Singular behavior of 1 P 1 + - quarkonium and positronium annihilation decays and relevance of relative energy

Using a four dimensional approach, we show that the singularities for small gluon momenta, which arise in the usual three dimensional treatment of the annihilation decay, disappear if all poles in the relative energy are taken into account correctly in the integration. We obtain an explicit formula for the decay width which involves a non-locality originating from the kinetic energy. We calculate not only the familiar logarithmic dependence on the binding energy, but also the constant to be added to the logarithm. The logarithmic term agrees with previous values in the literature. In QCD the constant turns out to be quite small, but only because there is an almost perfect cancellation between the tree graph and a non-abelian loop graph which contributes to the decay amplitude to the same order.Received: 31 March 2004, Revised: 5 May 2004, Published online: 2 July 2004     

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E in a given reference frame were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We show that a tetrad field contains two informations about local rotation, which usually do not coincide. We compute the energy operator in the inertial and the rotating frame, using three different tetrad fields. We find that Mashhoon’s term is there if the spatial triad rotates as does the reference frame—but then it is also there in the energy operator for the inertial frame. In fact, if one uses the same given tetrad field, the Dirac Hamiltonian operators in two reference frames in relative rotation differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame.     

飞秒脉冲参量影响金属表面热特性的研究

采用有限差分法对约化后的双温方程进行数值模拟.研究了飞秒激光与金属铜相互作用时,脉冲形状对烧蚀结果的影响.结果表明：脉冲能量确定时,脉冲形状对烧蚀结果影响不大;多脉冲作用时,脉冲重复频率只有在一定范围内（随材料属性改变）,脉冲间的热累积效应才存在;对传导性好的金属材料,热累积效应不明显.并实验证实了上述结果.     

On-shell faddeev equations: A democritean approach to the three-body problem

Coupling the mass-energy relationδE≧mc² to the uncertainty relationδE δt ≧ ? produces fluctuations in the number of particles at short distances and scatterings of particle pairs independent of any specific “interaction” mechanism. This observation allows the construction of a scattering theory in which there are only particles and the void, but particle number can change. We consider a system of three massive particles (hadrons) in the energy region below the first production threshold for a fourth hadron and above the first anomalous threshold for the presence of a fourth “virtual” hadron. The on-shell Faddeev equations, containing only two-particle scattering phases for positive two particle energies, provide a convergent, unitary, and readily soluble dynamics for this system. If any of the pairs can coalesce into a different particle with a rest energy less than the sum of the rest energies of the pair, the equations can be readily extended to describe 3-2 and 2–3 transitions involving this particle (coalescence, breakup) elastic scattering from it, and if there is more than one such particle 2-2 rearrangements. The three-body “bound state” requires a well defined analytic continuation. Features of more conventional calculations of three-nucleon problems which provide examples of this structure are discussed. Since only free particles occur in the theory, and the only failure of energy conservation is that required by the uncertainty principle for (free-particle) intermediate states, these one-variable equations might be extended to particles with the relativistic connection between mass, energy and momentum, and transitions in which the full rest energy of the particle which appears or disappears must be provided. The non-linear “crossed” theory for such particles has not been written down, but if the relativistic boundary condition model of Brayshaw is viewed as representing these crossed processes by a phenomenological core, then a crossed theory requiring the π to be a bound state of three π's might predict the π-π S-wave scattering length in theI=0 state in terms of the pion Compton wavelength (and hence the position and the width of the?) and will then show that the? in turn generates asingle ω resonance at about the right place. Implications are discussed.     

Threshold anomaly in non-central forces

The behaviour of the threshold anomaly for non-central potentials, which account for collective excitations in heavy-ion collisions, is investigated. It is shown that the non-central potentials should exhibit an energy dependence at energies in the vicinity of the Coulomb barrier. This energy dependence is, however, different from that of the elastic optical potential, occurring at lower energies. It if further shown that there are corrections to the traditional collective model such that, if the transition potential is expressed as the derivative of the optical potential, the corresponding deformation length will be complex and energy-dependent. Simple model calculations are presented.     

Generalization of Faraday's Law to include nonconservative spin forces

The usual Faraday's Law E=-dPhi/dt determines an electromotive force E which accounts only for forces resulting from the charge of electrons. In ferromagnetic materials, in general, there exist nonconservative spin forces which also contribute to E. These might be included in Faraday's Law if the magnetic flux Phi is replaced by [Planck's constant/(-e)]gamma, where gamma is a Berry phase suitably averaged over the electron spin direction. These contributions to E represent the requirements of energy conservation in itinerant ferromagnets with time dependent order parameters.     

