\hat sl(2) \oplus \hat sl(2)/\hat sl(2) coset theory is a Hamiltonian reduction of the \hat D(2|1;\alpha ) superalgebra

It is shown that $\hat sl(2)_{k_1 } \oplus \hat sl(2)_{k_2 } /\hat sl(2)_{k_1 + k_2 } $ coset theory is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra $\hat D(2|1;\alpha )$ . In addition, the W algebra of this theory is the commutant of the U _q D(2|1;a) quantum group.     

Phonon-Exchange Attraction. Optical Phonons and Type II Superconductivity, and d-Wave Cooper Pairs

The electron-pair density matrix (k ₁, k ₂; k ₃, k ₄, t) =: (1, 2; 3, 4, t) changes in time, following a quantum Liouville equation \rho (5,6;3,4,t) - < 5,6|v_c |3,4 >\rho (1,2,5,6,t)} \right]} } $$ " align="middle" border="0"> with : = 4\pi e^2 k_0 (\Omega q^2 )^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_s - k_1 ,q} $$ " align="middle" border="0"> in the presence of a Coulomb interaction _c, where is the volume. If the virtual phonon exchange is in action, the density matrix is shown to change similarly with an effective interaction _e, \hfill \\ = |V_q |^2 \bar h\omega _q |(\varepsilon _3 - \varepsilon _1 )^2 - \bar h^2 \omega _q^2 |^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_3 - k_1 ,q} \hfill \\ \end{gathered} $$ " align="middle" border="0"> , by using a time-dependent perturbation theory and a Markoffian approximation. The dominant longitudinal-acoustic-(optical)-phonon-exchange attraction at 0K is shown to be q-independent (-dependent). The results are used to discuss the Cooper pair size, the origin of type II superconductivity and the formation of d-wave Cooper pairs in the cuprates.     

The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity

By virtue of the method of multiple-scale and the quasi-discreteness approach, we have discussed the nonlinear vibration equation of a 3D discrete monatomic lattice with its nearest-neighbours interaction. The 3D simple cubic lattices have the same localized modes as a 1D discrete monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop solitons in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/6$a_{0}$ in the Brillouin zone, as well as has 3D vortices in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/$a_{0}$ in the Brillouin zone.     

A New Set of Limiting Gibbs Measures for the Ising Model on a Cayley Tree

For the Ising model (with interaction constant J>0) on the Cayley tree of order k≥2 it is known that for the temperature T≥T _c,k =J/arctan?(1/k) the limiting Gibbs measure is unique, and for T<T _c,k there are uncountably many extreme Gibbs measures. In the Letter we show that if \(T\in(T_{c,\sqrt{k}}, T_{c,k_{0}})\), with \(\sqrt{k} then there is a new uncountable set \({\mathcal{G}}_{k,k_{0}}\) of Gibbs measures. Moreover \({\mathcal{G}}_{k,k_{0}}\ne {\mathcal{G}}_{k,k'_{0}}\), for k ₀≠k′₀. Therefore if \(T\in (T_{c,\sqrt{k}}, T_{c,\sqrt{k}+1})\), \(T_{c,\sqrt{k}+1} then the set of limiting Gibbs measures of the Ising model contains the set {known Gibbs measures}\(\cup(\bigcup_{k_{0}:\sqrt{k}.     

New General Approach for Normally Ordering Coordinate-Momentum Operator Functions

By virtue of integration technique within ordered product of operators and Dirac’s representation theory we find a new general formula for normally ordering coordinate-momentum operator functions, that is \(f(g\hat {{Q}}+h\hat {P})= :\exp [\textstyle {g^{2}+h^{2} \over 4}\textstyle {{\partial ^{2}} \over {\partial (g\hat {{Q}}+h\hat {P})^{2}}}]f(g\hat {{Q}}+h\hat {P})\):, where \(\hat {Q}\) and \(\hat {P}\) are the coordinate operator and momentum operator respectively, the symbol :: denotes normal ordering. Using this formula we can derive a series of new relations about Hermite polynomial and Laguerre polynomial, as well as some new differential relations.     

