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 ${\mathcal{W}_e}$ .     

Haag Duality and the Distal Split Property for Cones in the Toric Code

We prove that Haag duality holds for cones in the toric code model. That is, for a cone ??, the algebra ${\mathcal{R}_{\Lambda}}$ of observables localized in ?? and the algebra ${\mathcal{R}_{\Lambda^c}}$ of observables localized in the complement ?? ^c generate each other??s commutant as von Neumann algebras. Moreover, we show that the distal split property holds: if ${\Lambda_1 \subset \Lambda_2}$ are two cones whose boundaries are well separated, there is a Type I factor ${\mathcal{N}}$ such that ${\mathcal{R}_{\Lambda_1} \subset \mathcal{N} \subset \mathcal{R}_{\Lambda_2}}$ . We demonstrate this by explicitly constructing ${\mathcal{N}}$ .     

Femtosecond relaxation kinetics of highly excited \mathrm{M}_{\mathrm{Na}}^{**} states in CaF2 at 3.2 eV and 4.7 eV

Femtosecond (fs) laser pulses at variable delay times allowed us to track the fast non-radiative transitions between the manifold of highly excited $\mathrm{M}_{\mathrm{Na}}^{**}$ states to the lower lying fluorescent $\mathrm{M}_{\mathrm{Na}}^{*}$ state in CaF₂. Two distinct $\mathrm{M}_{\mathrm{Na}}^{**}$ states of the manifold at 3.16?eV ( $\mathrm{M}_{\mathrm{Na}2}^{**}$ ) and 4.73?eV ( $\mathrm{M}_{\mathrm{Na}3}^{**}$ ) were populated using the second (SH) and third harmonics (TH) of fs laser light at 785?nm. The population kinetics of the fluorescent $\mathrm{M}_{\mathrm{Na}}^{*}$ state in the 2?eV excitation energy range was revealed by depleting its fluorescence centered at 740?nm using fundamental near infrared (NIR) fs laser pulses. The related time constants for $\mathrm{M}_{\mathrm{Na}2,3}^{**}{\sim}{>} \mathrm{M}_{\mathrm{Na}}^{*}$ relaxation amounted to 1.0±0.14?ps and 3.0±0.3?ps upon SH and TH excitation, respectively.     

Fast proton conduction path in {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{2.9 - \delta }} membrane

The effect of metal-to-oxide grain boundary layer in $ {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{3 - \delta }} $ (BCY) cermet membrane on hydrogen permeation was studied by applying the different size of oxide grain on Ni-BCY membranes. Two types of cermet membranes having different grain size of oxide were prepared by using different starting particle size of oxide powder. The hydrogen flux of coarse-oxide-grain membrane showed higher flux than that of small-oxide-grain membrane. It was understood that the negative potential at metal-to-oxide grain boundary, reference to the bulk oxide ( $ \phi _{0} < \phi _{\infty } = 0 $ ), was developed, and the accumulation of the effectively positively charged protons may occur at the grain boundary layer (space charge layer), which may result in providing highly conductive proton path by shifting the charge neutrality condition from $ {\left[ {OH^{ \bullet }_{O} } \right]} = {\left[ {Y^{/}_{{Ce}} } \right]} $ to $ {\left[ {OH^{ \bullet }_{O} } \right]} = n $ .     

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.     

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 ${h_\mathcal{S}}$ .     

How to Add a Boundary Condition

Given a conformal QFT local net of von Neumann algebras ${\mathcal {B}_2}$ on the two-dimensional Minkowski spacetime with irreducible subnet ${\mathcal {A} \otimes \mathcal {A}}$ , where ${\mathcal {A}}$ is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to ${\mathcal {B}_2}$ : we provide a procedure to construct a Boundary CFT net ${\mathcal {B}}$ of von Neumann algebras on the half-plane x >  0, associated with ${\mathcal {A}}$ , and locally isomorphic to ${\mathcal {B}_2}$ . All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of ${\mathcal {B}_2}$ to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S ¹.     

