Does the Aharonov–Bohm Effect Exist?

We draw a distinction between the Aharonov–Bohm phase shift and the Aharonov–Bohm effect. Although the Aharonov–Bohm phase shift occurring when an electron beam passes around a magnetic solenoid is well-verified experimentally, it is not clear whether this phase shift occurs because of classical forces or because of a topological effect occurring in the absence of classical forces as claimed by Aharonov and Bohm. The mathematics of the Schroedinger equation itself does not reveal the physical basis for the effect. However, the experimentally observed Aharonov–Bohm phase shift is of the same form as the shift observed due to electrostatic forces for which the consensus view accepts the role of the classical forces. The Aharonov–Bohm phase shift may well arise from classical electromagnetic forces which are simply more subtle in the magnetic case since they involve relativistic effects of the order v ² /c ² . Here we first review the experimentally observable differences between phenomena arising from classical forces and phenomena arising from the quantum topological effect suggested by Aharonov and Bohm. Second we point out that most discussions of the classical electromagnetic forces involved when a charged particle passes a solenoid are inaccurate because they omit the Faraday induction terms. The subtleties of the relativisitic v ² /c ² classical electromagnetic forces between a point charge and a solenoid have been explored by Coleman and Van Vleck in their analysis of the Shockley–James paradox; indeed, we point out that an analysis exactly parallel to that of Coleman and Van Vleck suggests that the Aharonov–Bohm phase shift is actually due to classical electromagnetic forces. Finally we note that electromagnetic velocity fields penetrate even excellent conductors in a form which is unfamiliar to many physicists. An ohmic conductor surrounding a solenoid does not screen out the magnetic field of the passing charge, but rather the time-integral of the magnetic field is an invariant; this time integral is precisely what is involved in the classical explanation of the Aharonov–Bohm phase shift. Thus the persistence of the Aharonov–Bohm phase shift when the solenoid is surrounded by a conductor does not exclude a classical force-based explanation for the phase shift. At present there is no experimental evidence for the Aharonov–Bohm effect.     

Manifestations of the dynamic Jahn-Teller effect in trigonally distorted defect centres

General effects resulting from the dynamic Jahn-Teller interaction on the single cubic symmetry T ₂ orbital state, which in C_3v forms a basis for the A ₁ + E symmetry representations, are investigated. As a result of the discussion of the types of centre in various host lattices which are likely to exhibit these effects, we are led to consider the centre responsible for the ‘self-activated emission’ in II–VI semiconductors. It is shown that a combination of theory with the experimental E.S.R. and optical polarization data strongly suggests that a dynamic Jahn-Teller interaction is occurring in these centres.     

Classical Electromagnetism and the Aharonov–Bohm Phase Shift

Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v ² /c ² analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that a treatment exactly analogous to that given by Coleman and Van Vleck predicts classical electromagnetic forces which provide the basis for the Aharonov–Bohm phase shift. The magnetic force on the solenoid due to the passing charge leads to a displacement of the solenoid center of energy which must be balanced by the displacement of the passing charge. This classical displacement of the passing charge is exactly what is required to account for the Aharonov–Bohm phase shift. Also, we discuss a magnetic moment model which appears frequently in the literature and note that although the model provides conservation of linear momentum, it does not satisfy the general requirements for relativistic theories. We give an example suggesting that the new equation of motion for a magnetic moment proposed by Aharonov, Pearle, and Vaidman based upon the hidden momentum of the magnetic moment is completely inappropriate. Finally, we emphasize that the Aharonov–Casher phase shift is also explained by classical electromagnetic forces exactly parallel to those explaining the Aharonov–Bohm phase shift.     

The static potential in quantum chromodynamics

The effective interaction between a static quark-antiquark pair is computed within the framework of 〈G_μv^aG_a^μv〉 ≠ 0. Due to the static approximation the interaction takes the form of a potential, which is in striking agreement with phenomenological potentials.     

静态场分量的直接模拟求解

本文探讨了静态场分量直接模拟的一般原理。作为此法的一个用例,对半无限长实心螺线管的场进行了模拟研究。所得结果表明,对于一些特殊的静态场系统能够实现直接模拟,而且具有不少独特优点。上述螺线管的模拟解已用B_z曲线及ψ曲线给出,利用这些曲线可以方便地求解任意螺线管的场分布及力线形状。     