Interaction Energy of Two Trapped Bosons with Long Scattering Lengths

 I study two interacting bosons confined to a harmonic trap. The interaction is assumed to be of zero range and is expressed in terms of the s-wave scattering length. The energy shifts of the harmonic-oscillator states due to the atom-atom interaction are calculated analytically. It is found that for an ordinary potential the interaction energy depends only on the scattering length, while if the scattering length is modified by a near-threshold Feshbach resonance there is also a dependence on the width of the resonance. Received October 25, 2001; accepted for publication November 9, 2001     

Use of catastrophe theory to obtain a fundamental understanding of elementary particle stability

Using Arnold's Classification Theorem applied to a four-dimensional manifold, it is shown that there is only a finite number of ways in which energy can discontinuously change state. It is demonstrated that each of these energy flow pathways can be associated with a distinct elementary particle. The theory not only shows how the formation of particles from the stress-energy present in the space-time manifold can be predicted from first principles, but also that there must exist five fundamental forces in a universe in which discontinuous energy transitions are possible. Finally, the existence of a new, as yet undiscovered particle is predicted, which is associated with this new fifth force.     

Relationship between the classical transport coefficients and hydrodynamic kernels for quantum-field models

A study is made of the classical limit of nonlocal hydrodynamics, describing quantum systems of many particles. The quantum-field model is not specified, it being assumed only that there are local laws governing the conservation of energy — momentum and the number of particles. Changing over to the classical limit corresponds in nonlocal hydrodynamics to the limit of slow processes and long waves. It is shown that a hydrodynamics with viscosity and self-diffusion but without heat conduction is obtained in this case because the velocity of the medium is determined in terms of the energy flux, which is natural for quantum-field systems. Heat conduction can be introduced if velocity is instead determined in terms of particle flux. Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika No. 8, pp. 61–66, August, 1996.     

Further experimental evidence for fast fission

Fusion-fission products have been studied for three reactions: Ar + Au, Ar + Bi and Ar + U (5.25–7.5 MeV/u). By measuring symmetric fragmentation components (fission-like events), cross sections for fusion were deduced and compared with the predictions of static and dynamic models. With increasing projectile energy, the width of the mass distributions strongly increases for the two lighter systems. By contrast, for Ar + U it remains essentially constant at a very large value. These results clearly demonstrate that the large increase of the width of the mass distribution cannot be attributed simply to large values of the angular momentum. However, they can be explained by the occurence of a different dissipative process, fast fission, which can be expected if there is no barrier to fission. For the reaction Ar + Au, the total kinetic-energy distributions were also studied in detail. In this case fast fission occurs only at high incident energy. The average total kinetic energy (TKE) was found to be constant with increasing energy whereas the widths of the TKE distribution increase.     

晶体摆动场的辐射衰减与能量增益

由于晶体弯曲、电子多重散射和晶格热振动引起的粒子退道,辐射同原子相互作用引起的电离损失,以及系统非线性引起的全局分叉与混沌行为等,晶体摆动场辐射面临的问题比自由电子激光要复杂得多。首先,引入晶体摆动场自发辐射谱分布,并在简谐近似下讨论了运动方程、系统增益和能量衰减。结果表明:一般情况下辐射谱只有少数几条谱线,而在简谐近似下,谱线只有一条。其次,指出了辐射能量比较高时,衰减是主要的,选择的晶体长度必须小于衰减长度,且可选择正电子或质子作炮弹;当辐射能量比较低时,退道是主要的,选择的晶体长度必须小于退道长度,且可选择重离子作炮弹。     

Thermodynamic limitation on the conversion of heat into coherent radiation

From the thermodynamical point of view there is the possibility of supplying a small amount of the energy of coherent radiation from a thermal reservoir. This possibility is attributed to the finite flow of entropy of light which is coherent but shows amplitude and/or phase fluctuations even if the radiation field consists of only a single mode.     

The derivation and solution of the modal flux equations for backscattering in a duct in the presence of random space and time fluctuations

Abstract

In this paper we first derive the equations governing the energy fluxes propagating in each of the modes of a duct. In each mode there is a forward and backward component and the equations are intended to treat ducts in which backscattering plays a major role. The modal fluxes are coupled since there is transfer of energy between the modes that occurs as a result of random time and space sound-speed fluctuations in the medium in the duct. Since the fluctuations are both space and time dependent the governing equations are radiation transport equations. This is not the case if the fluctuations depend only on space. The basic method is to develop a coupled set of equations for the energy spectra in the modes and then to integrate over the frequency to obtain the fluxes. In the second section of this paper the modal flux equations are solved. A numerical result is presented to show how energy is transferred between modes. It is also shown how the reflected energy varies as a function of duct length.     

