Baxter Q-operators and representations of Yangians

We develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the Yang–Baxter equation connected with harmonic oscillator algebras. These infinite-state solutions of the Yang–Baxter equation serve as elementary, “partonic” building blocks for other solutions via the standard fusion procedure. As a first example of the method we consider gl(n)$\mathfrak{gl}(n)$ compact spin chains and derive the full hierarchy of operatorial functional equations for all related commuting transfer matrices and Q-operators. This leads to a systematic and transparent solution of these chains, where the nested Bethe equations are derived in an entirely algebraic fashion, without any reference to the traditional Bethe Ansatz techniques.     

On the Maximal Excess Charge of the Chandrasekhar–Coulomb Hamiltonian in Two Dimension

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom – or the corresponding magnetic quantum dot – the maximal number of electrons does not exceed twice the nuclear charge. The result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of $$|{\bf x}| T({\bf p}) + T({\bf p} ) |{\bf x}|$$ which – in two dimensions – is false for the non-relativistic case T(p) = p ²/2, but is proven in this paper for T(p) = |p|, i.e., the ultra-relativistic kinetic energy.     

On Baxter {\mathcal Q} -Operators and their Arithmetic Implications

We consider Baxter ${\mathcal Q}$ -operators for various versions of quantum affine Toda chain. The interpretation of eigenvalues of the finite Toda chain Baxter operators as local Archimedean L-functions proposed recently is generalized to the case of affine Lie algebras. We also introduce a simple generalization of Baxter operators and local L-functions compatible with this identification. This gives a connection of the Toda chain Baxter ${\mathcal Q}$ -operators with an Archimedean version of the Polya–Hilbert operator proposed by Berry-Keating. We also elucidate the Dorey–Tateo spectral interpretation of eigenvalues of ${\mathcal Q}$ -operators. Using explicit expressions for eigenfunctions of affine/relativistic Toda chain we obtain an Archimedean analog of Casselman–Shalika–Shintani formula for Whittaker function in terms of characters.     

Fast calculation of HELAS amplitudes using graphics processing unit (GPU)

We use the graphics processing unit (GPU) for fast calculations of helicity amplitudes of physics processes. As our first attempt, we compute $u\overline{u}\rightarrow n\gamma$ (n=2 to 8) processes in pp collisions at $\sqrt{s}=14$  TeV by transferring the MadGraph generated HELAS amplitudes (FORTRAN) into newly developed HEGET (HELAS Evaluation with GPU Enhanced Technology) codes written in CUDA, a C-platform developed by NVIDIA for general purpose computing on the GPU. Compared with the usual CPU programs, we obtain a 40–150 times better performance on the GPU.     

Proofs of two conjectures related to the thermodynamic Bethe Ansatz

We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel $$\frac{{e^{ - (u(\theta ) + u(\theta \prime ))} }}{{\cosh ^{\frac{{\theta - \theta \prime }}{2}} }}$$ .     

Relating the Quantum Mechanics of Discrete Systems to Standard Canonical Quantum Mechanics

Standard canonical quantum mechanics makes much use of operators whose spectra cover the set of real numbers, such as the coordinates of space, or the values of the momenta. Discrete quantum mechanics uses only strictly discrete operators. We show how one can transform systems with pairs of integer-valued, commuting operators $P_i$ and $Q_i$ , to systems with real-valued canonical coordinates $q_i$ and their associated momentum operators $p_i$ . The discrete system could be entirely deterministic while the corresponding (p, q) system could still be typically quantum mechanical.     

Spatial representation of groups of automorphisms of von Neumann algebras with properly infinite commutant

Theorem. Let a topological groupG be represented (a→φ _a ) by *-automorphisms of a von Neumann algebraR acting on a separable Hilbert spaceH. Suppose that

1. G is locally compact and separable,
2. R′ is properly infinite,
3. for anyT∈R,x,y∈H the function

$$a \to \left\langle {\phi _a (T)x,y} \right\rangle _H $$ is measurable onG. Then there exists a strongly continuous unitary representation ofG onH,a→U _a , such that forT∈R,a∈G, $$\phi _\alpha (T) = U_a TU_a *.$$ .     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

Quinazoline-2,4(1H,3H)-diones inhibit the growth of multiple human tumor cell lines

Quinazoline-2,4( $1H,3H$ )-diones exhibit a wealth of biological activities including antitumor proliferation. We established an improved method for the synthesis of quinazoline-2,4( $1H,3H$ )-dione derivatives with three points of molecular diversity. Data indicate that compounds 60 (average $\text{ logGI}_{50} \!=\! -6.1$ ), 65 (average $\text{ logGI}_{50} \!=\! -6.13$ ), 69 (average $\text{ logGI}_{50} \!=\! -6.44$ ), 72 (average $\text{ logGI}_{50} \!=\! -6.39$ ), and 86 (average $\text{ logGI}_{50} = -6.45$ ) significantly inhibited the in vitro growth of 60 human tumor cell lines tested. Structure–activity relationship analyses indicate that chlorophenethylureido is the necessary substituent at the $\text{ D}_{3}$ diversity point (7-position of quinazoline-2,4( $1H,3H$ )-dione), in particular, $o$ -chlorophenethylurea (69) achieved optimal activity. $o$ - or $m$ -Chlorophenethyl substitutions (69 and 72) at the $\text{ D}_{2}$ diversity point (3-position of quinazo line-2,4( $1H,3H$ )-dione) gave the most potent compounds. Methoxyl and 4-methylpiperazin-1-yl substitution at the $\text{ D}_{1}$ diversity point (6-position of quinazoline-2,4( $1H,3H$ )-dione skeleton) may yield better activity than other groups. The quinazoline-2,4( $1H,3H$ )-dione scaffold can be effectively replaced by 2 $H$ -benzo[b][1,4]thiazin-3(4 $H$ )-one.     