Magnetoelastic waves in an in-plane magnetized ferromagnetic plate

The spectrum of magnetoelastic waves propagating along the magnetic field in an in-plane magnetized ferromagnetic plate is numerically investigated in the exchangeless approximation. No restrictions are imposed either on the field pattern of backward volume magnetostatic waves (BVMSWs) or elastic waves supported by a plate of a given geometry across the plate or on the relationship between the sound velocity v _S and the phase velocity of the magnetoelastic waves v=ω/q (ω is the frequency, q is the wave number). The resonance interaction of the BVMSWs and elastic waves is accompanied, as a rule, by the formation of “stop” bands δω that are proportional to the magnetoelastic coupling constant b. When the BVMSWs are in resonance with Lamb and shear elastic modes the values of the magnetoelastic gaps δω at v≈v _S turn out to be of the same order. For v≫v _S , the efficiency of the interaction between the BVMSWs and transverse Lamb modes is almost one order of magnitude higher. If the frequency spacing Δω between the elastic modes is smaller than the mag-netoelastic gap in the spectrum (Δω≤δω), which takes place, particularly, in the region of crowding the elastic mode spectrum (v≈v _S), the resonant interaction results in mixing the dispersion laws for the elastic modes. Namely, a surface mode may transform into a volume one and a shear mode, into the Lamb mode or into a shear mode with another number. The resonance interaction of the shear and Lamb elastic modes not only forms the magnetoelastic gaps δω∼b ² but also changes the efficiency of elastic wave coupling with the magnetic subsystem. This may show up as the coexistence of the effects of “repulsing” both the dispersion laws and the damping decrements of the elastic waves at the resonance frequency. It is shown that magnetostriction splits the cutoff frequencies of both transverse Lamb modes and shear modes, as well as the long-wave (q → 0) frequency limits f ₀ of the BVMSW modes. This may cause the resonance interaction between BVMSW modes of equal evenness in a narrow frequency band Δ∼b near f ₀.     

Quadrupole interactions in MoCl5 intercalated in graphite

The time-differential perturbed angular correlation technique was used to investigate quadrupole interactions following the decay of⁹⁹Mo as a probe in the intercalation compound graphite-molybdenum pentachloride. Analysis of the 740-(44) 141 keV γ-γ correlation in⁹⁹Tc reveals the presence of two sites with static electric field gradient interactions, one of which corresponds to a moderately damped (δ∼16%), high-frequency interaction (v _q∼630 MHz), the other to a heavily damped (δ∼28%), low-frequency (v _q∼283 MHz) component.     

N.M.R. investigation of critical orientational order fluctuations below the nematic-isotropic transition in liquid crystals

The high-resolution infra-red spectrum of SiH₄ in the region 2101 cm^-1 to 2265 cm^-1 has been analysed. Most of the lines observed have been assigned to transitions of the v ₃ and v ₁ bands of the abundant isotopic species ²⁸SiH₄. The v ₁ band is formally forbidden in the infra-red, but a vibration-rotation interaction between v ₁ and v ₃ lends intensity to the v ₁ transitions. The spectrum has been fitted by diagonalizing the v ₃ = 1 and v ₁ = 1 hamiltonians coupled by the vibration-rotation interaction term. 500 transitions have been fitted with an overall standard deviation of 0·007 cm^-1, using only 15 adjustable parameters (ten in the v ₃ = 1 hamiltonian, four in the v ₁ = 1 hamiltonian, and one interaction coefficient). The calculated intensities are also in good agreement with experiment. Transitions of the other isotopic species ²⁹SiH₄ and ³⁰SiH₄ have also been observed, but these spectra have not been analysed in detail.     

Electromagnetic field perturbation by an internal void in a conducting cylinder excited by a wire loop

A thin prolate spheroidal void in an infinite conducting circular cylinder is used to model an internal flaw in a wire rope. The rope is excited by an electric ring current which is a model for a thin solenoid or multi-turn wire loop. The anomalous external fields are computed from the induced electric and magnetic dipole moments of the void. For this type of excitation, the induced axial magnetic dipole moment is the dominant contributor to the scattered field. The results have application to nondestructive testing of wire ropes.     

Theory of melting,vacancy model

A theory of melting based on vacancy model is formulated. The polymer solution theory is used for derivation of the melting equation for a two-species model of melting solid. Under simplifying assumptions the analysis leads to a simple correlation betweenT _m and 〈v〉, the average energy of interaction between the vibrating atoms. Pseudopotential method is used for calculating 〈v〉 for the alkali metals lithium, sodium, potassium and rubidium at temperatureT _m. The calculated values ofT _m〈v〉 are in accord with those expected from our model. Application to the high pressure melting curves of solids is also discussed.     

