Casimir friction in terms of moving harmonic oscillators: equivalence between two different formulations

The Casimir friction problem can be dealt with in a simplified way by considering two harmonic oscillators moving with constant relative velocity. Recently we calculated the energy dissipation ΔE for such a case [Europhys. Lett. 91, 60003 (2010); Eur. Phys. J. D 61, 335 (2011)]. A recent study of Barton [New J. Phys. 12, 113044 (2010)] seemingly leads to a different result for the dissipation. If such a discrepancy really were true, it would imply a delicate difficulty for the basic theory of Casimir friction. In the present note we show that the expressions for ΔE are in fact physically equivalent, at T = 0.     

Kronecker product decomposition for Poincaré-like groups I. A general constructive method

For Poincaré-like groupsW=T×G, i.e. such Type I-groups which are semidirect products of a regularity embedded abelian normal subgroupT with a locally compact groupG, the problem of the Kronecker product decomposition has been solved, in the framework of induced representations theory, up to a reduction of little group representations. For practical applications some computational hints are given.The autors would like to thank Prof. H.Boseck, Dr. J.Niederle and Dr. J.Tolar for helpful and interesting discussions. One of us (Th. G.) would also like to thank Dr. J.Tolar for his kind hospitality during a stay at the Czech Technical University, Prague.     

The geometry of gauge fields

Principal fibre bundles with connections provide geometrical models of gauge theories. Bundles allow for a global formulation of gauge theories: the potentials used in physics are pull-backs, by means of local sections, of the connection form defined on the total spaceP of the bundle. Given a representationP of the structure (gauge) groupG in a vector spaceV, one defines a (generalized) Higgs field as a map fromP toV, equivariant under the action ofG inP. If the image of is an orbitW V ofG, then a breaks (spontaneously) the symmetry: the isotropy (little) group ofw ₀ W is the unbroken groupH. The principal bundleP is then reduced to a subbundleQ with structure groupH. Gravitation corresponds to a linear connection, i.e. to a connection on the bundle of frames. This bundle has more structure than an abstract principal bundle: it is soldered to the base. Soldering results in the occurrence of torsion. The metric tensor is a Higgs field breaking the symmetry fromGL (4,R) to the Lorentz group.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.Work on this paper was supported in part by the Polish Research Programme MR. I. 7.This paper is based in part on the research done in 1976–77 when I was Visiting Professor at the State University of New York at Stony Brook. I thankChen Ning Yang for encouragement, discussions and hospitality at the Institute for Theoretical Physics, SUSB. I have also learned much from conversations with D. Z.Freedman, A. S.Goldhaber, P.van Nieuwenhuizen, J.Smith, P. K.Townsend, W. I.Weisberger, and D.Wilkinson.     

Study of magnetic interactions of the Fe2+ ions and the protons of crystallization water in FeSO4.n H2O hydrates

The paper deals with a study of interactions of protons in crystallization water of paramagnetic hydrates FeSO₄.n H₂O (wheren=1, 4, 5 and 7). The interaction of protons and paramagnetic ions Fe²⁺ and the nuclear dipole-dipole interaction of protons have been studied by means of the parameters expressing the dependence of the second moment of the proton nuclear magnetic resonance (NMR) spectrum on the external magnetic field, by means of the volume magnetic susceptibilities and the relaxation timesT ₁ of the investigated series of hydrates.We are grateful to Prof. Dr. hab. Z.Pajak, director of Department of Radiospectroscopy IF UAM in Poznan, and to his coworkers Dr. J.Kapturczak, Dr. K.Jurga, Dr. S.Glowinkowski and Mgr. F.Brych for facilitating our measurements mentioned in the paper as well as for a valuable discussion.     

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Summary Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the ?cage? results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H₂ molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.     

