Hilbert Schemes, Separated Variables, and D-Branes

We explain Sklyanin's separation of variables in geometrical terms and construct it for Hitchin and Mukai integrable systems. We construct Hilbert schemes of points on T ^*Σ for Σ=C, C ^* or elliptic curve, and on C ²/Γ and show that their complex deformations are integrable systems of Calogero–Sutherland–Moser type. We present the hyperk?hler quotient constructions for Hilbert schemes of points on cotangent bundles to the higher genus curves, utilizing the results of Hurtubise, Kronheimer and Nakajima. Finally we discuss the connections to physics of D-branes and string duality. Received: 2 November 2000 / Accepted: 7 May 2001     

反常波海面参数计算方法及其色散关系

提出了一种计算反常波海面参数及色散关系的数值方法.将反常波海面看成变幅变频的波列,在各个具体时间、空间点用不同参数的延拓正弦波进行插值.在具体的时间、空间点处,根据海面及其一阶、二阶导数关系,求出相应的延拓正弦波各个参数.数值模拟出的振幅结果表明该方法有效,利用该方法计算的反常波海面参数进行海面重构的结果与原海面完全符合.比较非线性海面波数和角频率的关系式ω²/k与重力加速度g值,发现反常波海面的主要非线性色散区域不是位于反常波区域,而是位于 关键词： 反常波 非线性 色散     

Spin fluctuations in metals: Application to the actinides

We present here a review of the spin fluctuation theory and of its applications to transition and actinide systems, with a particular emphasis to the latter where some very anomalous properties find an explanation in terms of spin fluctuation effects. Firstly, we summarize the development of the spin fluctuation model which had been initially applied to transition metals and alloys such as palladium or Pd–Ni alloys. Then, we present the extension of the paramagnon model to nearly magnetic actinide systems by taking into account explicitly the temperature dependence of the Stoner susceptibility, because the 5f-band of actinides is much narrower than the d-band of transition metals. As a result the paramagnon contribution to the resistivity departs from the usual T ² and T power laws at temperatures higher than the spin fluctuation one and saturates at high temperatures, with eventually the presence of a maximum at intermediate temperatures. We present also the calculation of the other properties of actinide systems, namely the thermal resistivity, the thermoelectric power, the magnetic susceptibility, the specific heat capacity and the NMR relaxation rate, which are generally enhanced by the presence of paramagnons. Finally, we have introduced the concept of ‘antiferromagnetic-like’ spin fluctuations which have a maximum of the q-dependent susceptibility _χ(q) at a q value different from q =0, in contrast to the regular ferromagnetic spin fluctuations; both types of spin fluctuation give the same resistivity behaviour, while they yield a markedly different behaviour of the magnetic susceptibility, in agreement with experiment. The spin fluctuation theory is applied successfully to the different properties of neptunium and plutonium metals and of many nearly magnetic compounds such as UAl₂.     

Calculation of magnetic multipole moment integrals using translation formulas for Slater-type orbitals

Using translation formulas for Slater type orbitals (STO’s) the infinite series through the overlap integrals are derived for the magnetic multipole moment integrals. By the use of the derived expressions the magnetic multipole moment integrals, therefore, the magnetic properties of molecules can be evaluated most efficiently and accurately. The convergence of the series is tested by calculating concrete cases. An accuracy of 10⁻⁵ for the computer results is obtained in the case 2 ^p -pole magnetic moment integrals for 1 ≤ v ≤ 5, and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.     

Unconventional semiclassical method for calculating the energetic values of diatomic molecules

In previous papers we proved that the geometrical elements of the wave described by the Schrödinger equation, namely the wave surfaces and their normals, denoted by C curves, are solutions of the Hamilton–Jacobi equations, written for the same system, in the case of stationary systems. The C curves correspond to the same constants of motion as the eigenvalues of the Schrödinger equation. In two recent papers we presented a central field method for the calculation of the C curves, and of the corresponding energetic values. The method was verified for the atoms He, Li, Be, B, C, N and O. In this paper we extend this method, using the symmetry properties of the systems, in the case of the diatomic molecules, with exemplification for Li₂, Be₂, B₂, C₂, LiH, BeH, BH and CH. The accuracy of the method is, as in the case of the atoms, comparable to the accuracy of the Hartree–Fock method, for the same system. This could be a potential useful result, because our approach predicts also basic properties of the molecules in discussion.     

Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins

In this paper each helicity amplitude of the two-body scattering of particles with arbitrary spins is considered as an element of a special class of Hilbert spacesH ^[u]. This space, which is called reproducing kernel Hilbert space (RKHS) has many special properties that appear to make it a natural space of functions to associate with the scattering helicity amplitudes. Some of the special properties of the RKHS are developed and then used to characterization of reproducing kernel (RK) ofH ^[u] as the solution to certain extremal problems. Then, it was shown that the optimal scattering state from the RKHS of the helicity amplitudes is analogous to the coherent state from the RKHS of the wave functions. The essential characteristic features of the scattering of particles with arbitrary spins in the optimal state dominance limit are established. An important alternative to the partial wave helicity analysis in terms of a fundamental set of optimal states is presented.     