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.     

Structure of Neutron-Rich Be Hyper Isotopes

The deformation change of ${^{9}_\Lambda}$ Be and the low-lying states of ${^{12}_{\Lambda}}$ Be are studied by using the antisymmetrized molecular dynamics for hypernuclei (HyperAMD). In ${^{9}_{\Lambda}}$ Be, the Λ hyperon in p orbit enhances nuclear quadrupole deformation, while the Λ hyperon in s orbit reduces it. In ${^{12}_{\Lambda}}$ Be, the ground state parity inverted in ¹¹Be is reverted in ${^{12}_{\Lambda}}$ Be by adding a Λ hyperon as an impurity (impurity effect).     

Level-Rank Duality via Tensor Categories

We give a new way to derive branching rules for the conformal embedding $$(\hat{\mathfrak{sl}}_n)_m\oplus(\hat{\mathfrak{sl}}_m)_n\subset(\hat{\mathfrak{sl}}_{nm})_1. $$ In addition, we show that the category ${\mathcal{C}(\hat{\mathfrak{sl}}_n)_m^0}$ of degree zero integrable highest weight ${(\hat{\mathfrak{sl}}_n)_m}$ -representations is braided equivalent to ${\mathcal{C}(\hat{\mathfrak{sl}}_m)_n^0}$ with the reversed braiding.     

Self-Avoiding Walk is Sub-Ballistic

We prove that self-avoiding walk on ${\mathbb{Z}^d}$ is sub-ballistic in any dimension d ≥ 2. That is, writing ${\| u \|}$ for the Euclidean norm of ${u \in \mathbb{Z}^d}$ , and ${\mathsf{P_{SAW}}_n}$ for the uniform measure on self-avoiding walks ${\gamma : \{0, \ldots, n\} \to \mathbb{Z}^d}$ for which γ ₀ = 0, we show that, for each v > 0, there exists ${\varepsilon > 0}$ such that, for each ${n \in \mathbb{N}, \mathsf{P_{SAW}}_n \big( {\rm max}\big\{\| \gamma_k \| : 0 \leq k \leq n\big\} \geq vn \big) \leq e^{-\varepsilon n}}$ .     

Theoretical study of collision and collision-free radiative lifetimes of {{\text{S}}_2}\left( {{{\text{B}}^3}\Sigma_{\text{u}}^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right)

We calculate multireference configuration-interaction wavefunctions and the potential-energy curves for the $ {B^3}\Sigma_u^{-} $ and $ {X^3}\Sigma_g^{-} $ states of the collision-free S₂ molecule and the T-shape collision complex S₂?CHe using cc-pVQZ basis sets. We obtain the transition dipole moments of the $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \to {X^3}\Sigma_g^{-} } \right) $ and the Franck?CCondon factors between the vibrational levels of this two states. We evaluate the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ levels of the collision complex and the collision-free molecule and compare them with the experiments. The collision provides little change in the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ according to the previous calculations. We obtain excellent agreement between the theoretical results and the experiments. The data calculated are very useful in the study of the microwave-driven high-pressure sulfur lamp and an S₂ laser pumped by a transverse fast discharge.     

On q-Deformed {\mathfrak{gl}_{\ell+1}}-Whittaker Function II

A representation of a specialization of a q-deformed class one lattice ${\mathfrak{gl}_{\ell+1}}$ -Whittaker function in terms of cohomology groups of line bundles on the space ${\mathcal{QM}_d(\mathbb{P}^{\ell})}$ of quasi-maps ${\mathbb{P}^1 \to \mathbb{P}^{\ell}}$ of degree d is proposed. For ? = 1, this provides an interpretation of the non-specialized q-deformed ${\mathfrak{gl}_{2}}$ -Whittaker function in terms of ${\mathcal{QM}_d(\mathbb{P}^1)}$ . In particular the (q-version of the) Mellin-Barnes representation of the ${\mathfrak{gl}_2}$ -Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Γ-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution (J-function) of q-deformed ${\mathfrak{gl}_2}$ -Toda chain is also discussed.     

