From monotonic to oscillatory decay of correlations: Analytical approximation for the two-dimensional,one-component plasma

An approximate evaluation of the pair distribution and the structure factor is performed analytically for the two-dimensional, one-component plasma at any value of the coupling constant. The approximate distribution remains positive and satisfies three sum rules, including the compressibility one. When 0 or 2, exact results are found. At=2 the transition from monotonie (<2) to oscillatory (>2) decay of correlations takes place. Comparison with the Monte Carlo simulations shows good agreement for 0<<4.     

Pseudo-Jahn-Teller effect in tetragonal local centers

The shape of the light absorption band by a local tetragonal center at the transition _{1 5}(x, y) is investigated in a semiclassical approximation. In addition to interaction with fully-symmetric (₁), Jahn-Teller (₃, ₄) vibrations, inter-action is also taken into account with vibrations ₅, which admix an electron level ₄(z) to the electronic state ₅, which is separated from ₅ by the energetic gap . An analytic computation of the band shape is performed in the first order of the expansion of the form function in ^–1. An asymmetric two-hump band is obtained, where the long-wave maximum always has higher intensity than the shortwave maximum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 62–67, December, 1987.     

Методика измерения к омплексной диэлектр ической проницаемости и нели нейных свойств диэле ктриков В диапазоне дециметр овых волн

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Energy-band structure of semiconductors having the chalcopyrite lattice

The pseudopotential method is used to calculate the band structure of several A^IIB^IVC^V semiconductors. The calculations are carried out at the most important symmetry points of the Brillouin zone: , T, N, and P. The top of the valence band and the bottom of the conduction band are shown to correspond to point . The dispersion law near is described approximately by the Kane equations.Translated from Izvestiya VUZ. Fizika, No. 7, pp. 17–22, July, 1970.     

Two-body correlations and pair formation in the two-dimensional Coulomb gas

We investigate pair correlations in the two-dimensional Coulomb gas made up of two species of point ions carrying electric charges Z₁ e(>0) and Z₂ e(<0), and interaction by the logarithmic Coulomb potential. This system is known to be classically stable for couplings=e ²/k _BTc=2/¦Z₁Z₂¦ (whereT is the temperature). Correlations between equally charged ions are shown to be greatly modified at short distances, in the range _c/2<< _c, due to gradual ion condensation. The usual integral equations for the pair correlation functions admit no solutions in that range. Preliminary Monte Carlo simulations for the symmetric case (Z₁=–Z₂) reveal a striking chemical equilibrium between tightly bound ion pairs and free ions, which is reasonably well described by a simple Bjerrum model.     

On the mechanism of rendering visible dislocations on the surface of iron crystals by anodic dissolving

The paper contains further results of studying dislocations rendered visible by anodic dissolving on the surface of single crystals of alpha-iron. The influence of the crystallographic orientation of the surface is investigated, the effect of carbon is confirmed and the anodic process is studied. The mechanism of dissolving of the crystal is given and a new more suitable method of rendering dislocations visible is derived.

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The author thanks F. Kroupa and J. Hejduk for critical remarks and discussion.     

Two-Frequency Mutual Coherence Function of Millimeter Wave in Rain

In this paper, the general formulations of two-frequency mutual coherence function, , for a pulse wave propagating in random discrete media are summarized. The relations of the amplitudes and phases of the to _d are given by Ishimaru et al, based on average particle in cloud and rain. In practice, since the particles sizes in random discrete media are in a size distribution spectrum, the ought to be derived from a particles size distribution. Based on an approximately solution, we describe these examples of millimeter waves (94, 220GHz) pulse propagating in rain and show that the 's amplitudes and phases obvious varies as rainfall and frequency. For a kind of rain, considering raindrops size distribution and average raindrop size, respectively, the 's amplitudes and phases are calculated. The numerical results show that the differences between the results calculated by raindrops size spectrum and by average size are remarkable, especially for heavy rainfall. Therefore, It is shown that the calculated by a particles size distribution is more reasonable than by average size. For the numerical analyses, particles size distribution ought to be adopted. This study is important for us to provide adequate bandwidths to achieve high-rate pulse communications and improve MMW radar system performances and atmospheric remote-sensing techniques.     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