Canonical realizations of classical lie algebras

We construct sets of canonical realizations for all classical Lie algebras (A _n ,B _n ,C _n ,D _n ). These realizations depend ond parameters,d=1, 2, 3,...,n; all Casimir operators are realized by multiples of identity. For most of the real forms of these algebras we give sets of realizations which are, moreover, in well-defined sense skew-Hermitian. Further we study extremal cases of the presented realizations. The realizations with minimal numbers of canonical pairs are discussed from the point of view of general results concerning minimal realizations. On the other hand, a connection is found between our maximal realizations ofA _n and the Gel'fand-Kirillov Conjecture.The authors would like to thank Prof. A.Uhlmann for his kind interest in this work. They are very grateful to Prof. A. A.Kirillov and Prof. D. P.Zhelobenko for helpful discussions and to Prof. J.Dixmier for his informative letter concerning the problem mentioned in Sect. 5.One of the authors (W. L.) thanks Prof. I.Úlehla for the hospitality at the Nuclear Center of the Charles University, Praha.     

Microwave heating of electrons of a dense plasma column at frequencies higher than electron cyclotron frequency

In this experimental study the absorption of plasma waves, excited in a dense plasma column, was investigated and the localization of the regions of efficient heating of electrons were determined in a broad range of parameters: 1>_ce/>0·1, 0·3<n/n _UH <25, 10^–5<v/< <10^–3. The heating of electrons near the second electron cyclotron harmonic was investigated in greater detail.We are grateful to the members of the Staff of the Institute of Plasma Physics Drs. P.unka, R.Klí'ma, V.Kopecký, J.Musil for discussion of the results. We also thank Drs. J.Musil, F.áek for the help and advice in the early stages of experimental work during construction of different diagnostic devices. Our thanks are due to the director of the Institute Dr. J.Váa for encouraging support of this experimental program.     

Interplay between elastic fields due to gravity and a partial dislocation for a hard-sphere crystal coherently grown under gravity: driving force for defect disappearance

We previously observed that an intrinsic staking fault shrunk through a glide of a Shockley partial dislocation terminating its lower end in a hard-sphere crystal under gravity coherently grown in ?001? by Monte Carlo simulations [Mori et al., Molec. Phys. 105, 1377 (2007)]; it was an answer to a one-decade long standing question why the stacking disorder in colloidal crystals reduced under gravity [Zhu et al., Nature 387, 883 (1997)]. Here, we present an elastic energy calculation; in addition to the self-energy of the partial dislocation [Mori et al., Prog. Theor. Phys. Suppl. 178, 33 (2009)] we calculate the cross-coupling term between elastic field due to gravity and that due to a Shockley partial dislocation. The cross-term is an increasing function of the linear dimension R over which the elastic field expands, showing that a driving force arises for the partial dislocation moving toward the upper boundary of a grain.     

Drag effects in a two-layer system of spatially separated electrons and excitons

We discuss drag effects in a two-layer system of spatially separated electrons and excitons: the entrainment of excitons by moving electrons, and the entrainment of electrons by moving excitons. For the case of excitons entrained by electrons we find the drag velocity υ _drag, and for electrons entrained by excitons we compute the induced electric field E ₂. These drag effects can be sensitive indicators of the phase state of the excitons and of phase transitions in the exciton system (to a liquid phase, superfluid state, etc.) Zh. éksp. Teor. Fiz. 111, 1107–1119 (March 1997)     

Mobility of carbon ions and C+(4P) in helium computed from quantum-mechanical transport cross sections

On the light of a previous work and its recommendations by Matoba et al. [J. Phys. B 41, 145205 (2008)], this paper proposes to look at the mobility of ground and metastable-excited states of C⁺ ions moving into a helium buffer gas. The calculations, based on the three-temperature theory for solving the Boltzmann kinetic equation, are accomplished with quantum-mechanical transport cross sections at the low temperatures 4.3 and 77?K. The obtained mobility results are contrasted with the available theoretical data and experimental measurements, which show acceptable agreements.     

Nonlinear waves in a waveguide partially filled with a plasma

Nonlinear waves have been studied in a circular waveguide partially filled with a cold magnetized collisionless plasma. The solution obtained is periodical with the frequency increasing as a square root of the amplitude of the solution in the first approximation.The author is indebted to K.Jungwirth, R.Klíma and J.Preinhaelter for valuable discussions.     

