Joint System Quantum Descriptions Arising from Local Quantumness

We study the entropy flux in the stationary state of a finite one-dimensional sample ${\mathcal{S}}$ connected at its left and right ends to two infinitely extended reservoirs ${\mathcal{R}_{l/r}}$ at distinct (inverse) temperatures ${\beta_{l/r}}$ and chemical potentials ${\mu_{l/r}}$ . The sample is a free lattice Fermi gas confined to a box [0, L] with energy operator ${h_{\mathcal{S}, L}= - \Delta + v}$ . The Landauer-Büttiker formula expresses the steady state entropy flux in the coupled system ${\mathcal{R}_l + \mathcal{S} + \mathcal{R}_r}$ in terms of scattering data. We study the behaviour of this steady state entropy flux in the limit ${L \to \infty}$ and relate persistence of transport to norm bounds on the transfer matrices of the limiting half-line Schrödinger operator ${h_\mathcal{S}}$ .     

Dirac multimode ket-bra operators’ \mathfrak{Q}-ordered and \mathfrak{P}-ordered integration theory and general squeezing operator

We develop quantum mechanical Dirac ket-bra operator’s integration theory in $\mathfrak{Q}$ -ordering or $\mathfrak{P}$ -ordering to multimode case, where $\mathfrak{Q}$ -ordering means all Qs are to the left of all Ps and $\mathfrak{P}$ -ordering means all Ps are to the left of all Qs. As their applications, we derive $\mathfrak{Q}$ -ordered and $\mathfrak{P}$ -ordered expansion formulas of multimode exponential operator $e^{ - iP_l \Lambda _{lk} Q_k } $ . Application of the new formula in finding new general squeezing operators is demonstrated. The general exponential operator for coordinate representation transformation $\left| {\left. {\left( {_{q_2 }^{q_1 } } \right)} \right\rangle \to } \right|\left. {\left( {_{CD}^{AB} } \right)\left( {_{q_2 }^{q_1 } } \right)} \right\rangle $ is also derived. In this way, much more correpondence relations between classical coordinate transformations and their quantum mechanical images can be revealed.     

Towards Asymptotic Completeness of Two-Particle Scattering in Local Relativistic QFT

We consider the problem of existence of asymptotic observables in local relativistic theories of massive particles. Let ${\tilde{p}_1}$ and ${\tilde{p}_2}$ be two energy-momentum vectors of a massive particle and let ${\Delta}$ be a small neighbourhood of ${\tilde{p}_1 + \tilde{p}_2}$ . We construct asymptotic observables (two-particle Araki–Haag detectors), sensitive to neutral particles of energy-momenta in small neighbourhoods of ${\tilde{p}_1}$ and ${\tilde{p}_2}$ . We show that these asymptotic observables exist, as strong limits of their approximating sequences, on all physical states from the spectral subspace of ${\Delta}$ . Moreover, the linear span of the ranges of all such asymptotic observables coincides with the subspace of two-particle Haag–Ruelle scattering states with total energy-momenta in ${\Delta}$ . The result holds under very general conditions which are satisfied, for example, in ${\lambda{\phi}_{2}^{4}}$ . The proof of convergence relies on a variant of the phase-space propagation estimate of Graf.     

The Refined BPS Index from Stable Pair Invariants

A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact Calabi–Yau spaces is introduced based on a virtual Bialynicki-Birula decomposition with respect to a ${\mathbb{C}^{*}}$ action on the stable pair moduli space, or alternatively the equivariant index of Nekrasov and Okounkov. This effectively calculates the refined index for M-theory reduced on these Calabi–Yau geometries. Based on physical expectations we propose a product formula for the refined invariants extending the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local ${\mathbb{P}^1}$ . We explicitly compute refined invariants in low degree for local ${\mathbb{P}^2}$ and local ${\mathbb{P}^1\,\times\,\mathbb{P}^1}$ and check that they agree with the predictions of the direct integration of the generalized holomorphic anomaly and with the product formula. The modularity of the expressions obtained in the direct integration approach allows us to relate the generating function of refined PT invariants on appropriate geometries to Nekrasov’s partition function and a refinement of Chern–Simons theory on a lens space. We also relate our product formula to wall crossing.     