A DFG-based cavity ring-down spectrometer for trace gas sensing in the mid-infrared

Continuing studies into an all-diode laser-based 3.3 μm difference frequency generation cavity ring-down spectroscopy system are presented. Light from a 1,560 nm diode laser, amplified by an erbium-doped fibre amplifier, was mixed with 1,064 nm diode laser radiation in a bulk periodically poled lithium niobate crystal to generate 16 μW of mid-IR light at 3,346 nm with a conversion efficiency of $0.05\,\%\,{\text{W}}^{-1}\,{\text{cm}}^{-1}$ . This radiation was coupled into a 77 cm long linear cavity with average mirror reflectivities of 0.9996, and a measured baseline ring-down time of $6.07\pm 0.03\,\upmu{\rm s}$ . The potential of such a spectrometer was illustrated by investigating the $P(3)$ transition in the fundamental $\nu_{3}(F_{2})$ band of ${\text{CH}}_4$ both in a 7.5 ppmv calibrated mixture of ${\text{CH}}_4$ in air and in breath samples from methane and non-methane producers under conditions where the minimum detectable absorption coefficient ( $\alpha_{\rm min}$ ) was $2.8 \times 10^{-8}\,{\rm cm}^{-1}$ over 6 s using a ring-down time acquisition rate of 20 Hz. Allan variance measurements indicated an optimum $\alpha_{\rm min}$ of $2.9\times 10^{-9}\,{\rm cm}^{-1}$ over 44 s.     

Selectivity of anion exchange membrane modified with polyethyleneimine

Previous works have been made on the improvement of selectivity of ion exchange membranes using adsorption of polyelectrolyte on the surface of the materials. The modification of the surface material in the case of an anion exchange membrane concerns the hydrophilic/hydrophobic balance properties and its relationship with the hydration state. Starting from this goal, the AMX membrane has been modified, in this work, by adsorption of polyethyleneimine on its surface. Many conditions of modification of the AMX membrane surface were studied. A factorial experimental design was used for determining the influent parameters on the AMX membrane modification. The results obtained have shown that the initial concentration of polyethyleneimine and the pH of solution were the main influent parameters on the adsorption of polyethyleneimine on the membrane surface. Competitive ion exchange reactions were studied for the modified and the unmodified membrane involving $ {\text{C}}{{\text{l}}^{ - }} $ , $ {\text{NO}}_3^{ - } $ and $ {\text{SO}}_4^{{2 - }} $ ions. All experiments were carried out at constant concentration of 0.3?mol?L^?1 and at 25?°C. Ion exchange isotherms for the binary systems $ \left( {{\text{C}}{{\text{l}}^{ - }}/{\text{NO}}_3^{ - }} \right) $ , $ \left( {{\text{C}}{{\text{l}}^{ - }}/{\text{SO}}_4^{{2 - }}} \right) $ and $ \left( {{\text{NO}}_3^{ - }/{\text{SO}}_4^{{2 - }}} \right) $ were studied. The obtained results show that chloride was the most sorbed and the selectivity order both for the modified membrane and the unmodified one is: $ {\text{Cl}} > {\text{NO}}_3^{ - } > {\text{SO}}_4^{{2 - }} $ , under the experimental conditions. Selectivity coefficients $ {\text{K}}_{{{\text{C}}{{\text{l}}^{ - }}}}^{{{\text{NO}}_3^{ - }}} $ , $ {\text{K}}_{{2{\text{C}}{{\text{l}}^{ - }}}}^{{{\text{SO}}_4^{{2 - }}}} $ and $ {\text{K}}_{{2{\text{NO}}_3^{ - }}}^{{{\text{SO}}_4^{{2 - }}}} $ for the three binary systems and for the two membranes were determined. It was also observed that for the modified membrane the selectivity towards sulfate ion decrease and the modified membrane became more selective towards monovalent anions.     