“Electron collisional excitation of argon-like Ni XI using the Breit-Pauli R-matrix method”

In a recent paper, Verma et al. [Eur. Phys. J. D 42, 235 (2007)] have reported results for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions among the lowest 17 levels of the (1s²2s²2p⁶)3s²3p⁶, 3s²3p⁵3d and 3s3p⁶3d configurations of Ni xi. They adopted the civ3 and R-matrix codes for the generation of wavefunctions and the scattering process, respectively. In this paper, through two independent calculations performed with the fully relativistic darc (along with grasp) and fac codes, we demonstrate that their results are unreliable. New data are presented and their accuracy is assessed.     

Bose-Einstein condensation in a static scalar field from the standpoint of the Goursat problem

The Goursat problem, developed by the present authors in previous papers [Ukr. Fiz. Zh. (Russ. Ed.) 27, 1602 (1982); Differentsial’nye Uravneniya 20, 302 (1984); J. Math. Phys. 33, 233 (1996)], is used to study the energy spectrum of a scalar relativistic particle in a static axisymmetric external scalar field of an attractive nature. This is obviously a model. It is shown that the problem formulated in this way has no unstable solutions, i.e., solutions increasing with time, in contrast to the Cauchy problem, where such solutions appear when the square of the particle frequency (energy) vanishes (in other words, in a Bose-Einstein condensation) Zh. éksp. Teor. Fiz. 112, 1167–1175 (October 1997)     

The individual success of musicians, like that of physicists, follows a stretched exponential distribution by J.A. Davies

Comment on Eur. Phys. J. B 27, 445 (2002) We analyze the distribution of success of musicians, comparing a stretched exponential (found by J.A. Davies [Eur. Phys. J. B 27, 445 (2002)]) with a distribution of the family of the q-exponential (presenting an intermediate power-law regime with a crossover to an exponential tail). We find that both assumptions yield comparable results, within the available range of data, hence a definite conclusion cannot yet be taken. But this example joins many others that has been found to be fairly described by q-exponentials (or variations of it), which may be indicative that there is a (significantly large) class of systems described by nonextensive statistical mechanics, from where q-exponentials naturally appear. Received 17 October 2002 Published online 31 December 2002     

Effect of an electric field on the bifurcation of a biaxially stretched incompressible slab rubber

This paper describes the effect of an electrical field on the bifurcation phenomenon that appears in a biaxially stretched slab of Mooney-Rivlin material (M. Mooney, J. Appl. Phys. 11, 582 (1940)) subjected to equal dead loads. The main conclusion of the analysis is that the stretch ratio at which the bifurcation phenomenon appears crucially depends on the configuration of the system rubber slab-electrodes. The theoretical foundations of the present study are based on a recent formulation on this subject carried out by Dorfmann and Ogden (A. Dorfmann, R.W. Ogden, Acta Mech. 174, 167 (2005); J. Elasticity 82, 99 (2006)).     

Two-Particle Irreducible Effective Action in Gauge Theories

The goal of this paper is to develop the formalism of the two-particle irreducible (2PI) (G. Baym (1962). Physical Review 127, 1391; H. D. Dahmen and G. Jona Lasino (1962). Nuovo Cimento A 52, 807; C. de Dominicis and P. Martin (1964). Journal of Mathematical Physics 5, 14; J. Luttinger and J. Ward (1960). Physical Review 118, 1417; B. Vanderheyden and G. Baym (1998). Journal of Statistical Physics 98, 843; B. Vanderheyden and G. Baym (2000). In Progress in Nonequilibrium Green's Functions, World Scientific, Singapore). (or Cornwall–Jackiw–Tomboulis (CJT) (J. Cornwall, R. Jackiw, and E. Tomboulis (1974). Physical Review D 10, 2428; U. Kraemmer and A. Rebhan (2004). Reports on Progress in Physics 67, 351; R. Norton and J. Cornwall (1975). Annals of Physics 91, 106) effective action (EA) in a way appropiate to its application to nonequilibrium gauge theories. We hope this review article will stimulate new work into this field.     