Statistics of directed self-avoiding walks on percolation clusters at the percolation threshold

We here study directed self-avoiding walks on site diluted square lattice at the percolation threshold by two parameter real space renormalization group method. We found \(v_\parallel ^{p_c } = 1.00\) and \(v_ \bot ^{p_c } = 0.4348\) from cell-to-cell transformation method. This \(v_ \bot ^{p_c } \) value is then compared with the modified Alexander-Orbach formula that \(v_ \bot ^{p_c } = {{d_S } \mathord{\left/ {\vphantom {{d_S } {2d_L }}} \right. \kern-0em} {2d_L }}\) whered _s is the fracton dimension andd _L is the spreading dimension of the infinite directed percolation cluster.     

Analysis of the \frac{1} {2}^ - and \frac{3} {2}^ - heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the $\frac{1} {2}^ -$ and $\frac{3} {2}^ -$ heavy and doubly heavy baryon states $\Sigma _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi '_Q \left( {\frac{1} {2}^ - } \right)$ , $\Omega _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Omega _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Sigma _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Omega _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ and $\Omega _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ by subtracting the contributions from the corresponding $\frac{1} {2}^ +$ and $\frac{3} {2}^ +$ heavy and doubly heavy baryon states with the QCD sum rules in a systematic way, and make reasonable predictions for their masses.     

Influence of assortativity and degree-preserving rewiring on the spectra of networks

Newman’s measure for (dis)assortativity, the linear degree correlation coefficient $\rho _{D}$ , is reformulated in terms of the total number N _k of walks in the graph with k hops. This reformulation allows us to derive a new formula from which a degree-preserving rewiring algorithm is deduced, that, in each rewiring step, either increases or decreases $\rho _{D}$ conform our desired objective. Spectral metrics (eigenvalues of graph-related matrices), especially, the largest eigenvalue $\lambda _{1}$ of the adjacency matrix and the algebraic connectivity $\mu _{N-1}$ (second-smallest eigenvalue of the Laplacian) are powerful characterizers of dynamic processes on networks such as virus spreading and synchronization processes. We present various lower bounds for the largest eigenvalue $\lambda _{1}$ of the adjacency matrix and we show, apart from some classes of graphs such as regular graphs or bipartite graphs, that the lower bounds for $\lambda _{1}$ increase with $\rho _{D}$ . A new upper bound for the algebraic connectivity $\mu _{N-1}$ decreases with $\rho _{D}$ . Applying the degree-preserving rewiring algorithm to various real-world networks illustrates that (a) assortative degree-preserving rewiring increases $\lambda _{1}$ , but decreases $\mu _{N-1}$ , even leading to disconnectivity of the networks in many disjoint clusters and that (b) disassortative degree-preserving rewiring decreases $\lambda _{1}$ , but increases the algebraic connectivity, at least in the initial rewirings.     

Gauge Theories on ALE Space and Super Liouville Correlation Functions

We present a relation between ${\mathcal{N}=2}$ quiver gauge theories on the ALE space ${\mathcal{O}_{\mathbb{P}^1}(-2)}$ and correlators of ${\mathcal{N}=1}$ super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the ${\mathcal{N}=2^*}$ instanton partition function is given by the product of the character of ${\widehat{SU}(2)_2}$ times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.     