Study of Light Hypernuclei by the (e,e′K +) Reaction

We have been performing Λ hypernuclear spectroscopic experiments by the (e,e′K ⁺) reaction since 2000 at Thomas Jefferson National Accelerator Facility (JLab). The (e,e′K ⁺) experiment can achieve a few 100 keV (FWHM) energy resolution compared to a few MeV (FWHM) by the (K ^?, π ^?) and (π ⁺, K ⁺) experiments. Therefore, more precise Λ hypernuclear structures can be investigated by the (e,e′K ⁺) experiment. ${^{7}_{\Lambda}{\rm He}}$ , ${^{9}_{\Lambda}{\rm Li}}$ , ${^{10}_{\Lambda}{\rm Be}}$ , ${^{12}_{\Lambda}{\rm B}}$ , ${^{28}_{\Lambda}{\rm Al}}$ , and ${^{52}_{\Lambda}{\rm V}}$ were measured in the experiment at JLab Hall-C. In addition, ${^{9}_{\Lambda}{\rm Li}}$ , ${^{12}_{\Lambda}{\rm B}}$ , and ${^{16}_{\Lambda}{\rm N}}$ were measured in the experiment at JLab Hall-A.     

Fomenko–Mischenko Theory, Hessenberg Varieties, and Polarizations

The symmetric algebra ${S(\mathfrak{g})}$ over a Lie algebra ${\mathfrak{g}}$ has the structure of a Poisson algebra. Assume ${\mathfrak{g}}$ is complex semisimple. Then results of Fomenko–Mischenko (translation of invariants) and Tarasov construct a polynomial subalgebra ${{\mathcal {H}} = {\mathbb C}[q_1,\ldots,q_b]}$ of ${S(\mathfrak{g})}$ which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of ${\mathfrak{g}}$ . Let G be the adjoint group of ${\mathfrak{g}}$ and let ? = rank ${\mathfrak{g}}$ . Using the Killing form, identify ${\mathfrak{g}}$ with its dual so that any G-orbit O in ${\mathfrak{g}}$ has the structure (KKS) of a symplectic manifold and ${S(\mathfrak{g})}$ can be identified with the affine algebra of ${\mathfrak{g}}$ . An element ${x\in \mathfrak{g}}$ will be called strongly regular if ${\{({\rm d}q_i)_x\},\,i=1,\ldots,b}$ , are linearly independent. Then the set ${\mathfrak{g}^{\rm{sreg}}}$ of all strongly regular elements is Zariski open and dense in ${\mathfrak{g}}$ and also ${\mathfrak{g}^{\rm{sreg}}\subset \mathfrak{g}^{\rm{ reg}}}$ where ${\mathfrak{g}^{\rm{reg}}}$ is the set of all regular elements in ${\mathfrak{g}}$ . A Hessenberg variety is the b-dimensional affine plane in ${\mathfrak{g}}$ , obtained by translating a Borel subalgebra by a suitable principal nilpotent element. Such a variety was introduced in Kostant (Am J Math 85:327–404, 1963). Defining Hess to be a particular Hessenberg variety, Tarasov has shown that ${{\rm{Hess}}\subset \mathfrak{g}^{\rm{sreg}}}$ . Let R be the set of all regular G-orbits in ${\mathfrak{g}}$ . Thus if ${O\in R}$ , then O is a symplectic manifold of dimension 2n where n = b ? ?. For any ${O\in R}$ let ${O^{\rm{sreg}} = \mathfrak{g}^{\rm{sreg}} \cap O}$ . One shows that O ^sreg is Zariski open and dense in O so that O ^sreg is again a symplectic manifold of dimension 2n. For any ${O\in R}$ let ${{\rm{Hess}}(O) = {\rm{Hess}}\cap O}$ . One proves that Hess(O) is a Lagrangian submanifold of O ^sreg and that $${\rm{Hess}} = \sqcup_{O\in R}{\rm{Hess}}(O).$$ The main result of this paper is to show that there exists simultaneously over all ${O\in R}$ , an explicit polarization (i.e., a “fibration” by Lagrangian submanifolds) of O ^sreg which makes O ^sreg simulate, in some sense, the cotangent bundle of Hess(O).     