2H-NMR Study of ammonium ion rotational tunneling and reorientation in (ND4)2SnCl6 single crystal

Because of the quadrupole interaction, the²H-NMR spectra of a tunneling ND ₄ ⁺ ion depend on the Larmor frequencyv ₀ and the tunneling frequencyv _t , when both frequencies are less than 20 MHz. Calculated single crystal spectra visualize features to be expected. Significant broadening and asymmetry are observed at level crossing regions aroundv _t =v ₀ orv _t =2v ₀. Angular, frequency and temperature dependences of the spectra are studied using an (ND₄)₂SnCl₆ single crystal. Experimental spectra obtained for different frequencies at 4.2K are fitted withv _t as a parameter. The tunneling frequency is also checked by measurements of the deuteron spin-lattice relaxation timeT ₁ as a fuction ofv ₀. Both methods give consistentlyv _t =7.15±0.10 MHz.     

Dynamic optical visualization on the interaction between propagating crack and stationary crack

Dynamic interactions between the propagating crack and the static crack in PMMA material are studied by combining high-speed Schardin camera with optical caustic method. A series of dynamic optical bifocal patterns (the specimen-focused image and the off-focused image) around the propagating crack tip and the static crack tip are recorded for PMMA thin strip which contains two collinear-edge-cracks subjected to tensile loading, the variations of the caustic diameter and the distortion of the caustic shape are revealed due to the influence of local stress singularity at the crack tip. Interactions between the moving crack and the static crack are analyzed by means of the evolution of dynamic fracture parameters. The influence of crack interaction on fracture parameters is discussed based on both a K-dominance assumption and a higher order transient crack-tip expansion. These results will be useful to the evaluation of dynamic properties and the design of structures in the cracked polymer material.     

An experimental scheme to verify the dynamics of the Aharonov--Bohm effect

There are two different viewpoints on the Aharonov--Bohm (A--B) effect. One asserts that the A--B effect is due to the existence of the vector potential A. The other asserts that the A--B effect is due to the interaction energy between the magnetic field produced by the moving charges and the magnetic field in the solenoid. The difference of these two viewpoints is analyzed in this paper. To judge which viewpoint is right, this paper suggests a new experimental method.     

High-resolution FTIR spectroscopy of the v11 and v2 + v7 bands of ethylene-d4

The Fourier transform infrared spectrum of the v₁₁ band of ethylene-d₄ (C₂D₄) has been recorded with an unapodized resolution of 0.006 cm^?1 in the frequency range 2150 to 2250cm^?1. The v₁₁ band, with a band centre of about 2201 cm^?1, was found to be perturbed by the nearby v₂ + v₇ band centred at about 2235 cm^?1 by a b-type Coriolis interaction. By fitting a total of 772 infrared transitions of v₁₁ using a Watson's A-reduced Hamiltonian in the I^r representation with the inclusion of b-type Coriolis interaction term, two sets of constants, up to quartic distortion constants for the v₁₁ = 1 state, and principal rotational constants for the v₂ + v₇ = 1 dark state, were derived. The inertia defect of the v₁₁ state was found to be 0.0693 ± 0.0004u Ų.     

A phenomenology of boundary lubrication: the lumped junction model

We propose a phenomenological model of boundary lubricated junctions consisting of a few layers of small molecules which describes the rheological properties of these sytems both in the static, frozen, and sliding, molten, states as well as the dynamical transition between them. Two dynamical regimes can be distinguished, according to the level of internal damping of the junction, which depends on its thickness and on the normal load. In the overdamped regime, under driving at constant velocity v through an external spring, the motion evolves continuously from “atomic stick-slip” to modulated sliding. Underdamped systems exhibit, under given external stress, a range of dynamic bistability where the sheared static state coexists with a steadily sliding one. The frictional dynamics under shear driving is analyzed in detail, it provides a complete account of the qualitative dynamical scenarios observed by Israelashvili et al., and yields semiquantitative agreement with experimental data. A few complementary experimental tests of the model are suggested. Received: 18 December 1997 / Received in final form and accepted: 26 March 1998     

LOCV calculation of nuclear matter with relativistic Hamiltonian

The equation of state of symmetric nuclear matter is calculated using the relativistic Hamiltonian (H_R) with potentials which have been fitted with the N -N scattering data using the relativistic two-body Hamiltonian ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and the non-relativistic two-body Hamiltonian, i.e. the Argonne V₁₄ interaction. The boost interaction corrections as well as the relativistic one-body and two-body kinetic energy corrections in cluster expansion energy within the lowest-order-constrained variational method are calculated. It is shown that the relativistic corrections reduce the binding energy by 1.5MeV for [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and AV₁₄ interactions. The symmetric nuclear-matter saturation energy is about -16.43 MeV at r \rho = 0.253 (fm^-3) with [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} interaction plus relativistic corrections. Finally, various properties of the symmetric nuclear matter are given and a comparison is made with the other many-body calculations.     

