Anisotropy of infrared optical absorption in layered superconductors

We analyze the problem of infrared optical absorption in a clean layered London superconductor in the vicinity of the gap =2. We conclude that absorption of light with wave vectorqc is enhanced over ordinary Drude absorption (qc) due to resonance absorption (Landau damping). Experimental absorption studies with qc might therefore improve chances to observe a superconducting gap in the high-T _c superconductors.     

Short-wavelength plasmons in low-dimensional systems

The dispersion of plasma waves in systems of various dimensions is investigated up to the end point of the spectrum. In 2D and 3D systems, the plasmon spectrum still ends (due to Landau damping) within the applicability range of the quasi-classical approximation, i.e., for ?k ? p _F (?k is the plasmon momentum and p _F is the electron Fermi momentum). In 1D systems, the results are qualitatively different, since the Landau damping is concentrated in a region where the quantum effects cannot be ignored. This peculiarity of 1D systems gives rise to undamped branches of acoustic plasmons with a phase velocity lower than the electron Fermi velocity in multicomponent 1D plasmas.     

The generalized point interaction in one dimension

We show that various self-adjoint extensions of the operatorH ₀ ⁰ =–d²/dx²,D(H ₀ ⁰ )= =C (R{o}) describes a particle moving under additional influence of the generalized Fermi pseudopotential.I am indebted to Dr. H. Englisch for stimulating discussions. I am also grateful to the Department of Mathematics at the Karl-Marx-Universität Leipzig where this work was done.     

The gauge invariance,kinematical singularities and the electro- and photopion production amplitudes

The kinematical singularities connected with the gauge invariance are considered and the conventional sets of invariant amplitudes discussed. A new set of invariant amplitudes for electro-production of pions on nucleons is proposed, which contains the transversal subset of photo-production amplitudes, is free of kinematical singularities and more convenient for practical calculations.I would like to thank Dr. M. Petrá for a valuable discussion on some points, Dr. P. Lichard and Dr. J. Piút for useful remarks and Dr. F. A. Berends for a valuable correspondence. I am also indebted to Prof. Moorhouse for drawing my attention to some important papers and sending me a preprint of one of them.     

Single particle inclusive spectra of charged particles from antiproton-proton interactions at 5.7 GeV/c

A systematic study of single particle inclusive spectra of charged particles from ¯pp interactions at 5.7 GeV/c is presented and discussed in the framework of the Mueller-Regge approach to inclusive reactions. A comparison of our results with data at other energies points to specific properties of antiproton-proton interactions.I have greatly benefited from discussions with Dr. J. Cvach and Dr. V. imák. To Dr. V. imák I am also indebted for the encouragement during the preparation of this paper.     

Diffusion of thermonuclear alpha particles under the influence of intense LH waves

Recently, a new mechanism was proposed by Fisch and Rax which should lead to amplification of lower hybrid (LH) waves at the expense of alpha particles energy, improving thus the LH current drive efficiency. The present contribution investigates the possibility of achieving the conditions on which this mechanism — based on the spatial diffusion of fusion alpha particles — could become operative. The analysis performed shows that in reactor grade tokamaks, the penetration of LH waves into the plasma column is very poor due to the intense electron Landau damping and the complicated geometry of the equilibrium magnetic fields. Consequently, at acceptable LHW input power levels, the waves do not reach the regions where fusion alpha particle power could reasonably compensate the losses of LHW energy due to the damping by electrons. The model of Fisch and Rax is based on special features of the induced diffusion of alpha particles in the energy-configuration space. Using suitable Hamiltonian formalism, the LHW induced radial diffusion of alpha particles and the energy transport between LHW and alpha particles in the frame of generalized quasilinear lines of diffusion constraint is also investigated. A rather strong change ofk of LHW along the ray trace can contribute to the change of energy transport between LHW and alpha particles as well.The authors are indebted to Dr. R. Klíma for valuable discussions.     

Giant quantum oscillations of the skin layer in semimetals

We study theoretically the effect of electron energy quantization in a magnetic field on the penetration of radio waves into a semimetal in a geometry in which a constant magnetic field H is directed along the trigonal axis of a crystal. In this geometry, strong magnetic Landau damping in semimetals prevents wave propagation and is responsible for the skin effect. It is shown that quantization of the transverse energy of electrons considerably influences the effectiveness of collisionless absorption of the wave. As a result, the magnetic Landau damping and the skin depth experience giant oscillations upon a change in magnetic field H.     

On ferromagnetic resonance damping in metals

The Landau-Lifshitz damping coefficient is defined in terms of spin-orbital torque correlations in the one-electron model and estimated as a function of the orbital collision frequency. The formal results are compared with previous studies and the results of a numerical calculation for nickel are compared with known experimental data.I would like to thank Dr. L.Hodges for a copy of his thesis and Dr. A. V.Gold, Dr. J. R.Anderson, Dr. V.Dvoák, Dr. Z.Frait and Mr. M.Kolá for valuable discussions at various stages of this work.     

Bremsstrahlung of Debye plasma

The effect of Debye screening on the bremsstrahlung spectrum and total bremsstrahlung intensity of plasma is calculated. As compared with the Coulomb field approximation (infinitely large Debye radiusL) an additional density and temperature dependence of the radiation intensity is found. Results are expressed in terms of a dimensionless parameter=²/2mL ² kT, wherem is the rest mass of an electron and other symbols have their standard meaning. Deviations from the Coulomb field approximation become significant for the values 10^–3.I am grateful to Dr. J.Horáek and Dr. J.Obdrálek for their help in performing the numerical calculations.     