Spectroscopic properties of Ho 3 + -doped K–Sr–Al phosphate glasses

Trivalent holmium-doped K–Sr–Al phosphate glasses ( $\mathrm{P}_{2}\mathrm{O}_{5}$ – $\mathrm{K}_{2}\mathrm{O}$ –SrO– $\mathrm{Al}_{2}\mathrm{O}_{3}$ – $\mathrm{Ho}_{2}\mathrm{O}_{3}$ ) were prepared, and their spectroscopic properties have been evaluated using absorption, emission, and excitation measurements. The Judd–Ofelt theory has been used to derive spectral intensities of various absorption bands from measured absorption spectrum of 1.0 mol% $\mathrm{Ho}_{2}\mathrm{O}_{3}$ -doped K–Sr–Al phosphate glass. The Judd–Ofelt intensity parameters ( $\varOmega_{\lambda}$ , $\times10^{-20}~\mathrm{cm}^{2}$ ) have been determined of the order of $\varOmega_{2} = 11.39$ , $\varOmega_{4} = 3.59$ , and $\varOmega_{6} = 2.92$ , which in turn used to derive radiative properties such as radiative transition probability, radiative lifetime, branching ratios, etc. for excited states of $\mathrm{Ho}^{3+}$ ions. The radiative lifetimes for the ${}^{5}F_{4}$ , ${}^{5}S_{2}$ , and ${}^{5}F_{5}$ levels of $\mathrm{Ho}^{3+}$ ions are found to be 169, 296, and 317 μs, respectively. The stimulated emission cross-section for 2.05-μm emission was calculated by the McCumber theory and found to be $9.3\times10^{-2 1}~\mathrm{cm}^{2}$ . The wavelength-dependent gain coefficient with population inversion rate has been evaluated. The results obtained in the titled glasses are discussed systematically and compared with other $\mathrm{Ho}^{3+}$ -doped systems to assess the possibility for visible and infrared device applications.     

Mössbauer spectroscopy in the investigation of new mineral–related materials

New materials based on the composition of the mineral schafarzikite, FeSb $_{2}\textit {O}_{4}$ , have been synthesised. $^{57}$ Fe- and $^{121}$ Sb- Mössbauer spectroscopy shows that iron is present as Fe $^{2+}$ and that antimony is present as Sb $^{3+}$ . The presence of Pb $^{2+}$ on the antimony sites in materials of composition FeSb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ induces partial oxidation of Fe $^{2+}_{}$ to Fe $^{3+}$ . The quasi-one-dimensional magnetic structure of schafarzikite is retained in FeSb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ and gives rise to weakly coupled non-magnetic Fe $^{2+}$ ions coexisting with Fe $^{3+}$ ions in a magnetically ordered state. A similar model can be applied to account for the spectra recorded from the compound Co $_{0.5}$ Fe $_{0.5}$ Sb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ .     

Local structure of Fe-doped In 2 O 3 films investigated by X-ray absorption fine structure spectroscopy

$(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ $(x=0.07, 0.09, 0.16, 0.22, 0.31)$ films were deposited on Si (100) substrates by RF-magnetron sputtering technique. The influence of Fe doping on the local structure of films was investigated by X-ray absorption spectroscopy (XAS) at Fe K-edge and L-edge. For the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ films with $x=0.07, 0.09 \mbox{ and } 0.16$ , Fe ions dissolve into $\mathrm{In}_{2}\mathrm{O}_{3}$ and substitute for $\mathrm{In}^{3+}$ sites with a mixed-valence state ( $\mathrm{Fe}^{2+}/\mathrm{Fe}^{3+}$ ) of Fe ions. However, a secondary phase of Fe metal clusters is formed in the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ films with $x=0.22 \mbox{ and } 0.31$ . The qualitative analyses of Fe-K edge extended X-ray absorption fine structure (EXAFS) reveal that the Fe–O bond length shortens and the corresponding Debye–Waller factor ( $\sigma^{2}$ ) increases with the increase of Fe concentration, indicating the relaxation of oxygen environment of Fe ions upon substitution. The anomalously large structural disorder and very short Fe–O distance are also observed in the films with high Fe concentration. Linear combination fittings at Fe L-edge further confirm the coexistence of $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ with a ratio of ${\sim}3:2$ ( $\mathrm{Fe}^{2+}: \mathrm{Fe}^{3+}$ ) for the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ film with $x=0.16$ . However, a significant fraction ( ${\sim}40~\mbox{at\%}$ ) of the Fe metal clusters is found in the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ film with $x=0.31$ .     