The Essence of Operators’ Weyl Ordering Scheme and New Operator Identities for Converting Q−P Ordering to Weyl Ordering

We find new operator formulas for converting Q?P and P?Q ordering to Weyl ordering, where Q and P are the coordinate and momentum operator. In this way we reveal the essence of operators’ Weyl ordering scheme, e.g., Weyl ordered operator polynomial ${_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}}$ , $$\begin{aligned} {_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}} =&\sum_{l=0}^{\min (m,n)} \biggl( \frac{-i\hbar }{2} \biggr) ^{l}l!\binom{m}{l}\binom{n}{l}Q^{m-l}P^{n-l} \\ =& \biggl( \frac{\hbar }{2} \biggr) ^{ ( m+n ) /2}i^{n}H_{m,n} \biggl( \frac{\sqrt{2}Q}{\sqrt{\hbar }},\frac{-i\sqrt{2}P}{\sqrt{\hbar }} \biggr) \bigg|_{Q_{\mathrm{before}}P} \end{aligned}$$ where ${}_{:}^{:}$ ${}_{:}^{:}$ denotes the Weyl ordering symbol, and H _m,n is the two-variable Hermite polynomial. This helps us to know the Weyl ordering more intuitively.     

Three Dimensionality and Orbital Characters of the Fermi Surface in (Tl,Rb)_{y}Fe_{2-x}Se_{2}

We report a comprehensive angle-resolved photoemission spectroscopy study of the tridimensional electronic bands in the recently discovered Fe selenide superconductor (Tl,Rb)_{y}Fe_{2-x}Se_{2} (T_{c}=32 K). We determined the orbital characters and the k_{z} dependence of the low energy electronic structure by tuning the polarization and the energy of the incident photons. We observed a small 3D electron Fermi surface pocket near the Brillouin zone center and a 2D like electron Fermi surface pocket near the zone boundary. The photon energy dependence, the polarization analysis and the local-density approximation calculations suggest a significant contribution from the Se 4p_{z} and Fe 3d_{xy} orbitals to the small electron pocket. We argue that the emergence of Se 4p_{z} states might be the cause of the different magnetic properties between Fe chalcogenides and Fe pnictides.     

Dimensionally frustrated diffusion towards fractal adsorbers

Diffusion towards a fractal adsorber is a well-researched problem with many applications. While the steady-state flux towards such adsorbers is known to be characterized by the fractal dimension (D{F}) of the surface, the more general problem of time-dependent adsorption kinetics of fractal surfaces remains poorly understood. In this Letter, we show that the time-dependent flux to fractal adsorbers (1相似文献   

Universality of the Local Regime for the Block Band Matrices with a Finite Number of Blocks

We consider the block band matrices, i.e. the Hermitian matrices $H_N$ , $N=|\Lambda |W$ with elements $H_{jk,\alpha \beta }$ , where $j,k \in \Lambda =[1,m]^d\cap \mathbb {Z}^d$ (they parameterize the lattice sites) and $\alpha , \beta = 1,\ldots , W$ (they parameterize the orbitals on each site). The entries $H_{jk,\alpha \beta }$ are random Gaussian variables with mean zero such that $\langle H_{j_1k_1,\alpha _1\beta _1}H_{j_2k_2,\alpha _2\beta _2}\rangle =\delta _{j_1k_2}\delta _{j_2k_1} \delta _{\alpha _1\beta _2}\delta _{\beta _1\alpha _2} J_{j_1k_1},$ where $J=1/W+\alpha \Delta /W$ , $\alpha < 1/4d$ . This matrices are the special case of Wegner’s $W$ -orbital models. Assuming that the number of sites $|\Lambda |$ is finite, we prove universality of the local eigenvalue statistics of $H_N$ for the energies $|\lambda _0|< \sqrt{2}$ .     