Vibrational relaxation in liquids

A new theory is presented for vibrational energy relaxation in a liquid. It is shown that a vibrationally excited probe molecule relaxes through interaction with the density fluctuations in the surrounding solvent fluid. This interaction occurs through a potential V(k), which is expressed in terms of the intermolecular force between the excited probe molecule and the surrounding fluid molecules. By assuming spherically symmetric solvent particles the T ₁ energy relaxation time for direct V-T processes is related to the translational dynamic structure factor for the fluid S(k, ω_v), evaluated at the vibrational resonance frequency. It is shown that this is described by gas-like particle motions on a very short distance scale corresponding to k vectors lying well beyond the first or second peaks of the fluid structure factor S(k). Such motions can be pictured as high-frequency, short-distance distortions of the local equilibrium configuration of the solvent particles around the probe. T ₁ ^-1 is found to be proportional to ρ_e T ^1/2 ω_v ^-3. The V-V energy exchange relaxation time is also calculated. This is found to be proportional to S(k, ω′) evaluated at a frequency ω′, corresponding to the vibrational energy missmatch. An energy gap law for the V-V process is derived.     

Electric field gradients created by near neighbour impurity atoms in a cubic silver host

The electric quadrupole interactions produced by near neighbour impurity atoms of Cu, Au, Zn, In, Sn and Bi on¹¹¹Cd probe nuclei in a cubic Ag lattice were studied by the TDPAC method. The effects of the type of impurity and its concentration have been investigated. The results show the presence of a high-frequency interactionv _Q ^h superimposed to a smeared out low frequencyv _Q ^l . The high frequency interaction, in the range 20 to 600 MHz, is attributed to impurity atoms located in nearest neighbour sites, while the low frequency interaction, in the range 2 to 12 MHz, is generated by impurities distributed at various different atomic distances from the probe nuclei. Bothv _Q ^h andv _Q ^l increase with impurity concentration leaving the ratiov _Q ^h /v _Q ^l almost constant. The results show that the high frequencyv _Q ^h is linearly dependent on the solute valence, and a logarithmic function of the impurity concentration, in the range 0.5 to 4.5 at. %. Large size effects have been observed in CuAg and BiAg alloys. Instead for ZnAg and SnAg, thev _Q ^h andv _Q ^l variation is attributed basically to charge effects.Work supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Financiadora de Estudos e Projetos (FINEP).     

Sensitivity of the dynamics of Na + Na$\mathsf{_2}$ collisions on the three-body interaction at ultralow energies

We have studied the quantum dynamics of collisions between spin-stretched Na atoms and Na₂ molecules. Cross-sections and rate coefficients for vibrational relaxation of Na₂(v,j = 0) have been computed in the 1 nK-0.1 mK energy range using an accurate time-independent method based on hyperspherical coordinates. The complex scattering length and the extension of the Wigner region have been determined. A detailed study of the sensitivity of collisional quantities on the three-body interaction at short distance has been performed. They are very sensitive to three-body effects for the vibrational state v = 1 of Na₂. Rotational distributions have also been calculated and show a more pronounced sensitivity on the three-body interaction, even for v = 2 and 3.Received: 29 March 2004, Published online: 22 June 2004PACS: 34.50.-s Scattering of atoms and molecules     

Plasma heating by a strong laser field with statistically distributed parameters

Summary The energy absorption rate by a classical homogeneous plasma irradiated by a strong fluctuating laser field via inverse bremsstrahlung is considered. A chaotic-field model is used and comparison is made with the fundamental model of a purely coherent field. In the present analysis, the emphasis is put on the interplay between the laser field statistics and the plasma electron energy distribution. Numerical calculations are concerned with the dependence of the energy absorption rates on laser intensity and frequency. Laser intensity values up to 4.6\10¹⁵ W/cm² are considered. The multiphoton structure of the energy absorption is analysed as well. Concerning the joint influence of the radiation and particle statistics on the absorption rate, the basic result may be stated as follows. For situations where the particle thermal velocityv _T is larger than the oscillatory velocityv ₀ imparted by the field (v _T ≥v ₀, relatively weak field), the absorption rate is only weakly dependent on the field statistics. For situations, instead, whenv ₀≫v _T , which occurs for very high intensities, the reverse becomes true: now the initial particle velocity distribution plays the modest role of a velocity spread of an electron beam oscillating atv ₀. In general, for very high intensities (v ₀≫v _T ), the energy absorption via bremsstrahlung becomes less effective because the high oscillatory velocityv ₀ reduces the time available to electrons for the interaction with the ions, the third body which makes possible the exchange for energy between electrons and a radiation field. We report also, for the first time, results on the Marcuse effect for the case of a chaotic laser field, along with calculations of the absorption rate for a directed electron beam.