On Dirichlet-to-Neumann Maps, Nonlocal Interactions, and Some Applications to Fredholm Determinants

We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrödinger operators describing nonlocal interactions in ${L^2(\Omega; d^n x)}$ , where ${\Omega \subset \mathbb{R}^n}$ , ${n\in\mathbb{N}}$ , ${n\geq 2}$ , are open sets with a compact, nonempty boundary ${\partial\Omega}$ satisfying certain regularity conditions. As an application we describe a reduction of a certain ratio of Fredholm perturbation determinants associated with operators in ${L^2(\Omega; d^{n} x)}$ to Fredholm perturbation determinants associated with operators in ${L^2(\partial\Omega; d^{n-1} \sigma)}$ , ${n\in\mathbb{N}}$ , ${n\geq 2}$ . This leads to an extension of a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with a Schrödinger operator on the half-line ${(0,\infty)}$ , in the case of local interactions, to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation.     

Preliminary studies of the Raman spectra of \hbox {Ag}_{2}\hbox {Te}\hbox { and }\hbox {Ag}_{5}\hbox {Te}_{3}

The theoretical calculations indicated that the monoclinic low-temperature phase of silver telluride $(\upbeta \hbox {-Ag}_{2}\hbox {Te})$ is a new binary topological insulator with highly anisotropic single Dirac cone surface. We obtained $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ crystal ingots containing few grains by the Bridgman method. We also deposited thin films of tellurium, $\hbox {Ag}_{5}\hbox {Te}_{3}\hbox { and }(\hbox {Te+Ag}_{5}\hbox {Te}_{3})$ by thermal evaporation method. The Raman spectra of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ were measured at three excitation wave lengths: 633, 515 and 488 nm. The Raman active modes of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ are situated at frequencies below 300  $\hbox {cm}^{-1}$ while vibrations of other phases appear at higher frequencies.     

Quasi solid state dye-sensitized solar cells based on polyvinyl alcohol (PVA) electrolytes containing \mathbf{I}^{\mathbf{-}}/\mathbf{I}_{\mathbf{3}}^{\mathbf{-}} redox couple

Quasi solid state dye-sensitized solar cells (DSSCs) have been fabricated with electrolytes containing $\text{ I }^{-}/\text{ I }_{3}^{-}$ redox couple using 80 % hydrolyzed polyvinyl alcohol (PVA) doped with potassium iodide (KI) and a mixture of potassium iodide and tetrapropyl ammonium iodide ( $\text{ Pr }_{4}\text{ NI }$ ) salts. The quasi solid state gel polymer electrolytes were prepared using 1:1 ethylene carbonate (EC):propylene carbonate (PC) mixture. The solar cells have the structure of ITO/ $\text{ TiO }_{2}$ /N3-Dye/electrolyte/Pt/ITO. The conductivity of the electrolytes has been calculated from the bulk resistance value determined using the electrochemical impedance spectroscopy. The performance of the DSSCs has been studied by varying the concentration of the doping salts in the electrolyte and incident light intensity. The DSSC fabricated with the KI salt electrolyte containing 9.9 wt% PVA, 39.6 wt% EC, 39.6 wt% PC, 10.9 wt% KI $(+\text{ I }_{2})$ exhibited the best power conversion efficiency of 1.97 %. However, the DSSC with a double-salt electrolyte containing 9.9 wt% PVA: 39.6 wt% EC: 39.6 wt% PC: (6.5 wt% KI: 4.4 wt% $\text{ Pr }_{4}\text{ NI }$ ) ( $+\text{ I }_{2}$ ) exhibited a higher efficiency of 3.27% under $100 \text{ mW/cm }^{2}$ light intensity. The efficiency of this cell increased to 4.59 % under dimmer light of intensity of $54 \text{ mW/cm }^{2}$ .     

Finite W-Superalgebras and Truncated Super Yangians

Let ${Y_{m|n}^{\ell}}$ be the super Yangian of general linear Lie superalgebra for ${\mathfrak{gl}_{m|n}}$ . Let ${e \in \mathfrak{gl}_{m\ell|n\ell}}$ be a “rectangular” nilpotent element and ${\mathcal{W}_e}$ be the finite W-superalgebra associated to e. We show that ${Y_{m|n}^{\ell}}$ is isomorphic to ${\mathcal{W}_e}$ .     