Twisted Lie Group C*-Algebras as Strict Quantization

A nonzero 2-cocycle Z2(g, R) on the Lie algebra g of a compact Lie group G defines a twisted version of the Lie–Poisson structure on the dual Lie algebra g*, leading to a Poisson algebra C (g*()). Similarly, a multiplier c Z2(G, U(1)) on G which is smooth near the identity defines a twist in the convolution product on G, encoded by the twisted group C-algebra C*(G,c). Further to some superficial yet enlightening analogies between C (g*()) and C*(G,c), it is shown that the latter is a strict quantization of the former, where Plancks constant assumes values in (Z\{0})-1. This means that there exists a continuous field of C*-algebras, indexed by 0 (Z\{0})-1, for which A0= C0(g*) and A=C*(G,c) for 0, along with a cross-section of the field satisfying Diracs condition asymptotically relating the commutator in A to the Poisson bracket on C(g*()). Note that the quantization of does not occur for =0.     

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N , the number of mobile particles of charge e. As expected, the distribution of N has, for large , a Gaussian form with a variance which grows only as ^||, where || is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^() decreases to an asymptotic value ^()^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length _L=2^/ associated with charge fluctuations behaves very differently from that of the Debye length, _D1/ , which it approaches as 0. The pair correlation function of the OCP is also studied.     

Radiation effects in the production and decay of ψ mesons by leptons

A new expression _e is obtained for resonance in the reaction e⁺e^– ar ^+– with allowance for the radiative corrections, which also contain the emission of hard photons by the final leptons and the final value of the energy resolution E. An expression is obtained for the total probability of radiative lepton decay. A numerical analysis of the experimental data is made for the reaction ^+–, and the parameters e⁺e^– (3, 1) e⁺e^–, and _e ² /, _e, and are determined for (3, 1) resonance-with allowance for the radiative corrections.This paper was read (November 17–21, 1975) at a session on high-energy physics of the Department of Nuclear Physics of the Academy of Sciences of the USSR.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–34, March, 1977.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

A General-Relativistic Fermat Principle for Extended Light Sources and Extended Receivers

In an arbitrary Lorentzian manifold, we fix a spacelike submanifold P and a timelike submanifold . We interpret P as (the surface of) a light source at a particular instant of time, and we interpret as the history of (the surface of) a receiver. We prove the following version of Fermat's principle. Among all lightlike curves from P to , the lightlike geodesics which are perpendicular to P and spatially perpendicular to are characterized by stationary arrival time. Here, the arrival time is defined with the help of an arbitrary time function on . Moreover, we show that the second variation of the arrival time at a stationary point is characterized by a Morse index theorem.     

The electronic structure of Rhodium: Angle-resolved studies of photoelectron and secondary electron emission

We report electron spectroscopic studies of the Rh(111) surface, with the aim to obtain bulk band-structure information. We have measured normal photoemision using tunable synchrotron radiation in the range of photon energies between 11 eV and 55 eV, and angle-dependent photoemission along the LUX and LKL azimuths using the He resonance lines (=21.2 eV, 40.8 eV). To complement these data, we studied angleresolved secondary electron emission after excitation with electrons and photons. We derive parts of the one-electron energy dispersionE(k) along L, and determine the energies of several bulk critical points (in eV):E(> ₇₊/₈₊)=–2.75±0.10,E(> ₈₊=–0.85±0.10,E(> _7–=16.1±0.5,E(> _6–/> _8–)=20.5±0.5,E(X ₇₊)=–5.0±0.1,E(L ₆₊)=–5.6±0.5,E(L ₆₊/L ₄₊₊₅₊)=–2.65±0.10,E(L ₆₊)=9.0±0.5 eV. Our results are compared to several available band structure calculations.     

