The short-range interaction between skyrmions

We consider the interaction between skyrmions at small separations, and argue that for identical skyrmions it varies as 1/r, where r is the distance between them. There are significant many-body forces which have the effect of making interaction energies small except for skyrmions in direct contact with one another. Our results differ considerably from those found using the product ansatz, in which the unitary matrix describing the pion field is taken to be a product of the matrices for free skyrmions, and we show how these differences may be resolved. We also show how the n^4/3 behaviour of the energy density of dense matter at high baryon densities n may be understood in terms of the skyrmion-skyrmion interaction.     

Excited TBA equations II: massless flow from tricritical to critical Ising model

We consider the massless tricritical Ising model perturbed by the thermal operator _1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massless thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A₄ lattice model of Andrews, Baxter and Forrester (ABF) in Regime IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandermonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.     

Universal enveloping algebra and differential calculi on inhomogeneous orthogonal q-groups

We review the construction of the multiparametric quantum group ISO_q,r(N) as a projection from SO_q,r (N + 2) and show that it is a bicovariant bimodule over SO_q,r(N). The universal enveloping algebra U_q,r(iso(N)), characterized as the Hopf algebra of regular functionals on ISO_q,r(N), is found as a Hopf subalgebra of U_q,r(so(N + 2)) and is shown to be a bicovariant bimodule over U_q,r(so(N)).

An R-matrix formulation of U_q,r(iso(N)) is given and we prove the pairing U_q,r(iso(N)) — ISO_q,r(N)). We analyze the subspaces of U_q,r(iso(N)) that define bicovariant differential calculi on ISO_q,r(N).     

Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Towards a naturally small cosmological constant from branes in 6D supergravity

We investigate the possibility of self-tuning of the effective 4D cosmological constant in 6D supergravity, to see whether it could naturally be of order 1/r⁴ when compactified on two dimensions having Kaluza–Klein masses of order 1/r. In the models we examine supersymmetry is broken by the presence of non-supersymmetric 3-branes (on one of which we live). If r were sub-millimeter in size, such a cosmological constant could describe the recently-discovered dark energy. A successful self-tuning mechanism would therefore predict a connection between the observed size of the cosmological constant, and potentially observable effects in sub-millimeter tests of gravity and at the Large Hadron Collider. We do find self-tuning inasmuch as 3-branes can quite generically remain classically flat regardless of the size of their tensions, due to an automatic cancellation with the curvature and dilaton of the transverse two dimensions. We argue that in some circumstances six-dimensional supersymmetry might help suppress quantum corrections to this cancellation down to the bulk supersymmetry-breaking scale, which is of order 1/r. We finally examine an explicit realization of the mechanism, in which 3-branes are inserted into an anomaly-free version of Salam–Sezgin gauged 6D supergravity compactified on a 2-sphere with nonzero magnetic flux. This realization is only partially successful due to a topological constraint which relates bulk couplings to the brane tension, although we give arguments why these relations may be stable against quantum corrections.     

Spectator fermion binding of bosons

We consider a two-component mixture of charged fermions on neutralizing background with all sign combinations and arbitrarily small mass ratios. In the two-impurity limit for the heavier component we show that the pair forms a bound state for all charge combinations. In the lowest order approximation we derive a closed-form expression for V_eff(r), the binding potential which has short-range repulsion followed by attraction. In the classical limit, when the mass of embedded particles is large, m₂ å m, we can calculate from V_eff(r) also the cohesive energy E and the bond length R of a metallic crystal such as lithium. For lithium metal the lowest-order result is R = 3.1 Å, E = −1.8 eV, while the corresponding experimental values are 3.4 Å and −1.6 eV. The same interaction for two holes on a parabolic band with m₂ > m gives the quantum mechanical bound state which one may interpret as a boson or local pair in the case of high-T_c and heavy-fermion superconductors.     

Two types of the effective mass divergence and the Grüneisen ratio in heavy-fermion metals

The behavior of the specific heat c_p, effective mass M^*, and the thermal expansion coefficient of a Fermi system located near the fermion condensation quantum phase transition (FCQPT) is considered. We observe the first type behavior if the system is close to FCQPT: the specific heat , , while the thermal expansion coefficient . Thus, the Grüneisen ratio Γ(T)=/c_p does not diverges. At the transition region, where the system passes over from the non-Fermi liquid to the Landau Fermi liquid, the ratio diverges as . When the system becomes the Landau Fermi liquid, Γ(T,r)∝1/r, with r being a distance from the quantum critical point. Provided the system has undergone FCQPT, the second type takes place: the specific heat behaves as , M^*∝1/T, and =a+bT with a,b being constants. Again, the Grüneisen ratio diverges as .     