On phase transitions in Schlögl's second model

We study Schlögl's second model, characterized by chemical reactions $$\begin{array}{*{20}c} {2X\underset{{k_2 }}{\overset{{k_1 }}{\longleftrightarrow}}3X,} & {X\underset{{k_4 }}{\overset{{k_3 }}{\longleftrightarrow}}0,} \\ \end{array} $$ ind-dimensional space. The reactions are assumed to be local; local fluctuations are fully taken into account, and particle transport occurs via diffusion. In contrast to previous investigations, we find no phase transition whenk ₄≠0 andd<4. Fork ₄=0,k ₃≠0, and 1≦d<4, we find a second-order phase transition which is in the same universality class as the transition in Schlögl's first model. Only ford≧4 we do find the first-order transition found also by previous authors. These claims are supported by extensive Monte Carlo calculations for various realizations of this process on discrete space-time lattices.     

Theoretical analysis of somatostatin receptor 5 with antagonists and agonists for the treatment of neuroendocrine tumors

We report on SSTR5 receptor modeling and its interaction with reported antagonist and agonist molecules. Modeling of the SSTR5 receptor was carried out using multiple templates with the aim of improving the precision of the generated models. The selective SSTR5 antagonists, agonists and native somatostatin SRIF-14 were employed to propose the binding site of SSTR5 and to identify the critical residues involved in the interaction of the receptor with other molecules. Residues Q2.63, D3.32, Q3.36, C186, Y7.34 and Y7.42 were found to be highly significant for their strong interaction with the receptor. SSTR5 antagonists were utilized to perform a 3D quantitative structure–activity relationship study. A comparative molecular field analysis (CoMFA) was conducted using two different alignment schemes, namely the ligand-based and receptor-based alignment methods. The best statistical results were obtained for ligand-based (\({q}^{2} = 0.454\), \({r}^{2}\) = 0.988, noc = 4) and receptor-guided methods (docked mode 1:\({q}^{2} = 0.530\), \({r}^{2} = 0.916\), noc = 5), (docked mode 2:\({q}^{2}\) = 0.555, \({r}^{2 }= 0.957\), noc = 5). Based on CoMFA contour maps, an electropositive substitution at \(\hbox {R}^{1}\), \(\hbox {R}^{2}\) and \(\hbox {R}^{4}\) position and bulky group at \(\hbox {R}^{4}\) position are important in enhancing molecular activity.     

Zener polaron ordering variants induced by A-site ordering in half-doped manganites

We have studied the magnetism of the half-doped charge ordered manganite YBaMn2O6. A formation of ferromagnetic plaquettes of four Mn atoms in the charge ordered phase below T_{CO} approximately 480 K is inferred from high temperature magnetic susceptibility data and the magnetic structure, as determined by neutron powder diffraction at T=1.5 K. The results indicate that new fourfold Mn paramagnetic units form between T_{N}相似文献   

Hyperfine structure and isotope shift study in singly ionized lead

Hyperfine structure and isotope shifts in five optical transitions: 424.5 nm ( – ), 537.2 nm ( – ), 554.5 nm ( – ), 560.9 nm ( – ) and 666.0 nm ( – ) of Pb  II have been measured. As a light source the discharge tube was used. The hyperfine structure measurements were performed using metallic isotope ²⁰⁷Pb. For isotope shifts measurements natural lead was used. The high resolution spectral apparatus consisted of a silver coated Fabry-Perot etalon and a grating spectrograph combined with a CCD camera used as a detector. In the analysis of the spectra a computer simulation technique was used. The hyperfine structure observations yielded the splitting constants A for seven levels of Pb II. The isotope shift studies enabled to separate the mass and the field shifts and to determine values of changes of the mean square nuclear charge radii.     

