Neutral meson oscillations and equivalence principle for particles and antiparticles

Oscillations of neutral meson (K ⁰-$ \overline {K^0 } $ \overline {K^0 } , D ⁰-$ \overline {D^0 } $ \overline {D^0 } , and B ⁰-$ \overline {B^0 } $ \overline {B^0 } are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc ²—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field of the galaxy center, we obtain the estimate from experimental data on K ⁰-$ \overline {K^0 } $ \overline {K^0 } oscillations:

Thermal States in Conformal QFT. I

We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A{{\mathcal A}} of von Neumann algebras on \mathbb R{\mathbb R} . In this first part, we focus on the completely rational net A{{\mathcal A}} . Our main result here states that, if A{{\mathcal{A}}} is completely rational, there exists exactly one locally normal KMS state j{\varphi} . Moreover, j{\varphi} is canonically constructed by a geometric procedure. A crucial r?le is played by the analysis of the “thermal completion net” associated with a locally normal KMS state. A similar uniqueness result holds for KMS states of two-dimensional local conformal nets w.r.t. the time-translation one-parameter group.     

Mössbauer Study of Microstructure and Magnetic Properties (Co,Ni)–Zr Substituted Ba Ferrite Particles

The β-NMR of short-lived β-emitter in a rutile TiO₂ single crystal has been measured as functions of temperature and external magnetic field. Atomic motion induced spin lattice relaxation was observed for two known sites, O substitutional and interstitial sites. The data were analyzed in terms of the thermal atomic jump, which suggests that the motion of defects around the substitutional ¹²N atom for O, and of the interstitial ¹²N atom are attributed to the spin lattice relaxation. The electric field gradients have shown temperature dependence for both sites, which is probably due to the thermal expansion of rutile.     

Kochen–Specker Theorem for von Neumann Algebras

The Kochen–Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we first offer a new, non-combinatorial proof for quantum systems with a type I_n factor as algebra of observables, including I_∞. Afterwards, we give a proof of the Kochen–Specker theorem for an arbitrary von Neumann algebra without summands of types I₁ and I₂, using a known result on two-valued measures on the projection lattice . Some connections with presheaf formulations as proposed by Isham and Butterfield are made.     

Spin freezing in the van der Waals material Mn2Ga2S5

Geometrical frustration in low-dimensional magnetic systems has been an intriguing research aspect, where the suppression of conventional magnetic order may lead to exotic ground states such as spin glass or spin liquid. In this work we report the synthesis and magnetism study of the monocrystalline Mn$_2$Ga$_2$S$_5$, featuring both the van der Waals structure and a bilayered triangular Mn lattice. Magnetic susceptibility reveals a significant antiferromagnetic interaction with a Curie-Weiss temperature $\theta_{\rm w}\sim-260$ K and a high spin $S=5/2$ Mn$^{2+}$ state. However, no long range magnetic order has been found down to 2 K, and a spin freezing transition is found to occur at around 12 K well below its $\theta_{\rm w}$. This yields a frustration index of $f = -\theta_{\rm w}/T_{\rm f} \approx 22$, an indication that the system is highly frustrated. The absence of a double-peak structure in magnetic specific heat compared with the $TM_2$S$_4$ compounds implies that the spin freezing behavior in Mn$_2$Ga$_2$S$_5$ is a result of the competition between exchange interactions and the 2D crystalline structure. Our results suggest that the layered Mn$_2$Ga$_2$S$_5$ would be an excellent candidate for investigating the physics of 2D magnetism and spin disordered state.     