Quantum statistical mechanics for superstable interactions: Bose-Einstein statistics

We study quantum systems of interacting Bose particles confined to a bounded region ofR ^v . For any superstable and (strong) lower regular interaction, we obtain uniform bounds on the expectations of exponentials of local number operators for any activity and for any temperature. The method we use here is an improvement over our previous method on the same subject. As a consequence of the bounds, any infinite volume limit states are entire analytic and locally normal. Furthermore under an integrability condition on the interaction, the limit states are modular states. In this case, we use the Green's function method to construct an infinite volume limit Hilbert spece, a strongly continuous time evolution group of unitary operators and an invariant vector. Moreover we prove the existence of the pressure and its independence of boundary conditions.     

Fundamental interactions

Trapped and stored charged particles, atoms and molecules offer a number of opportunities to measure exact values of important fundamental constants such as lepton magnetic anomalies, the fine structure constant and the electron mass. New Physics can be searched for by comparing precise measurements and highly accurate calculations of particle properties. Some recent experiments differ by a few standard deviations from standard theory predictions, such as the muon magnetic anomaly and ²¹Na β-decay; for a clarification further work is needed. This work is in part supported by the Dutch Stichting voor Fundamenteel Onderzoek der Materie under programme 48 (TRIμP).     

Nonequilibrium properties of re-entrant spin glasses in a magnetic field

In this paper the authors discuss how the re-entrant spin-glass state arises in the disordered alloys Ni_100−x Mn_x (x=19, 21, 23), along with the nonequilibrium magnetic properties of these alloys. It is shown that near the Gabay-Toulouse phase line the time it takes the system to reach equilibrium is comparable to times required to perform static experiments (10¹–10⁴ s); cooling the sample into the region of crossover with the de Almeida-Thouless line causes these times to increase to astronomical values of more than 10¹⁶ s. A method is proposed for constructing magnetic phase diagrams of systems of this type in “magnetic field-temperature” coordinates. Fiz. Tverd. Tela (St. Petersburg) 41, 2028–2033 (November 1999)     

Characterization of magnetic labels for bioassays

Magnetic nanoparticles differing by their size have been synthesized to use them for multiparametric testing, based on their differing magnetic properties. The nanoparticle has two essential roles: to act as a probe owing to its specific magnetic properties and to carry on its surface precursor groups for the covalent coupling of biological recognition molecules, such as antibodies, nucleic acids. A totally unique, newly patented, method has been used to characterize magnetic signatures using the MIAplex technology. The MIAplex reader, developed by Magnisense, measures the non-linear response of the magnetic labels when they are exposed to a multi-frequency alternating magnetic field. This specific signature based on d²B(H)/dH² was correlated to other more conventional magnetic detection methods (superconducting quantum interference devices (SQUID) and Mössbauer).     

Photostimulated electron transfer and its action on paramagnetism of Sp<Subscript>3</Subscript>Cr(C<Subscript>2</Subscript>O<Subscript>4</Subscript>)<Subscript>3</Subscript> single crystals

The effect of irradiation by ultraviolet light on the effective magnetic moment of a paramagnetic single crystal based on photochrome spiropyran (Sp) and chromium oxalates Sp₃Cr(C₂O₄)₃ molecules is detected. It is shown that the deviation of the temperature dependence of the magnetic moment from the Curie law is caused not by the exchange interaction, but by electron redistribution between Cr³⁺ and Cr⁴⁺ ions and spiropyran molecules Sp⁰ and Sp⁺. Analysis of the angular dependence of EPR spectra makes it possible to determine the contribution of Cr³⁺ ions to the magnetic properties of the crystals and to determine the crystal field parameters D = 0.619 cm⁻¹ and E = 0.024 cm⁻¹. Irradiation of hydrated samples by ultraviolet light leads to intensity redistribution of EPR lines attributed to Cr³⁺ and Sp⁰. Thermally stimulated paramagnetism of triplet states of spiropyran ions Sp⁺ and the SpI salt is observed.     

Radioactive ions for solid-state investigations at magnetic surfaces and interfaces

Hyperfine interactions observed at isomeric states of radioactive probe nuclei are used as a tool for solid-state investigations. This method is sensitive to atomic-scale properties. In recent years surface and interface investigations using radioactive probes delivered many results which can hardly be achieved by any other method. Several groups, e.g., from Konstanz, Leuven, Groningen, Aarhus, Uppsala, Tel Aviv, Pennsylvania, contributed to this field. Our group studies magnetic properties at surfaces and interfaces performing perturbed angular correlation (PAC) measurements in the UHV chamber ASPIC (Apparatus for Surface Physics and Interfaces at CERN). We take advantage of the enhanced variety of PAC probes delivered by the on-line mass separator ISOLDE. First, we report on measurements of magnetic hyperfine fields ( B _hf) at Se adatoms on a ferromagnetic substrate using ⁷⁷Se as a PAC probe. The investigation of induced magnetic interactions in nonmagnetic materials is a further subject of our studies. Here the nonmagnetic 4d element Pd is investigated, when it is in contact with ferromagnetic nickel. An outlook will be given on studies to be done in the future. The experiments were performed at the HMI, Berlin, and at CERN, Geneva. Received: 1 May 2001 / Accepted: 4 December 2001     