Unusual magneto-optical phenomenon reveals low energy spin dispersion in the spin-1 anisotropic Heisenberg antiferromagnetic chain system NiCl2-4SC(NH2)_{2}

Electron paramagnetic resonance measurements of NiCl2-4SC(NH2)_{2} reveal the low-energy spin dispersion, including a magnetic-field interval in which the two-magnon continuum is within k_{B}T of the ground state, allowing a continuum of excitations over a range of k states, rather than only the k=0 single-magnon excitations. This produces a novel Y shape in the frequency-field EPR spectrum measured at T > or = 1.5 K. Since the interchain coupling J_{ perpendicular}相似文献   

Shift and broadening of emission lines in Nd<Superscript>3+</Superscript>:YAG laser crystal influenced by input energy

Spectroscopic properties of the flashlamp-pumped Nd ³⁺:YAG laser as a function of input energy were studied over the range of 18–75 J. The spectral widths and shifts of quasi-three-level and four-level inter-Stark emissions within the respective intermanifold transitions of \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {9/2}}\) and \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {11/2}}\) were investigated. The emission lines of \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -2.7pt}\mathrm {I}_{\mathrm {9/2}}\) shifted towards longer wavelength (red shift) and broadened, while the positions and linewidths of the \(^{\mathrm {4}}\mathrm {F}_{\mathrm {3/2}}\to ^{\mathrm {4}}{\kern -3.5pt}\mathrm {I}_{\mathrm {11/2}}\) transition lines remained constant by increasing the pumping energy. This is attributed to the thermal population as well as one-phonon and multiphonon emission processes in the ground state. This phenomenon degrades the output performance of the lasers.     

Quantum Image Encryption Based on Iterative Framework of Frequency-Spatial Domain Transforms

A novel quantum image encryption and decryption algorithm based on iteration framework of frequency-spatial domain transforms is proposed. In this paper, the images are represented in the flexible representation for quantum images (FRQI). Previous quantum image encryption algorithms are realized by spatial domain transform to scramble the position information of original images and frequency domain transform to encode the color information of images. But there are some problems such as the periodicity of spatial domain transform, which will make it easy to recover the original images. Hence, we present the iterative framework of frequency-spatial domain transforms. Based on the iterative framework, the novel encryption algorithm uses Fibonacci transform and geometric transform for many times to scramble the position information of the original images and double random-phase encoding to encode the color information of the images. The encryption keys include the iterative time t of the Fibonacci transform, the iterative time l of the geometric transform, the geometric transform matrix G i which is n × n matrix, the classical binary sequences K (\(k_{0}k_{1}{\ldots } k_{2^{2n}-1}\)) and \(D(d_{0}d_{1}{\ldots } d_{2^{2n}-1}\)). Here the key space of Fibonacci transform and geometric transform are both estimated to be 2²⁶. The key space of binary sequences is (2 ^n×n ) × (2 ^n×n ). Then the key space of the entire algorithm is about \(2^{2{n^{2}}+52}\). Since all quantum operations are invertible, the quantum image decryption algorithm is the inverse of the encryption algorithm. The results of numerical simulation and analysis indicate that the proposed algorithm has high security and high sensitivity.     

Hyperfine structure measurements in the ground states4 F 3/2,4 F 5/2 and4 F 7/2 of Ta181 with the atomic beam magnetic resonance method

Applying a recently developed evaporation technique for refractory elements the following results have been obtained for Ta¹⁸¹ in an atomic beam magnetic resonance experiment studying the hyperfine structure of 3 levels of the ground state multiplet⁴ F: $$\begin{gathered} g_J (^4 F_{3/2} ) = 0.45024 (4) \hfill \\ \Delta v (^4 F_{3/2} ;F = 5 \leftrightarrow F = 4) = 1822.389 (6) MHz \hfill \\ \Delta v (^4 F_{3/2} ;F = 4 \leftrightarrow F = 3) = 2325.537 (2) MHz \hfill \\ \Delta v (^4 F_{5/2} ;F = 6 \leftrightarrow F = 5) = 1451.476 (7) MHz \hfill \\ \Delta v (^4 F_{5/2} ;F = 5 \leftrightarrow F = 4) = 1537.530 (8) MHz \hfill \\ \Delta v (^4 F_{5/2} ;F = 4 \leftrightarrow F = 3) = 1444.685 (2) MHz \hfill \\ \Delta v (^4 F_{7/2} ;F = 4 \leftrightarrow F = 3) = 1218.372 (2) MHz. \hfill \\ \end{gathered}$$ From these measurements the following constants of the magnetic dipole interaction (A) and the electric quadrupole interaction (B) have been derived: $$\begin{gathered} A (^4 F_{3/2} ) = 509.0801 (8) MHz \hfill \\ B (^4 F_{3/2} ) = - 1012.251 (8) MHz \hfill \\ A (^4 F_{5/2} ) = 313.4681 (8) MHz \hfill \\ B (^4 F_{5/2} ) = - 834.820 (12) MHz. \hfill \\ \end{gathered}$$      