Co-Al-W基高温合金的团簇成分式

Co-Al-W基高温合金具有类似于Ni基高温合金的γ+γ'相组织结构.根据面心立方固溶体的团簇加连接原子结构模型,Ni基高温合金的成分式即最稳定的化学近程序结构单元可以描述为第一近邻配位多面体团簇加上次近邻的三个连接原子.本文应用类似方法,首次给出了Co-Al-W基高温合金的团簇成分式.利用原子半径和团簇共振模型,可计算出Co-Al-W三元合金的团簇成分通式,为[Al-Co_(12)](Co,Al,W)_3,即以Al为中心原子、Co为壳层原子的[Al-Co_(12)]团簇加上三个连接原子.对于多元合金,需要先将元素进行分类:溶剂元素——类Co元素Co (Co, Cr, Fe, Re, Ni,Ir,Ru)和溶质元素——类Al元素Al (Al,W,Mo, Ta,Ti,Nb,V等);进而根据合金元素的配分行为,将类Co元素分为Co~γ(Cr, Fe, Re)和Co~(γ')(Ni, Ir, Ru);根据混合焓,将类Al元素分为Al, W (W, Mo)和Ta (Ta, Ti, Nb, V等).由此,任何多元Co-Al-W基高温合金均可简化为Co-Al伪二元体系或者Co-Al-(W,Ta)伪三元体系,其团簇加连接原子成分式为[Al-Co_(12)](Co_(1.0)Al_(2.0))(或[Al-Co_(12)] Co_(1.0)Al_(0.5)(W,Ta)_(1.5)=Co_(81.250)Al_(9.375)(W,Ta)_(9.375) at.%).其中,γ与γ'相的团簇成分式分别为[Al-Co_(12)](Co_(1.5)Al_(1.5))(或[Al-Co_(12)] Co_(1.5)Al_(0.5)(W,Ta)_(1.0)=Co_(84.375)Al_(9.375)(W,Ta)_(6.250) at.%)和[Al-Co_(12)](Co_(0.5)Al_(2.5))(或[Al-Co_(12)] Co_(0.5)Al_(0.5)(W, Ta)_(2.0)=Co_(78.125)Al_(9.375)(W,Ta)_(12.500)at.%).例如,Co_(82)Al_9W_9合金的团簇成分式为[Al-Co_(12)]Co_(1.1)Al_(0.4)W_(1.4)(～[Al-Co_(12)]Co_(1.0)Al_(0.5)W_(1.5)),其中γ相的团簇成分式为[Al-Co_(12)]Co_(1.6)Al_(0.4)W_(1.0)(～[Al-Co_(12)]Co_(1.5)Al_(0.5)W_(1.0)),γ'相的团簇成分式为[Al-Co_(12)]Co_(0.3)Al_(0.5)W_(2.2)(～[AlCo_(12)]Co_(0.5)Al_(0.5)W_(2.0)).     

Quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$ via symmetry analysis

We investigate the quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$, which are composed of 4 (three flavors) quarks and an antiquark, by analyzing their inherent nodal structure in this paper. Assuming that the four quarks form a tetrahedron or a square, and the antiquark is at the ground state, we determine the nodeless structure of the states with orbital angular moment L≤3, and in turn, the accessible low-lying states. Since the inherent nodal structure depends only on the inherent geometric symmetry, we propose the quantum numbers J^P of the low-lying pentaquark states ${{\rm{P}}}_{c}^{+}$ may be ${\tfrac{3}{2}}^{-}$, ${\tfrac{5}{2}}^{-}$, ${\tfrac{3}{2}}^{+}$and ${\tfrac{5}{2}}^{+}$, independent of dynamical models.     

Measures on Classes of Subspaces Affiliated with a von Neumann Algebra

Let ℳ be a von Neumann algebra acting on a Hilbert space H and let S be a dense lineal in H that is affiliated with a von Neumann algebra ℳ. The “topological” definition of measures on the classes of orthoclosed and splitting subspaces of S affiliated with a von Neumann algebra ℳ is given and results on the relationships of these measures to measures on orthoprojections of the algebra ℳ are presented.     

Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

Braided Hopf Algebras Obtained from Coquasitriangular Hopf Algebras

In this paper, we study the generalized quantum double construction for paired Hopf algebras with particular attention to the case when the generalized quantum double is a Hopf algebra with projection. Applying our theory to a coquasitriangular Hopf algebra (H, σ), we see that H has an associated structure of braided Hopf algebra in the category of Yetter-Drinfeld modules over , where H _σ is a subHopf algebra of H ⁰, the finite dual of H. Specializing to the quantum group H = SL _q (N), we find that H _σ is , so that the duality between these quantum groups is just the evaluation map. Furthermore, we obtain explicit formulas for the braided Hopf algebra structure of SL _q (N) in the category of left Yetter-Drinfeld modules over . The second author held a postdoctoral fellowship at Mount Allison University from 2005 to 2007 and would like to thank Mount Allison for their warm hospitality. Support for the first author’s research and partial support for the postdoctoral position of the second author came from an NSERC Discovery Grant. The second author now holds research support from Grant 434/1.10.2007 of CNCSIS.     

The Automorphism Group of a Simple Tracially AI Algebra

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, is totally disconnected. Another consequence of our results is the following: Suppose A is the transformation group C*-algebra of a minimal Furstenberg transformation with a unique invariant probability measure. Then the automorphism group of A is an extension of a simple topological group by the discrete group .     