Antiproton reflection by a solid surface

The AE?IS experiment (Antimatter Experiment: Gravity, Interferometry, Spectroscopy (Drobychev et al., 2007)), aims at directly measuring the gravitational acceleration g on a beam of cold antihydrogen ( $\overline{\rm H}$ ). After production, the $\overline{\rm H}$ atoms will be driven to fly horizontally with a velocity of a few 100 m/s for a path length of about 1 meter. The small deflection, few tens of μm, will be measured using two material gratings coupled to a position-sensitive detector working as a Moiré deflectometer similarly to what has been done with atoms (Oberthaler et al., Phys Rev A 54:3165, 1996). Details about the detection of the $\overline{\rm H}$ annihilation point at the end of the flight path with a position-sensitive microstrip detector and a silicon tracker system will be discussed.     

Perpendicularev mass fromW decay

We point out properties of the “perpendicularev mass”, defined in terms of transverse momentap _t byM _T ² (ev)=2|p _eT | |p _vT |?2p _eT ·p _vT , that make it particularly well suited toW mass and width determinations. We give an analytic expression for its distribution inW production and subsequentW→ev decay a \(\bar pp\) colliders, accurate to order 〈p _WT ² /M _W ² 〉≈1%. A maximum likelihood fit of this formula to the five UA1 events givesM _W=80.3 _?3 ⁺⁶ GeV.     

Sekiguchi-Debiard Operators at Infinity

We construct a family of pairwise commuting operators such that the Jack symmetric functions of infinitely many variables ${x_1,x_2, \ldots}$ are their eigenfunctions. These operators are defined as limits at N → ∞ of renormalised Sekiguchi-Debiard operators acting on symmetric polynomials in the variables ${x_1 , \ldots , x_N}$ . They are differential operators in terms of the power sum variables ${p_n=x_1^n+x_2^n+\cdots}$ and we compute their symbols by using the Jack reproducing kernel. Our result yields a hierarchy of commuting Hamiltonians for the quantum Calogero-Sutherland model with an infinite number of bosonic particles in terms of the collective variables of the model. Our result also yields the elementary step operators for the Jack symmetric functions.     

The discovery of 3-(1-aminoethylidene)quinoline-2, 4(1H,3H)-dione derivatives as novel PSII electron transport inhibitors

Based on the structures of the 4-hydroxyphenylpyruvate dioxygenase inhibitor mesotrione and natural product fischerellin A, a series of imine derivatives of ( $E$ )-3-acyl-quinoline-2,4(1H,3H)-dione (6, 12 and 16) were designed, synthesized and systematically evaluated for their herbicidal activity. The bioassay results indicated that most of the synthesized compounds displayed good to excellent herbicidal activity, of which 6e, 6g, 6h, 6q and 6t exhibited more than 50 % inhibition against Brassica napus L., Amaranthus retroflexu or Digitaria adscendens at a dosage of $94\,\hbox {g}\,\hbox {ha}^{-1}$ or lower. The symptom of injured leaves in vivo, the high Hill reaction inhibitory activity of 6h in vitro ( $\hbox {IC}_{50}\,0.1\, \upmu \hbox {g}\,\hbox {mL}^{-1})$ and the computer-based binding model of compound 6h with D1 protein in photosystem II (PSII) reaction centre suggest this novel structure to likely be a new type of PSII electron transport inhibitor. Thus, we have found a novel type of diketone enamine structure targeted at the PSII reaction centre.     

Neutral and anionic duality of 1,2,4-triazole α-amino acid scaffold in 1D coordination polymers

A tiny supramolecular synthon, 4H-1,2,4-triazol-4-yl acetic acid (HGlytrz) which is bifunctional by design having an electronic asymmetry and conformational flexibility has been introduced to synthesize iron(II) complexes. Having 1,2,4-triazole or carboxylic extremities on the same framework HGlytrz could display dual functionality by acting as a neutral as well as anionic ligand based on the possibility of deprotonation of carboxylic group. Four new iron(II) HGlytrz complexes with ClO $_{4}^{-}$ (1), NO $_{3}^{-}$ (2), BF $_{4}^{-}$ (3) and CF₃SO $_{3}^{-}$ (4) anions were prepared. Formulation of their composition which is complicated due to ligand deprotonation is discussed. Unlike its ester protected counterpart ethyl-4H-1,2,4-triazol-4-yl-acetate (αGlytrz) which show hysteretic room temperature spin crossover, 1–4 remain in the high-spin state as revealed by ⁵⁷M?ssbauer spectroscopy. Prospects of such 1D coordination polymers with dangling unbounded carboxylic entities in the realm of self-assembled monolayer (SAM) are discussed.     

Second quantization of classical nonlinear relativistic field theory

The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field \(\hat \Phi \) is obtained. The construction of asymptotic local relativistic fields \(\hat \Phi _{in} \) and \(\hat \Phi _{out} \) associated with \(\hat \Phi \) is also given.     

Model independent bounds on the modulus of the pion form factor on the unitarity cut below the ωπ threshold

We study the structure of local baryon fields using the method of QCD sum rule. We only consider the single baryon fields and calculate their operator product expansions. We find that the octet baryon fields belonging to the chiral representations $[(\mathbf{3},\bar{\mathbf{3}}) \oplus(\bar{\mathbf{3}}, \mathbf{3})]$ and [(8,1)??(1,8)] and the decuplet baryon fields belonging to the chiral representations [(3,6)??(6,3)] lead to the baryon masses which are consistent with the experimental data of ground baryon masses. We also calculate their decay constants, check our normalizations for baryon fields in Chen et?al. (Phys. Rev.?D 81:054002, 2009) and find that they are well-defined.