Statistical analysis of the Perseus-Pisces redshift survey: spatial and luminosity properties

We analyze the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) Γ(r) is a power law up to the sample effective depth ( 30 h⁻¹ Mpc), showing the fractal nature of the galaxy distribution in this catalog. The fractal dimension turns out to be D 2. We also consider the CF ξ(r) and in particular the behavior of the “correlation length” r₀ (ξ(r₀)1) as function of the sample size. In this respect we find, unambiguously, that the luminosity segregation effect is not supported by any experimental evidence. In addition we have studied the galaxian number-density (n(r)) and number-counts (N(m)) in the VL subsamples finding a good agreement with the properties of a fractal distribution. In particular our conclusion is that the n(r) relation permits to extend the analysis of the fractal nature up to a deeper depth than that reached by the CF analysis, and, we find evidence for fractal properties up to the limiting depth of 130 h⁻¹ Mpc. We clarify the role of the small-scale fluctuations in the determination of the galaxy counts. Even in this case the results are in agreement with the previous ones. Finally we have considered the correlations between galaxy positions and luminosities by means of the multifractal analysis. We find clear evidence for self-similar behavior of the whole luminosity-space distribution. These results confirm and extend those of Coleman and Pietronero (1992).     

Electron paramagnetic resonance measurements for (La,Y)2/3(Ca,Ba)1/3MnO3

We have measured the paramagnetic (PM) resonance behavior as a function of temperature for various manganese perovskites (La,Y)_2/3(Ca,Ba)_1/3MnO₃ with an average A-site size r_A basically covering the whole region of ferromagnetic (FM) metallic ground state. We show that at least three regions with different magnetic behaviors can be distinguished by two phase lines: T_onset−r_A and T_c−r_A. For each given r_A, the complete PM and long-range FM behaviors appear above T_onset and below T_c, respectively; while some anomalous PM behaviors appear for the intermediate temperature range of T_onset<T<T_c . A possible magnetic transition process is discussed in order of decreasing temperature from high-T complete paramagnetism to low-T long-range ferromagnetism.     

具有时滞反馈的非对称双稳系统中的振动共振研究

研究了具有时滞反馈的非对称双稳系统中的振动共振现象. 在绝热近似条件下, 应用快慢变量分离法得到系统响应振幅的解析表达式Q, 分析了时滞参数α和不对称参数r对振动共振现象的影响. 结果表明: 在Q-α平台上, α可以诱导响应幅值的极大值以输入高频信号和低频信号的周期出现. 不对称参数并不影响共振发生的位置, 但是能够增强响应幅值. 在Q-B (B为高频信号振幅)平台上, 共振发生的位置B_VR随着α呈现两种不同的周期关系, 且周期分别为输入高频信号和低频信号的周期. 在Q-Ω (Ω高频信号频率)平台上, 随着时滞参数的增大, 当B较小时, 在Ω的小值区间内, Q呈现出多重共振现象, 在Ω的大值区间, Q趋于定值.     

Critical theory of overscreened Kondo fixed points

The low-temperature fixed point of the Kondo model, for k bands and a spin-s impurity, is well understood by Nozières' Fermi liquid theory for k 2s. However when k > 2s, a new type of non-trivial fixed point is known to occur. We study this fixed point using higher-level Kac-Moody conformal field theory and Cardy's approach to boundary critical phenomena. The specific heat and magnetization are shown to be determined by the leading irrelevant operator and the corresponding critical exponents are obtained exactly. The Wilson ratio is argued to be universal and its exact value is also calculated. The asymptotic finite-size spectrum is determined. Thermodynamic exponents agree precisely with the Bethe ansatz; for k = 2, S = 1/2, the Wilson ratio also agrees well with the approximate value obtained from the Bethe ansatz; the slope of the β-function agrees with the perturbative result in the large-k limit and the finite-size spectrum agrees excellently with approximate results obtained previously by Wilson's numerical renormalization group method in the case k = 2, S = 1/2.     

Kondo screening in gapless magnetic alloys

The low-energy physics of a spin- Kondo impurity in a gapless host, in which the density of band states ρ₀(ε)=|ε|^r/(|ε|^r+β^r) vanishes at the Fermi level ε=0, is studied by the Bethe ansatz. It is shown that the growth of the parameter Γ_r=βg^−1/r (where g is an exchange coupling constant) drives the ground state of the system from the Kondo regime with a screened impurity spin to the Anderson regime, where the impurity spin is unscreened. However, in a weak magnetic field H, the impurity spin exceeds its free value, , due to a strong coupling to a band.     

Proposal to identify the long range force in the low energy neutron-nucleus scattering

In the neutron-Pb scattering in the MeV. region, existence of the long range interaction has been known and people have hopefully expected to understand it as the effect of the electric polarization of the neutron. However the precise determination of _n in the very low energy region indicates that the polarizability of the neutron _n is around two order of magnitude smaller compared to what is expected in the phenomena in the MeV. region. In order to settle the problem, we propose to determine power of the long range tail ν(r) −C/r of the nuclear potential, by measuring precisely the angular distribution of the low energy n-Pb scattering.     