The Exoticness and Realisability of Twisted Haagerup–Izumi Modular Data

The quantum double of the Haagerup subfactor, the first irreducible finite depth subfactor with index above 4, is the most obvious candidate for exotic modular data. We show that its modular data \({\mathcal{D}{\rm Hg}}\) fits into a family \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\) , where n ≥  0 and \({\omega\in \mathbb{Z}_{2n+1}}\) . We show \({\mathcal{D}^0 {\rm Hg}_{2n+1}}\) is related to the subfactors Izumi hypothetically associates to the cyclic groups \({\mathbb{Z}_{2n+1}}\) . Their modular data comes equipped with canonical and dual canonical modular invariants; we compute the corresponding alpha-inductions, etc. In addition, we show there are (respectively) 1, 2, 0 subfactors of Izumi type \({\mathbb{Z}_7, \mathbb{Z}_9}\) and \({\mathbb{Z}_3^2}\) , and find numerical evidence for 2, 1, 1, 1, 2 subfactors of Izumi type \({\mathbb{Z}_{11},\mathbb{Z}_{13},\mathbb{Z}_{15},\mathbb{Z}_{17},\mathbb{Z}_{19}}\) (previously, Izumi had shown uniqueness for \({\mathbb{Z}_3}\) and \({\mathbb{Z}_5}\)), and we identify their modular data. We explain how \({\mathcal{D}{\rm Hg}}\) (more generally \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\)) is a graft of the quantum double \({\mathcal{D} Sym(3)}\) (resp. the twisted double \({\mathcal{D}^\omega D_{2n+1}}\)) by affine so(13) (resp. so\({(4n^2+4n+5)}\)) at level 2. We discuss the vertex operator algebra (or conformal field theory) realisation of the modular data \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\) . For example we show there are exactly 2 possible character vectors (giving graded dimensions of all modules) for the Haagerup VOA at central charge c = 8. It seems unlikely that any of this twisted Haagerup-Izumi modular data can be regarded as exotic, in any reasonable sense.     

The Invariant Eigen-Operator Method for?N?Harmonically Coupled Identical Oscillators

In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of arbitrary number of coupled identical oscillators and derive their invariant eigen-operator. The results show that, (1) for the system of arbitrary number of identical harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator of system always has the form of or ; (2) the energy level gap of the system has two kinds of possibilities: one is that gap only related to ω that the frequency of oscillators; another one is that gap not only related to ω that the frequency of oscillators, but also related to the number of the coupling oscillators.     

Spectra of Semi-Infinite Quantum Graph Tubes

The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half of the tube. The eigenfunctions associated to the spectrum of the half-tube involve all Floquet modes of the full tube. This requires solving the complex dispersion relation \({D(\lambda,k_1,k_2)=0}\) with \({(k_1,k_2)\in(\mathbb{C}/2\pi\mathbb{Z})^2}\) subject to the constraint \({a k_1 + bk_2 \equiv 0}\) (mod \({2\pi}\)), where a and b are integers. The number of Floquet modes for a given \({\lambda\in\mathbb{R}}\)  is  \({2\max\left\{ a, b \right\}}\). Rightward and leftward modes are determined according to an indefinite energy flux form. The spectrum may contain eigenvalues that depend on the boundary conditions, and some eigenvalues may be embedded in the continuous spectrum.