The Numerical Analysis of Two-Frequency Mutual Coherence Function for Infrared Laser Propagation in Clouds

The relations of the amplitudes and phases of the for laser pulse propagation in clouds to _d are given by Ishimaru et al, based on average particles in clouds. In practice, since the particles size in clouds is according to a size distribution spectrum, the ought to be derived from a particles size distribution. Based on the approximately solution which has been presented by Ishimaru and Hong, these examples of infrared laser pulse propagating in cloud are described and numerical analyses show the 's amplitude and phase obvious changes for tenuous and dense clouds. For a kind of cumulus and stratocumulus over Xi'an areas, considering cloud particles size distribution and mean particle size, respectively, the 's amplitudes and phases are calculated. These numerical results show that the differences between results calculated by applying particle size spectrum and mean size in clouds are remarkable, especially for the phase calculation. Therefore, It is shown that the calculated according to particles size distribution is more reasonable than by average particle size. This study is important for us to improve infrared laser ranging and image systems performances and atmospheric remote-sensing techniques.     

F.c.c. type-III antiferromagnetism in YbN

Neutron diffraction experiments performed for YbN in the temperature range from 7 mK to room temperature prove the existence of long-range f.c.c. antiferromagnetic ordering of type III belowT _N =(0.790±0.005) K. The low ordered magnetic moment of Yb at saturation, =(0.39±0.05)> _B , is presumably caused by Kondo hybridization. By means of inelastic neutron scattering the crystalfield level scheme was established to be ₆ – ₈(33 meV)– ₇(81 meV). The ₆ – ₈ transition was found to be split into two lines which may be due to a bound state between the crystal-field excitation and phonons.     

Higher order differential calculus on SL q(N)

Let be a bicovariant first order differential calculus on a Hopf algebra . There are three possibilities to construct a differential N ₀-graded Hopf algebra which contains as its first order part. In all cases is a quotient = /J of the tensor algebra by some suitable ideal. We distinguish three possible choices _u J, _s J, and _W J, where the first one generates the universal differential calculus (over ) and the last one is Woronowicz' external algebra. Let q be a transcendental complex number and let be one of the N ²-dimensional bicovariant first order differential calculi on the quantum group SL _q(N). Then for N 3 the three ideals coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant k-forms. In this case each bi-invariant form is closed. In case of 4D _± calculi on SL _q(2) the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed.     

On the decay width of multiply measured unstable state

In the case of multiple measurements we have found that there is nonzero decay width () (even for bound states) and that, for relatively long time intervals separating successive measurements, () tends like ^–k (k 1 according to the investigated model) to the asymptotic value _o for unstable states and to zero for bound states. We have shown that the detector efficiencyZ 1 is responsible for this effect and that the evolution operator acting in the considered subspace of states should be renormalized to avoid this effect. As an illustration we have considered electromagnetic levels in the Coulomb field as an example of unstable states.     

Conversion of hyperons in nuclear matter

The width of the N N conversion for hyperons in nuclear matter is calculated on the basis of the one-boson exchange model. It turns out that there is a substantial compensation of the contributions of different mesons to the conversion amplitude. As a result, is reduced by roughly a factor of two as compared to the value from the exchange of only a pion. Without taking the Pauli principle into account, we obtain = 15–25 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–7, December 1983.     

General relativity is a gauge type theory

It is shown that the Einstein-Maxwell theory of interacting electromagnetism and gravitation, can be derived from a first-order Lagrangian, depending on the electromagnetic field and on the curvature of a symmetric affine connection on the space-time M. The variation is taken with respect to the electromagnetic potential (a connection on a U(1) principal fiber bundle on M) and the gravitational potential (a connection on the GL(4, R) principal fiber bundle of frames on M). The metric tensor g does not appear in the Lagrangian, but it arises as a momentum canonically conjugated to . The Lagrangians of this type are calculated also for the Proca field, for a charged scalar field interacting with electromagnetism and gravitation, and for a few other interesting physical theories.