Practical aspects involved in the design and set up of a 0.15 T, 6-coil resistive magnet, whole body NMR imaging facility

Many technical and logistical questions must be addressed when planning the installation of an NMR imaging system. These considerations become particularly significant when the facility is being established within an existing medical center complex. This paper presents a report on the practical aspects and experience obtained in siting a 6-coil 0.15 T resistive magnet system. The topics discussed include: floor loading; ferromagnetic environment; the effect of iron on the magnet field strength and homogeneity characteristics; shimming procedures; temperature stability requirements; rf shielding; and effects of the magnetic field on common medical instrumentation and magnetic media. It was found that the field shift as a function of the distance of a steel mass from the center of the magnet exhibited an (1/r)^5.2±0.5 to (1/r)^4.2±0.3 dependence for axial and radial positions respectively which, as expected, is somewhat weaker than the (1/r)⁶ dependence expected by point dipole approximations. Field distortions caused by the presence of ferromagnetic material in radial positions may be essentially fully compensated with first order transverse shim coils (most conveniently, the x and y imaging gradient coils could be used). Axially distributed material requires, in addition to first order z-gradient correction, higher order axial shim compensation. The temperature stability of the magnet system over the scan period must be better than 0.2°C to insure that temperature-induced field fluctuations are less than the intrinsic static inhomogeneity: and, ideally, below 0.01°C to reduce these fluctuations to less than those caused by power supply instability.     

The particle emitter size dependence on energy in ee annihilations into hadrons

The nearly energy independent hadron emitter dimension r, measured in e⁺e⁻ annihilation in the energy range 10 to 91 GeV via the Bose–Einstein correlation of two identical charged pions, is shown to be well accounted for by choosing the hadron jets as independent pion sources. To this end the known normalised factorial cumulant moments dependence on particle sources is adapted to the Bose–Einstein correlation formalism to yield a relation between r and these sources. This approach is also able to account for the measured r values obtained for the Z⁰ decays into two and three hadron jets. Finally the estimated r value of the hadronic (9.46) decay via three gluons is expected to be higher by about 6 to 11% over that predicted for its one photon hadronic decay mode.     

On matching conditions in the WKB method

The modified matching conditions for quasiclassical wave functions on both sides of a turning point for the radial Schrödinger equation have been obtained. They differ significantly from the usual Kramers condition which holds for the one-dimensional case. Namely, the ratio C₂/C₁ in the subbarrier and the classical allowed regions is not a universal constant ( , as usual), but depends on the values of the orbital angular momentum l, energy E and on the behaviour of the potential V(r) at r → 0. The comparison with exact and numerical solutions of the Schrödinger equation shows that the modified matching conditions not only make the quasiclassical approximation in the subbarrier region asymptotically exact within the n → ∞ limit, but also considerably enhances its accuracy even in the case of small quantum numbers, n 1. The power-law, funnel and short-range potentials are considered in detail.     

用MCH方法研究库仑屏蔽势的高角动量能谱

以库仑屏蔽势为模型,用蒙特卡罗哈密顿方法对库仑屏蔽势束缚态进行研究,并把结果和传统的数值解一维薛定谔方程的方法相比较,在基态或激发态,都得出相一致的结果.     

A generalized Vlasov equation

A two-special dimension electronic system characterized by a plasma parameter Γ 1 is analyzed; then, by using a rigorous non-equilibrium statistical mechanical theory, the evolution of distribution function is considered. A generalized Vlasov equation (GVE) is derived. Compared to the usual Vlasov equation, GVE presents an additional velocity-dependent correlation term. Taking as a starting point the GVE, the phenomenological approximation to two-particles function, ƒ₂(r₁r₂p₁p₂; t) = ƒ₁(r₁p₁;t)f₁(r₂p₂;t)g(r₁−r₂), proposed by Singwi, Tosi, Landi and Sjolander is analyzed.     

The construction of c-number fields and their nonlinear equations of motion for quantum many-body fermion systems

A k-dependent state has been constructed from two paris of mutually commuting Fermi-Dirac operators by replacing the Grassmann numbers in the conventional definition of a fermion coherent state. The Heisenberg time-dependent form of this state was then combined with a particular spin state to give a resultant state |G, the spin component containing a series of unknown k-dependent weights. A classical c-number field, φ(r,t), was then defined by an expectation value of the quantum field, ψ, using |G and an energy and time-dependent phase. It is demonstrated that the form of the equation of motion for φ_c(r,t) is identical to that for ψ.     

Algebraic Bethe ansatz for the gl(1|2) generalized model and Lieb–Wu equations

We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model. Specifying the parameters appropriately, we obtain the Bethe ansatz equations of the supersymmetric t-J model, the Hubbard model, or of Yang's model of electrons with delta interaction. This means that the Bethe ansatz equations of these (and many other) models can be obtained from a common algebraic source, namely from the Yang–Baxter algebra generated by the gl(1|2) invariant R-matrix.