Generalized Jordan-Wigner transformations and the Ising-Onsager problem

Another possible method for obtaining Onsager’s solution for the 2D Ising model is presented. In contrast to previous methods, the method proposed here makes it possible to study the problem in a weak external magnetic field. Generalized Jordan-Wigner transformations in the form introduced by Kochmański [J. Tech. Phys. 36, 485 (1995)] are employed. Zh. éksp. Teor. Fiz. 111, 1717–1731 (May 1997)     

Dependence of V-A characteristics of amorphous semiconductor Ge15Te81S2As2 on hydrostatic pressure

The paper presents the functional expression of V-A characteristics dependent on hydrostatic pressure up to 5 kbar for chalcogenide glass Ge₁₅Te₈₁S₂As₂. The measured V-A characteristics and those derived on the assumption of a linear decrease of the energy gap due to pressure have been compared. Temperature changes caused by current passing through the sample in thermal contact with the environment have been taken into consideration similarly as in the case of paper (2).In conclusion we wish to express our thanks to Doc. J.Krempaský CSc., Ing. P.Dieka, Ing. J.Bielek for their kind help in discussing various points of the problem.     

An analysis of the destabilizing curvature effects on the turbulent flow over a rotating cylinder

An analysis based on the available experimental data and second-order closures is made for a turbulent shear flow over a rotating cylinder in a quiescent fluid. The near-wall behaviour of the non-linear model for the pressure-strain correlation proposed by Speziale, Sarkar and Gatski [J. Fluid Mech. 245, 227 (1991)] is enlarged; and the methodology proposed by Lai and So [J. Fluid Mech. 221, 641 (1990)] is adopted to take into account the wall-effects. The radial profile of the curvature parameter, R_s, is examined in connection with the logarithmic law. It is shown that the log-layer is associated to the region where the mean velocity profile, V, is related to the power of the radial distance as Computations reveal that this region corresponds to the state with the most destabilizing curvature effects; which can be chararacterized by the minimum value of the parameter B _c =2R _s (1+2R _s ), and not that one of the parameter B=2R _s (1+2R _s )/(1+R _s )² firstly introduced by Bradshaw [J. Fluid Mech. 36, 171 (1969)] and extensively used to characterize the turbulence structure in curved flows. Received 9 December 1997     

A study of Bi–Pb–Sn–Cd–Sb penta-alloys rapidly quenched from melt

Optical microscopy, X-ray diffractometry, the double bridge method, the Vickers microhardness testing and dynamic resonance techniques have been used to investigate structure, electrical resistivity, hardness, internal friction and elastic modulus of quenched Bi–Pb–Sn–Cd–Sb penta-alloys. The properties of these penta-alloys are greatly affected by rapid quenching. The intermetallic compound χ(Pb–Bi) or Bi₃Pb₇ is obtained after rapid quenching using the melt-spinning technique, and this is in agreement with reports by other authors [Marshall, T. J., Mott, G. T. and Grieverson, M. H. (1975). Br. J. Radiol., 48, 924; Kamal, M., El-Bediwi, A. B. and Karman, M. B. (1998). Structure, mechanical properties and electrical resistivity of rapidly solidified Pb–Sn–Cd and Pb–Bi–Sn–Cd alloys. J. Mater. Sci.: Mater. Electron., 9, 425; Borromêe-Gautier, C., Giessen, B. C. and Grrant, N. J. (1968). J. Chem. Phys., 48, 1905; Moon, K.-W., Boettinger, W. J., Kattner, U. R., Handwerker, C. A. and Lee, D.-J. (2001). The effect of Pb contamination on the solidification behavior of Sn–Bi solders. J. Electron. Mater., 30, 45.]. The quenched Bi_43.5Pb_44.5Cd₅Sn₂Sb₅ alloy has important properties for safety devices in fire detection and extinguishing systems.