The effect of neutron irradiation on the Barkhausen noise in amorphous Fe40Ni40B40 alloys

Theoretical expression for the power spectra of Barkhausen noise was used to obtain information on the dynamical properties of domain walls from the experimental spectra. It was shown that after irradiation the domain wall mobility increases due to the change of the effective mass of domain wallsm _ef, damping constant and the spring constant.Dedicated to Dr. S. Krupika on the occasion of his 65th birthday.The authors wish to thank I. Gverdciteli, of the State Committee for Science and Technology of the Georgian SSR, Tbilisi (USSR), for supplying boron isotopes.     

Time Asymptotics for Solutions of Vlasov–Poisson Equation in a Circle

We prove that there exists a class of solutions of the nonlinear Vlasov–Poisson equation (VPE) on a circle that converges weakly, as t , to a stationary homogeneous solution of VPE. This behavior is called, in the linear case, Landau damping. The result is obtained by constructing a suitable scattering problem for the solutions of the Vlasov–Poisson problem. A consequence of this result is that a class of stationary solutions of the Vlasov–Poisson equation is unstable in a weak topology.     

Dielectric constant of an ultrarelativistic plasma

An analytic expression is derived for the longitudinal dielectric constant _l of an isotropic collisionless high-temperature plasma which is valid for the entire range of phase velocities in which there is no Landau damping or it is exponentially small. This expression contains the formulas for _l given in the papers of Silin and Mikhailovskii as limiting cases. Numerical calculations for the temperatures 10 mc² and 100 mc² are illustrated graphically.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 57–60, September, 1982.     

Stability of ion acoustic turbulent states

Several proposed renormalized theories for strong ion acoustic turbulence are compared to the direct interaction approximation. These are applied to the calculation of the stability of ion acoustic turbulent states to the excitation of Langmuir waves. A kinetic instability proposed by Tsytovich, Stenflo, and Wilhelmsson is shown to be stabilized by resonant and nonresonant decay processes. The global kinetic stability of the Langmuir spectrum is enhanced through the coupling of opposite phase velocity Langmuir waves by the decay processes and by nonresonant scattering to regions of strong Landau damping.     

On the absorption of eigenvalues by continuous spectrum in the one and three dimensional Dirac equation

The situation when a Dirac eigenvalue is absorbed by the upper or lower continuum is investigated in great detail. The connection with a spontaneous positron creation in strong external electromagnetic fields is also discussed.On leave of absence from the Nuclear Centre, Faculty of Mathematics and Physics, Charles University, V Holeovikách 2, Prague 8, Czechoslovakia.I am indebted to Dr. J. Dittrich and Dr. P. Exner for very helpful discussions.     

Static potentials for quarkonia at finite temperatures

We review non-perturbative static potentials commonly used in potential models for quarkonia at finite T. Potentials derived from Polyakov loop correlators are shown to be inappropriate for this purpose. The free energy is physical but has the wrong spatial decay and perturbative limit. The so-called singlet free energy is gauge dependent and unphysical. An appropriate static real time potential can be defined through a generalisation of pNRQCD to finite T. In perturbation theory, its real part reproduces the Debye-screened potential, its imaginary part accounts for Landau damping. Possibilities for its non-perturbative evaluation are discussed.     

Instability of Bose-Einstein condensates moving in optical lattices

We investigate the Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at a finite temperature. Using a 1D tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence reveals the microscopic mechanism of the Landau instability.     

The permittivity tensor and bounce resonance effects on wave dissipation in toroidal plasmas

The asymptotic solution of Vlasov's equation in the drift approximation for a toroidal plasma geometry with circular magnetic surfaces is presented. The method of solution introduces Jacobi functions as variables, making it possible to obtain results in a relatively simple manner. The analytic evaluation of the parallel components of the dielectric permittivity tensor _3j is shown and the resulting strong influence of the bounce resonance of untrapped electrons on the wave dissipation is discussed. Additionally, a numerical calculation of ₃₃, together with a comparison between the toroidal and the cylindrical (Landau damping) results, are presented.The authors wish to thank Katherina von Bülow, from the Mathematical Institute of UERJ, for fruitful comments and careful reading of this paper, and CNPq of Brazil for financial support.     

Inverse problem of mechanics in momentum space

The problem is solved of reproducing a spherically symmetric potential by means of the velocity vector hodograph in a classical mechanics approximation. A definite transcendental equation is obtained for the radial velocity dependence. Considered as an illustration is the problem of the Maxwell fish eye. A relativistic generalization is given. The algorithms constructed can be used to retrieve potentials possessing internal symmetries in the classical or quantum cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 46–50, January, 1985.In conclusion, I am grateful to Prof. Yu. N. Demkov for active and stimulating interest in the research.     

A note on the hydrodynamics of viscous fluids

The cross-product of the velocity and the vorticity in a viscous incompressible fluid is formulated and its properties investigated. When the cross-product is identically null, either the flow is vortex-free, or the velocity and the vorticity are parallel to each other. The second case yields the following important result for three-dimensional flows: if the velocity and the vorticity are related by a position-independent scalar function, that function must be time-independent as well. (English translation of the seventy-five-years old Czech text — Trkal V.: asopis pro pstování mathematiky a fysiky48 (1919) 302–311.)The paper has been translated (by I. Gregora) from Czech original which appeared in asopis pro pstování mathematiky a fysiky, Vol. 48 (1919), pp. 302–311; see a contextualizing account in the preceding paper in this issue, p. 89. The reprints are available on request from the Editorial Office.I express my warm gratitude to Prof. Dr. F. Závika for his valuable comments.