Covalent hadronic molecules induced by shared light quarks

After examining Feynman diagrams corresponding to the ${\bar{D}}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$, ${\bar{D}}^{(* )}{{\rm{\Lambda }}}_{c}$, ${D}^{(* )}{\bar{K}}^{* }$, and ${D}^{(* )}{\bar{D}}^{(* )}$ hadronic molecular states, we propose a possible binding mechanism induced by shared light quarks. This mechanism is similar to the covalent bond in chemical molecules induced by shared electrons. We use the method of QCD sum rules to calculate its corresponding light-quark-exchange diagrams, and the obtained results indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so they obey the Pauli principle. We build a toy model with four parameters to formulize this picture and estimate binding energies of some possibly-existing covalent hadronic molecules. A unique feature of this picture is that the binding energies of the (I)J^P = (0)1⁺ $D{\bar{B}}^{* }/{D}^{* }\bar{B}$ hadronic molecules are much larger than those of the (I)J^P = (0)1⁺ ${{DD}}^{* }/\bar{B}{\bar{B}}^{* }$ ones, while the (I)J^P = (1/2)1/2⁺ $\bar{D}{{\rm{\Sigma }}}_{c}/\bar{D}{{\rm{\Sigma }}}_{b}/B{{\rm{\Sigma }}}_{c}/B{{\rm{\Sigma }}}_{b}$ hadronic molecules have similar binding energies.     

Spin (7)-Manifolds with Parallel Torsion Form

Any Spin (7)-manifold admits a metric connection ∇ ^c with totally skew- symmetric torsion T ^c preserving the underlying structure. We classify those with ∇ ^c -parallel T ^c ≠ 0 and non-Abelian isotropy algebra . These are isometric to either Riemannian products or homogeneous naturally reductive spaces, each admitting two ∇ ^c -parallel spinor fields. Supported by the SFB 647: ‘Space–Time–Matter’, German Research Foundation DFG.     

On the Identity of Some von Neumann Algebras and Some Consequences

Among von Neumann algebras, the Weyl algebra W{\mathcal{W}} generated by two unitary groups {U(α)} and {V(β)}, the algebra U{\mathcal{U}} generated by a completely non-unitary semigroup of isometries {U ₊(α)} and the Weyl algebra W₊^h{\mathcal{W}_{+}^{h}} pertaining to a semi-bounded space with homogeneous spectrum of the generator of {V(β)}, all share the property that their representations are completely reducible and the irreducible representations are equivalent. We trace this fact to the identity of these algebras, in the sense that any of them contains a representation of any of the remaining two algebras, which in turn contains the original algebra. We prove this statement by explicit construction. The aforementioned results about the representations of the algebras follow immediately from the proof for any of them. Also, by the above construction we prove for W^h₊{\mathcal{W}^{h}_{+}} the analog of a theorem by Sinai for W{\mathcal{W}} : given {V(β)} with semi-bounded homogeneous spectrum, there exists a completely non-unitary semigroup {U ₊(α)} such that {V(β)} and {U ₊(α)} generate W₊^h{\mathcal{W}_{+}^{h}}.     

New criterion for comparison of classical theory of nucleation in superheated liquids with experimental data

We have obtained inequality $ 1 - {{\Delta \bar \tau } \mathord{\left/ {\vphantom {{\Delta \bar \tau } {\bar \tau }}} \right. \kern-\nulldelimiterspace} {\bar \tau }} < \left( {J \cdot V \cdot \bar \tau } \right)^{ - 1} < 1 + {{\Delta \bar \tau } \mathord{\left/ {\vphantom {{\Delta \bar \tau } {\bar \tau }}} \right. \kern-\nulldelimiterspace} {\bar \tau }} $ 1 - {{\Delta \bar \tau } \mathord{\left/ {\vphantom {{\Delta \bar \tau } {\bar \tau }}} \right. \kern-\nulldelimiterspace} {\bar \tau }} < \left( {J \cdot V \cdot \bar \tau } \right)^{ - 1} < 1 + {{\Delta \bar \tau } \mathord{\left/ {\vphantom {{\Delta \bar \tau } {\bar \tau }}} \right. \kern-\nulldelimiterspace} {\bar \tau }} , where J is the frequency of homogeneous nucleation, V and $ \bar \tau $ \bar \tau are, respectively, volume and average lifetime of the superheated liquid, and $ {{\Delta \bar \tau } \mathord{\left/ {\vphantom {{\Delta \bar \tau } {\bar \tau }}} \right. \kern-\nulldelimiterspace} {\bar \tau }} $ {{\Delta \bar \tau } \mathord{\left/ {\vphantom {{\Delta \bar \tau } {\bar \tau }}} \right. \kern-\nulldelimiterspace} {\bar \tau }} is relative statistical error $ \bar \tau $ \bar \tau . Inequality appears to be a consequence of nucleation homogeneity and stability used at its deduction and taken in the theory as initial and determinant assumption. Calculations with the use of experimental data for the boundaries of the attainable superheating show that inequality is not satisfied. Thus, experimental data can not be considered a proof of the theory fundamentals.     