Is the evidence for dark energy secure?

Several kinds of astronomical observations, interpreted in the framework of the standard Friedmann–Robertson–Walker cosmology, have indicated that our universe is dominated by a Cosmological Constant. The dimming of distant Type Ia supernovae suggests that the expansion rate is accelerating, as if driven by vacuum energy, and this has been indirectly substantiated through studies of angular anisotropies in the cosmic microwave background (CMB) and of spatial correlations in the large-scale structure (LSS) of galaxies. However there is no compelling direct evidence yet for (the dynamical effects of) dark energy. The precision CMB data can be equally well fitted without dark energy if the spectrum of primordial density fluctuations is not quite scale-free and if the Hubble constant is lower globally than its locally measured value. The LSS data can also be satisfactorily fitted if there is a small component of hot dark matter, as would be provided by neutrinos of mass ∼0.5 eV. Although such an Einstein–de Sitter model cannot explain the SNe Ia Hubble diagram or the position of the “baryon acoustic oscillation” peak in the autocorrelation function of galaxies, it may be possible to do so, e.g. in an inhomogeneous Lemaitre–Tolman–Bondi cosmology where we are located in a void which is expanding faster than the average. Such alternatives may seem contrived but this must be weighed against our lack of any fundamental understanding of the inferred tiny energy scale of the dark energy. It may well be an artifact of an oversimplified cosmological model, rather than having physical reality.     

Le Châtelier–Braun principle in cosmological physics

Assuming that dark energy may be treated as a fluid with a well-defined temperature, close to equilibrium, we argue that if nowadays there is a transfer of energy between dark energy and dark matter, it must be such that the latter gains energy from the former and not the other way around.     

Solutions of Maxwell's equations for charge moving with the speed of light

It is shown that Maxwell's equations admit solutions for charge moving with the speed of light. These are globally regular, but if the charge is one of sign only, the total energy is infinite. However, if equal amounts of positive and negative charge are present, the total energy can be finite, and such solutions seem physically unobjectionable.     

On axially-symmetric finite-energy monopole configurations

Axially symmetric finite energy monopole configurations are investigated for the gauge group SO(3) with the Higgs field in the adjoint representation. To avoid the complications due to gauge freedom gauge invariant fields are introduced and used throughout. From topological and continuity considerations it is argued that the only regular axially symmetric magnetic charge distributions permitted are isolated charges of uniform strength and alternate sign located along the axis of symmetry. In particular, if there is only one sign, the magnetic charge must be located at a single point. For a zero Higgs potential the minimal energy (first order Bogomolny) field equations take a simple form when written in terms of the gauge-invariant fields. In general, there are nine equations for nine (axially symmetric) fields, but these reduce to five equations for five fields if a further symmetry (invariance under reflexions in planes through the axis of symmetry) is imposed. Remarkably, four of the equations are the same whether the reflexion symmetry is imposed or not, and these four equations can be completely solved in terms of a master potential. From these and the remaining equations (just one in the case of mirror symmetry) the asymptotic behaviour of the functions at large distances and in the neighbourhood of the origin (the location of the charge) is obtained and studied in some detail.     

Economics of isomeric energy

A high energy density source based on nuclear isomers may be conceptually attractive; but it is unrealistic if the energy’s price is too excessive. This paper estimates the price of isomeric energy, and shows that isomers can become practical only for low-energy applications.     

Brownian ratchets in physics and biology

Thirty years ago Feynman et al. presented a paradox in the Lectures on Physics: an imagined device could let Brownian motion do work by allowing it in one direction and blocking it in the opposite direction. In the chapter Feynman et al. eventually show that such ratcheting can only be achieved if there is, in compliance with the basic conservation laws, some energy input from an external source. Now that technology is going into ever smaller dimensions, ratcheting Brownian motion seems to be a real possibility in nanotechnological applications. Furthermore, Brownian motion plays an essential role in the action of motor proteins (individual molecules that convert chemical energy into motion).     

Incompatibility of BCS pairing and the Peierls distortion in linear chain systems

We have solved the coupled gap equations for a one dimensional electron gas which can undergo both a Peierls insulating and a BCS superconducting transition. We find that, except for a very special case, (i) only one of the order parameters can be non-vanishing and (ii) there is only one critical temperature. We conclude that, independent of the pairing interaction strength, if the Peierls transition occurs, there can be no BCS superconductivity, and conversely.