Energy dependence of {\bar{K}N} interaction in nuclear medium

When the $\bar{K}N$ system is submerged in nuclear medium the $\bar{K}N$ scattering amplitude and the final state branching ratios exhibit a strong energy dependence when going to energies below the $\bar{K}N$ threshold. A sharp increase of $\bar{K}N$ attraction below the $\bar{K}N$ threshold provides a link between shallow $\bar{K}$ -nuclear potentials based on the chiral $\bar{K}N$ amplitude evaluated at threshold and the deep phenomenological optical potentials obtained in fits to kaonic atoms data. We show the energy dependence of the in-medium K ^??? p amplitude and demonstrate the impact of energy dependent branching ratios on the Λ-hypernuclear production rates.     

Antineutrino science in KamLAND

The primary goal of KamLAND is a search for the oscillation of \({\bar{\nu }}_\mathrm{e}\) ’s emitted from distant power reactors. The long baseline, typically 180 km, enables KamLAND to address the oscillation solution of the “solar neutrino problem” with \({\bar{\nu }}_{e} \) ’s under laboratory conditions. KamLAND found fewer reactor \({\bar{\nu }}_{e} \) events than expected from standard assumptions about \(\overline{\nu }_e\) propagation at more than 9 \(\sigma \) confidence level (C.L.). The observed energy spectrum disagrees with the expected spectral shape at more than 5 \(\sigma \) C.L., and prefers the distortion from neutrino oscillation effects. A three-flavor oscillation analysis of the data from KamLAND and KamLAND + solar neutrino experiments with CPT invariance, yields \(\Delta m_{21}^2 \) = [ \(7.54_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) , \(7.53_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) ], tan \(^{2}\theta _{12}\) = [ \(0.481_{-0.080}^{+0.092} \) , \(0.437_{-0.026}^{+0.029} \) ], and sin \(^{2}\theta _{13}\) = [ \(0.010_{-0.034}^{+0.033} \) , \(0.023_{-0.015}^{+0.015} \) ]. All solutions to the solar neutrino problem except for the large mixing angle region are excluded. KamLAND also demonstrated almost two cycles of the periodic feature expected from neutrino oscillation effects. KamLAND performed the first experimental study of antineutrinos from the Earth’s interior so-called geoneutrinos (geo \({\bar{\nu }}_{e} \) ’s), and succeeded in detecting geo \({\bar{\nu }}_{e} \) ’s produced by the decays of \(^{238}\) U and \(^{232}\) Th within the Earth. Assuming a chondritic Th/U mass ratio, we obtain \(116_{-27}^{+28} {\bar{\nu }}_{e}\) events from \(^{238}\) U and \(^{232}\) Th, corresponding a geo \({\bar{\nu }}_{e}\) flux of \(3.4_{-0.8}^{+0.8}\times \) 10 \(^{6}\) cm \(^{-2}\)  s \(^{-1}\) at the KamLAND location. We evaluate various bulk silicate Earth composition models using the observed geo \({\bar{\nu }}_{e} \) rate.     

Mixing and CP violation: fromB^0 - \overline {B^0 } to T^0 - \overline {T^0 }

We extend from \(B^0 - \overline {B^0 } to T^0 - \overline {T^0 } \) the study of neutral pseudoscalar mesons with respect to mixing and CP violation. The possibility of a quite large top quark mass necessitates a more careful computation of the box diagram amplitude. Our result is that, while in \(B^0 - \overline {B^0 } \) systems CP violation is expected to be very small (～10^?6) and mixing quite large (10–20% or more), precisely the opposite occurs for \( T^0 - \overline {T^0 } \) . In particular, CP violation in the \( T_u^0 - \overline {T_u^0 } \) system could be of the same order of magnitude as in the \(K^0 - \overline {K^0 } \) system (～10^?3) while the mixing is totally negligible.     

Singular $$ \mathcal{R}$$ -Matrices and Drinfeld's Comultiplication

We compute the $\mathcal{R}$ -matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for ${\text{U}}_q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ . This $\mathcal{R}$ -matrix contains terms proportional to the δ-function. We construct the algebra $A\left( \mathcal{R} \right)$ generated by the elements of the matrices L^±(z) with relations determined by $\mathcal{R}$ . In the category of highest-weight representations, there is a Hopf algebra isomorphism between $A\left( \mathcal{R} \right)$ and an extension $\overline {\text{U}} _q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ of Drinfeld's algebra.