Dextran‐Coated Antiferromagnetic MnO Nanoparticles for a T1‐MRI Contrast Agent with High Colloidal Stability

A simple approach to synthesize carboxymethyl dextran‐coated MnO nanoparticles (CMDex‐MnONPs) with high colloidal stability in physiological saline solutions is described here for potential applications as a magnetic resonance imaging (MRI) T₁ contrast agent. The thermal decomposition methodology is used to produce uniform MnONPs with an average size of around 20 nm, and its hydrophobic surface is modified with CMDex molecules, conferring hydrophilic properties. After CMDex coating, the nanoparticle presents high colloidal stability in concentrations ranging from 10 to 50 μg mL^?1, average hydrodynamic size (Z‐average) of 130 nm, polydispersity degree of ≈12%, and negative surface charge in both simulated body fluid solutions and pure water with zeta‐potential of –20 and –40 mV, respectively. The CMDex‐MnONPs with 20 nm show antiferromagnetic behavior at room temperature, and the magnetic properties are found to be strongly dependent of the nanoparticle size, increasing the contribution of the ferromagnetic Mn₃O₄ phase with decreasing size for nanoparticles about 3 nm. Cytotoxicity evaluation in cancerous and noncancerous cells in the range of 5.0–50.0 μg mL^?1 shows low toxicity for cancerous cells and lack of the same for healthy cells lines. Related to the magnetic properties, CMDex‐MnONP presents significant r₁ relaxivity and low r₂/r₁ relaxivity ratio. The results suggest that these nanoparticles display characteristics for potential applications as an MRI T₁ contrast agent.     

Some Ideas About Quantitative Convergence of Collision Models to Their Mean Field Limit

We consider a stochastic N-particle model for the spatially homogeneous Boltzmann evolution and prove its convergence to the associated Boltzmann equation when N⟶∞, with non-asymptotic estimates: for any time T>0, we bound the distance between the empirical measure of the particle system and the measure given by the Boltzmann evolution in a relevant Hilbert space. The control got is Gaussian, i.e. we prove that the distance is bigger than xN ^−1/2 with a probability of type O(e^-x2)O(e^{-x^{2}}). The two main ingredients are a control of fluctuations due to the discrete nature of collisions and a kind of Lipschitz continuity for the Boltzmann collision kernel. We study more extensively the case where our Hilbert space is the homogeneous negative Sobolev space [(H)\dot]^-s\smash {\dot {H}}^{-s}. Then we are only able to give bounds for Maxwellian models; however, numerical computations tend to show that our results are useful in practice.     

Nuclear laser spectroscopy using a laser-microwave double-resonance method with an ion trap

With an RF-trap connected to an Isotope Separator On-Line (ISOL), we aim to study nuclear magnetic properties of nuclei far from stability through the hyperfine interaction by a laser-microwave double-resonance method. As a first step, the hyperfine splitting of the ground state of⁸⁷Sr⁺ was measured, and the magnetic dipole hyperfine constant was precisely determined to beA=−1,000,470.8(2.4) kHz.     

Classical Electromagnetic Interaction of a Point Charge and a Magnetic Moment: Considerations Related to the Aharonov–Bohm Phase Shift

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v ² /c ² is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v ² /c ² , does reveal a connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c ⁴ and hence is negligible in a 1/c ² analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c ² , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems.     

Convolution Inequalities for the Boltzmann Collision Operator

We study integrability properties of a general version of the Boltzmann collision operator for hard and soft potentials in n-dimensions. A reformulation of the collisional integrals allows us to write the weak form of the collision operator as a weighted convolution, where the weight is given by an operator invariant under rotations. Using a symmetrization technique in L ^p we prove a Young’s inequality for hard potentials, which is sharp for Maxwell molecules in the L ² case. Further, we find a new Hardy-Littlewood-Sobolev type of inequality for Boltzmann collision integrals with soft potentials. The same method extends to radially symmetric, non-increasing potentials that lie in some L^s_weak{L^{s}_{weak}} or L ^s . The method we use resembles a Brascamp, Lieb and Luttinger approach for multilinear weighted convolution inequalities and follows a weak formulation setting. Consequently, it is closely connected to the classical analysis of Young and Hardy-Littlewood-Sobolev inequalities. In all cases, the inequality constants are explicitly given by formulas depending on integrability conditions of the angular cross section (in the spirit of Grad cut-off). As an additional application of the technique we also obtain estimates with exponential weights for hard potentials in both conservative and dissipative interactions.     

Deformation Quantization for Hilbert Space Actions

Rieffel's theory of deformations of C^*-algebras for -actions can be extended to actions of infinite-dimensional Hilbert spaces. The CCR algebra over a Hilbert space H can be exhibited in this manner as a deformation of a commutative C^*-algebra of almost periodic functions on H. Received: 26 August 1996 / Accepted: 28 January 1997