On the Quasi-linear Elliptic PDE {-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_k a_k \delta_{s_k}} in Physics and Geometry

It is shown that for each finite number N of Dirac measures ${\delta_{s_n}}$ supported at points ${s_n \in {\mathbb R}^3}$ with given amplitudes ${a_n \in {\mathbb R} \backslash\{0\}}$ there exists a unique real-valued function ${u \in C^{0, 1}({\mathbb R}^3)}$ , vanishing at infinity, which distributionally solves the quasi-linear elliptic partial differential equation of divergence form ${-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_{n=1}^N a_n \delta_{s_n}}$ . Moreover, ${u \in C^{\omega}({\mathbb R}^3\backslash \{s_n\}_{n=1}^N)}$ . The result can be interpreted in at least two ways: (a) for any number N of point charges of arbitrary magnitude and sign at prescribed locations s _n in three-dimensional Euclidean space there exists a unique electrostatic field which satisfies the Maxwell-Born-Infeld field equations smoothly away from the point charges and vanishes as |s| ?? ??; (b) for any number N of integral mean curvatures assigned to locations ${s_n \in {\mathbb R}^3 \subset{\mathbb R}^{1, 3}}$ there exists a unique asymptotically flat, almost everywhere space-like maximal slice with point defects of Minkowski spacetime ${{\mathbb R}^{1, 3}}$ , having lightcone singularities over the s _n but being smooth otherwise, and whose height function vanishes as |s| ?? ??. No struts between the point singularities ever occur.     

Few-Body Aspects of Hypernuclear Physics

Recent development in the study of the structure of light Λ and double Λ hypernuclei is reviewed from the view point of few-body problems and interactions between the constituent particles. In the study the present author and collaborators employed Gaussian expansion method for few-body calculations; the method has been applied to many kinds of few-body systems in the fields of nuclear physics and exotic atomic/molecular physics. We reviewed the following subjects studied using the method: (1) Precise three- and four-body calculations of ${^7_{\Lambda}{\rm He}}$ , ${^7_{\Lambda}{\rm Li}}$ , ${^7_{\Lambda}{\rm Be}}$ , ${^8_{\Lambda}{\rm Li}}$ , ${^8_{\Lambda}{\rm Be}}$ , ${^9_{\Lambda}{\rm Be}}$ , ${^{10}_{\Lambda}{\rm Be}}$ , ${^{10}_{\Lambda}{\rm B}}$ and ${^{13}_{\Lambda}{\rm C}}$ provide important information on the spin structure of the underlying Λ N interaction by comparing the calculated results with the recent experimental data by γ-ray hypernuclear spectroscopy. (2) The Λ-Σ coupling effect was investigated in ${^4_{\Lambda}{\rm H}}$ and ${^4_{\Lambda}{\rm He}}$ on the basis of the N?+?N?+?N?+?Λ (Σ) four-body model. (3) A systematic study of double-Λ hypernuclei and the Λ Λ interaction, based on the NAGARA event data ( ${^6_{\Lambda\Lambda}{\rm He}}$ ), was performed within the α +?x?+?Λ +?Λ cluster model (x = n, p, d, t,³He and α) and α +?α +?n?+?Λ +?Λ cluster model, (4) The Demachi-Yanagi event was interpreted as observation of the 2⁺ state of ${^{10}_{\Lambda \Lambda}{\rm Be}}$ , (5) The Hida event was interpreted as observation of the ground state of ${^{11}_{\Lambda \Lambda}{\rm Be}}$ .