which was used to investigate fat percentages after T2* correction, showed a high correlation with 3-point Dixon and 6-point Dixon, suggesting that the multi-echo method is useful for accurately determining fat percentages.     

On Conjectures of A. Eremenko and A. Gabrielov for Quasi-Exactly Solvable Quartic

We study polynomials p(x) satisfying a differential equation of the form p′′?h′p′ + Hp = 0, where h = x ³/3 + ax and H is a polynomial. We prove a conjecture of A. Eremenko and A. Gabrielov.     

Evolution of a Modified Binomial Random Graph by Agglomeration

In the classical Erd?s–Rényi random graph G(n, p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n, p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the Erd?s-Rényi random graph G(n, p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G(n, p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G(n, p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real-world applications.     

Efimov Spectrum in Bosonic Systems with Increasing Number of Particles

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length a is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the N-body system by analysing the spectrum of N identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as \({E_N^0/E_3^0}\) and \({E_N^1/E_N^0}\) , with \({E_N^i}\) being the energy of the ground (i = 0) and first-excited (i = 1) state of the system, for \({N \leq16}\) . We discuss the extension of the Efimov radial law, derived by Efimov for N = 3, to general N.     

Setup and performance of a streak camera apparatus for transient absorption measurements in the ns to ms range

We describe the setup and performance of an apparatus for simultaneous time- and spectrally resolved measurements of transient absorption. The key component in this apparatus is a streak camera, yielding, for every excitation of the sample, a two-dimensional data array with 512 × 512 data points. The apparatus covers the spectral range 350–750 nm and time windows ranging from 500 ns up to 10 ms. Due to the large dynamic range of the streak camera of 10,000:1 we obtain a multiplex factor of more than 100 compared with sequential measurements at individual wavelengths. This makes it possible to extract the maximum amount of information from small amounts of sample, e.g. light-sensitive proteins. We show that already a single pump probe pulse sequence can yield useful spectra in a 20-μs time range, and that 10 pump-probe pulse sequences yield good time constants from a global lifetime analysis. An iterative method is presented for the treatment of artifacts due to scattered excitation laser light or strong fluorescence. As an alternative to a global lifetime analysis we propose a maximum entropy-based inverse Laplace transform for analysis of the data. This results in a wavelength-dependent distribution of amplitudes p(k, λ) for all rate constants k accessible with a given time window. This analysis is model free and yields a direct visual evaluation of the uncertainties in the rate constants.     

A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity

We revisit and prove some convexity inequalities for trace functions conjectured in this paper’s antecedent. The main functional considered is

$ \Phi_{p,q} (A_1,\, A_2, \ldots, A_m) = \left({\rm Tr}\left[\left( \, {\sum\limits_{j=1}^m A_j^p } \, \right) ^{q/p} \right] \right)^{1/q} $

for m positive definite operators A _j . In our earlier paper, we only considered the case q = 1 and proved the concavity of Φ _p,1 for 0 < p ≤ 1 and the convexity for p = 2. We conjectured the convexity of Φ _p,1 for 1 < p < 2. Here we not only settle the unresolved case of joint convexity for 1 ≤ p ≤ 2, we are also able to include the parameter q ≥ 1 and still retain the convexity. Among other things this leads to a definition of an L ^q (L ^p ) norm for operators when 1 ≤ p ≤ 2 and a Minkowski inequality for operators on a tensor product of three Hilbert spaces – which leads to another proof of strong subadditivity of entropy. We also prove convexity/concavity properties of some other, related functionals.

     

Measurement of the 2H(p,n) Breakup Reaction at 170 MeV and the Three-Nucleon Force Effects

The effects of three nucleon force (3NF) have been actively studied via the nucleon–deuteron (Nd) scattering states. The differential cross sections and the vector analyzing powers A _y of the ²H(p, n) inclusive breakup reaction at 170 MeV were measured for the study of 3NF effects in the intermediate energy region. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD₂) target and the energy of scattered neutrons were measured by using TOF method. The data were compared with the Faddeev calculations based on modern nucleon–nucleon (NN) forces with and without the 3NF. Concerning the differential cross sections, we can see large discrepancies between the data and the calculations in the region of scattered neutron energies are low, which is similar to the results of the ²H(p, p) inclusive breakup reaction at 250 MeV.     

Electrical properties, structure, and surface morphology of poly(p-xylylene)–silver nanocomposites synthesized by low-temperature vapor deposition polymerization

The crystalline structure, surface morphology, electrical, and optical properties of thin films of nanocomposites consisting of silver nanoparticles embedded in poly(p-xylylene) matrix prepared by low-temperature vapor deposition polymerization were studied. Depending on the filler content, the average size of silver nanoparticles varied from 2 to 5 nm for nanocomposites with 2 and 12 vol.% of silver, correspondingly. The optical adsorption in the visible region due to surface plasmon resonance also exhibited a clear correlation from silver content, revealing a red shift of the adsorption peak with the increase of the metal concentration. The temperature dependences of the dc resistance of pure p-xylylene condensate and p-xylylene–silver cocondensates during polymerization as well as temperature dependences of the formed poly(p-xylylene)–silver nanocomposites were examined. The observed variation of the temperature dependences of electrical resistance as a function of silver concentration are attributed to different conduction mechanisms and correlated with the structure of the composites. The wide-angle X-ray scattering and AFM measurements consistently show a strong effect of silver content on the nanocomposite structure. The evolution of the size of silver nanoparticles by thermal annealing was demonstrated.