Improved analysis of the rare decay processes of Λ_b

It is noted that in the new Particle Data Group(PDG) version the rare decays of the Λ_b baryon have been revised with more accuracy. The new results show that most of the existing theoretical results on the process Λ_b→Λ_γ Lgbare larger than those of experiments. With the improved higher-order light-cone distribution amplitudes of the Λ baryon, we reanalyze the process in the framework of light-cone quantum chromodynamics sum rules and the branching ratio is estimated to be Br (Λ_b→Λ_γ)=(7.38_(-0.39)~(+0.40))×10~(16), which is consistent with the new experimental result. Furthermore, another process Λ_b→Λl~+l~- is also analyzed in the same frame. The final branching ratio is calculated to be Br (Λ_b→Λl~+l~-)=1.20×10~(-6), which is in good accordance with the data from the PDG and other theoretical predictions.     

Parity-violating neutron spin rotation in hydrogen and deuterium

We calculate the (parity-violating) spin-rotation angle of a polarized neutron beam through hydrogen and deuterium targets, using pionless effective field theory up to next-to-leading order. Our result is part of a program to obtain the five leading independent low-energy parameters that characterize hadronic parity violation from few-body observables in one systematic and consistent framework. The two spin-rotation angles provide independent constraints on these parameters. Our result for np spin rotation is $\frac{1} {\rho }\frac{{d\varphi _{PV}^{np} }} {{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1} {2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1} {\rho }\frac{{d\varphi _{PV}^{np} }} {{dl}} = \left[ {4.5 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {2g^{\left( {^3 S_1 - ^3 P_1 } \right)} + g^{\left( {^3 S_1 - ^3 P_1 } \right)} } \right) - \left[ {18.5 \pm 1.9} \right] rad MeV^{ - \frac{1} {2}} \left( {g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 2} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), while for nd spin rotation we obtain $\frac{1} {\rho }\frac{{d\varphi _{PV}^{nd} }} {{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right)$\frac{1} {\rho }\frac{{d\varphi _{PV}^{nd} }} {{dl}} = \left[ {8.0 \pm 0.8} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^1 P_1 } \right)} + \left[ {17.0 \pm 1.7} \right] rad MeV^{ - \frac{1} {2}} g^{\left( {^3 S_1 - ^3 P_1 } \right)} + \left[ {2.3 \pm 0.5} \right] rad MeV^{ - \frac{1} {2}} \left( {3g_{\left( {\Delta {\rm I} = 0} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} - 2g_{\left( {\Delta {\rm I} = 1} \right)}^{\left( {^1 S_0 - ^3 P_0 } \right)} } \right), where the g ^(X-Y), in units of $MeV^{ - \frac{3} {2}}$MeV^{ - \frac{3} {2}}, are the presently unknown parameters in the leading-order parity-violating Lagrangian. Using naıve dimensional analysis to estimate the typical size of the couplings, we expect the signal for standard target densities to be $\left| {\frac{{d\varphi _{PV} }} {{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}} {m}$\left| {\frac{{d\varphi _{PV} }} {{dl}}} \right| \approx \left[ {10^{ - 7} \ldots 10^{ - 6} } \right]\frac{{rad}} {m} for both hydrogen and deuterium targets. We find no indication that the nd observable is enhanced compared to the np one. All results are properly renormalized. An estimate of the numerical and systematic uncertainties of our calculations indicates excellent convergence. An appendix contains the relevant partial-wave projectors of the three-nucleon system.     

On the Zero-Temperature Limit of Gibbs States

We exhibit Lipschitz (and hence Hölder) potentials on the full shift ${\{0,1\}^{\mathbb{N}}}We exhibit Lipschitz (and hence H?lder) potentials on the full shift {0,1}^\mathbbN{\{0,1\}^{\mathbb{N}}} such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are “exponentially decaying” interactions on the configuration space {0,1}^{\mathbb Z}{\{0,1\}^{\mathbb Z}} for which the zero-temperature limit of the associated Gibbs measures does not exist. In higher dimension, namely on the configuration space {0,1}^\mathbbZd{\{0,1\}^{\mathbb{Z}^{d}}}, d ≥ 3, we show that this non-convergence behavior can occur for the equilibrium states of finite-range interactions, that is, for locally constant potentials.     

Spectral Lattices

Spectral orthomorphisms between the spectral lattices of JBW algebras which preserve the scales extend to Jordan homomorphisms for a large class of algebras. Spectral lattice homomorphism is automatically a σ-lattice homomorphism. The range projection map is, up to a Jordan homomorphism, the only natural map from the spectral lattice onto the projection lattice. Continuity of the range projection determines finiteness of the algebra in Murray–von Neumann comparison theory.