A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ has the following exact asymptotic form for large k (k ? p_F; p_F, the Fermi momentum): $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉 =}\text{4}\text{9}\text{(}\text{αr}{}_{\mathrm{s}}\text{π}\text{)}{}^2\text{×(}\text{p}{}_{\mathrm{<mtext>F</mtext>}}{}^8\text{k}{}^8\text{) g?(0) + ?}$, where g?(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.     

A note on covariant Feynman rules for closed strings

It is established that covariant Feynman rules for closed string fields must decompose the moduli space of a four-punctured sphere with each diagram giving two copies of a fundamental region of the group of anharmonic ratios. This may help determining if such decomposition is possible without an elementary four closed-string interaction.     

A note on anomaly matching for finite density QCD

We note that the QCD phases at large finite density respect 't Hooft anomaly matching conditions. Specifically the spectrum of the light excitations possesses the correct quantum numbers required to obey global anomaly constraints. We argue that 't Hooft constraints can be used at finite density along with non perturbative methods to help selecting the correct phase.     

A note on entropic uncertainty relations of position and momentum

We consider two entropic uncertainty relations of position and momentum recently discussed in the literature. By a suitable rescaling of one of them, we obtain a smooth interpolation for both high-resolution and low-resolution measurements, respectively. Because our interpolation has never been mentioned in the literature before, we propose it as a candidate for an improved entropic uncertainty relation of position and momentum. Up to now, we have neither been able to falsify nor prove the new inequality. In our opinion, it is a challenge to do either one.     

An apparent momentum balance anomaly in the plasma focus

The validity of the snowplow model of plasma sheath propagation in a plasma focus (PF) and the localization of the magnetic field in the low density region behind the dense plasma sheath are two well-established experimental facts. It is shown that, when taken together, these two imply a deficiency in the momentum balance. The hypothesis that the current-carrying plasma layer is rotating while the dense plasma layer is not rotating is shown not only to resolve this momentum balance anomaly (MBA), but also to explain many observed phenomena in a unified manner     

Hawking radiation from the charged and magnetized BTZ black hole via covariant anomaly

This paper discusses Hawking radiation from the charged and magnetized Ba?ados--Teitelboim--Zanelli (BTZ) black hole from the viewpoint of anomaly, initiated by Robinson and Wilczek recently. It reconstructs the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. It employs the covariant anomaly cancellation method to determine the compensating fluxes of charge flow and energy-momentum tensor, which are shown to match with those of the 2-dimensional blackbody radiation at the Hawking temperature exactly.     

Hawking radiation from the dilaton-（anti） de Sitter black hole via covariant anomaly

Adopting the anomaly cancellation method, initiated by Robinson and Wilczek recently, this paper discusses Hawking radiation from the dilaton--(anti) de Sitter black hole. To save the underlying gauge and general covariance, it introduces covariant fluxes of gauge and energy--momentum tensor to cancel the gauge and gravitational anomalies. The result shows that the introduced compensating fluxes are equivalent to those of a 2-dimensional blackbody radiation at Hawking temperature with appropriate chemical potential.     

Quenching of magnetic transitions as an angular momentum effect

We investigate how the mechanisms of nuclear excitations and mesonic currents traditionally invoked to explain the quenching of low multipole magnetic transitions apply to higher spin operators. We find that there is a significant quenching of the low multipolarity spin-isospin operators by Δ-hole polarization, but that this effect decreases for higher multipoles. Conversely, the nucleon-hole polarization which has a negligible effect on low multipoles plays a predominant role in explaining the quenching of higher multipoles. Meson exchange currents provide a significant enhancement of the orbital operators but have only a slight effect on the spin components.     

A covariant view on the nucleons’ quark core

Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincaré-covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon’s mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the role of the pion cloud in such an approach.     

A new integrable system on the sphere and conformally equivariant quantization

Taking full advantage of two independent projectively equivalent metrics on the ellipsoid leading to Liouville integrability of the geodesic flow via the well-known Jacobi–Moser system, we disclose a novel integrable system on the sphere Sⁿ$S^n$, namely the dual Moser system. The latter falls, along with the Jacobi–Moser and Neumann–Uhlenbeck systems, into the category of (locally) Stäckel systems. Moreover, it is proved that quantum integrability of both Neumann–Uhlenbeck and dual Moser systems is ensured by means of the conformally equivariant quantization procedure.     

A Gauge and Lorentz covariant approximation for the quark propagator in an arbitrary gluon field

We decompose the quark propagator in the presence of an arbitrary gluon field with respect to a set of Dirac matrices. The four-dimensional integrals which arise in first order perturbation theory are rewritten as line-integrals along certain field lines, together with a weighted integration over the various field lines. It is then easy to transform the propagator into a form involving path ordered exponentials. The resulting expression is non-perturbative and has the correct behavior under Lorentz transformations, gauge transformations and charge conjugation. Furthermore it coincides with the exact propagator in first order of the coupling g. No expansion with respect to the inverse quark mass is involved, the expression can even be used for vanishing mass. For large mass the field lines concentrate near the straight line connection and simple results can be obtained immediately. Received: 31 March 2001 / Revised version: 3 May 2001 / Published online: 8 June 2001     

A note on the radiative energy loss from an ion-bombarded surface

It has recently been argued that the heat radiation from spikes, according to the Stefan-Boltzmann law, plays an important role in thermal behaviour of a copper target bombarded with 100keV Xe⁺ ions. In this work we have monitored the temperature evolution of a copper bar subjected to a 40 keV N⁺, Xe⁺, Sb₂ ⁺, and a 20 keV Sb⁺ ion bombardment. Our measurements have not revealed any substantial differences between light and heavy ion bombardment as well as between atomic and molecular implantation. Those results are in agreement with the time constant for radiation being long, of order 10⁻⁶s. They also agree with the calculations of the radiative energy loss from the spike, based upon both cylindrical and spherical spike models. In all reported cases, the energy lost from the spike via the heat radiation, although much different for different projectiles, is smaller than 1% of the ion deposited energy and its influence on the target temperature evolution lies within uncertainty of a typical ion current measurement. This work was carried out as a part of Research Project CPBP 01.09     

A remark on an anomaly of the spin-wave spectrum in spiral spin structures

It is shown that magnetic dipolar interaction gives rise to a discontinuity in the magnon dispersion relation for antiferromagnetic spiral spin structures. Some numerical results for the magnon energy in dysprosium are presented.     

A note on calculating stripping to an unbound state

Acta physica Academiae Scientiarum Hungaricae - A comparison of the most often used methods for describing stripping to an unbound state has been performed in an exactly soluble...