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.     

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.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

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.     

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.     

Monte Carlo study of the generalized reaction-diffusion lattice-gas model system

The reaction-diffusion lattice-gas model is an interacting particle system out of equilibrium whose microscopic dynamics is a combination of Glauber (reaction) and Kawasaki (diffusion) processes; the Glauber ratec(s; x) at sitex when the configuration iss satisfies detailed balance at temperatureT, while the Kawasaki ratec(s; x, y) between nearest-neighbor sitesx andy satisfies detailed balance at a different temperatureT. We report on the phase diagram of that system as obtained from a series of Monte Carlo simulations of steady states in two-dimensional lattices with arbitrary values forT,T, and; this generalizes previous analytical and numerical studies for and/orT. When the rates are implemented by the Metropolis algorithm, the system is observed to undergo various types of first- and second-order (nonequilibrium) phase transitions, e.g., one may identify Onsager (equilibrium) as well as Landau (mean-field) types of continuous phase transitions.Dedicated to Joel L. Lebowitz on the occasion of his 60th birthday.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field

The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where (,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form where _i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.     

Commutator Representations of Covariant Differential Calculi on Quantum Groups

Let (, d) be a first-order differential *-calculus on a *-algebra . We say that a pair (, F) of a *-representation of on a dense domain of a Hilbert space and a symmetric operator F on gives a commutator representation of if there exists a linear mapping : L( ) such that (adb) = (a)i[F, (b) ], a, b . Among others, it is shown that each left-covariant *-calculus of a compact quantum group Hopf *-algebra has a faithful commutator representation. For a class of bicovariant *-calculi on , there is a commutator representation such that F is the image of a central element of the quantum tangent space. If is the Hopf *-algebra of the compact form of one of the quantum groups SL _q (n+1), O _q (n), Sp _q (2n) with real trancendental q, then this commutator representation is faithful.     

Experimental study of ternary fission of U235 with thermal and resonance neutrons

The alpha particle spectra from ternary fission of U²³⁵ have been investigated in the thermal and the resonance neutron energy regions. The resonance neutrons have been obtained by passing the reactor neutron flux through a boron filter. A silicon surface barrier detector telescope technique for alpha particle detection has been used. In the resonance neutron energy region the ratio _f / _f has been found to be 1·02 ± 0·2 times the value of _f / _f in the thermal region. The non-gaussian tail of the LRA energy distribution has been observed.The authors are indebted to Dr. I.Wilhelm, Mrs. M.Pospíilová, Mr. J.vanda for their kindly help in the experimental data handling and to Mr. V.Kvítek for his assistance during the experiment.     

Thickness dependence of the spin- and angle-resolved photoemission of ultrathin,epitaxial Ni(111)/W(110) layers

The thickness dependence of the magnetic band structure of ultrathin, epitaxial Ni(111)/W(110) layers has been studied by spin and angle-resolved photoemission spectroscopy. The changes of the spin-resolved photoemission intensities upon reducing the layer thickness depend strongly on the wavevector along the -L line of the Brillouin zone. The measured exchange splitting atk 1/3(-L) andk 1/2(-L) is found to be independent of the layer thickness for layers consisting of 3 or more atomic layers, while decreases rapidly with the layer thickness atk2/3(-L). This behavior is very similar to the temperature dependence of the spin-resolved photoemission spectra of bulk Ni(111) at the samek-points.     

Elastic constants and quadrupolar interactions in the (LaCe)B6 series

Elastic constants of (La_1–xCe_x)B₆(x=0.01, 0.03, 0.1) dilute alloys have been determined by ultrasonic measurements at temperatures between 0.5 K and 4.2 K. The temperature dependence ofc ₄₄ and (c ₁₁–c ₁₂)/2 is in excellent agreement with calculations including magnetoelastic and interionic quadrupolar interactions. The single ion coupling constantsg (=₃, ₃) are independent of concentration. The systematic concentration dependence of quadrupolar coupling constants g'g(x) from the dilute (x=0.01) alloy to the compound CeB₆ (x=1) has been studied. Evidence of Grüneisenparameter coupling in the bulk modulus but no indication for a ₈ ground state splitting or a quadrupolar Kondo effect has been found. In addition the magnetic field dependence of elastic constants up to 6.5 Tesla was investigated.     

Group actions on C*-algebras, 3-cocycles and quantum field theory

We study group extensions , where acts on a C^*-algebraA. Given a twisted covariant representation ,V of the pairA, we construct 3-cocycles on with values in the centre of the group generated byV(). These 3-cocycles are obstructions to the existence of an extension of byV() which acts onA compatibly with . The main theorems of the paper introduce a subsidiary invariant which classifies actions of onV() and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant and the 3-cocycle.     

On the equivalence of the relativistic theories of gravitation

Einstein's equations are rewritten in terms of a certain torsionless linear connection which differs, in general, from the Levi-Civita metric connection . The torsionless connection appears in a natural way as the canonical momentum of the gravitational field g . Einstein's equations have a simple interpretation in terms of the connection . The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.This work has been written under the financial support of Gruppo Nazionale per la Fisica Matematica of the Italian National Research Council.     

Some properties of an “aesthetic” field theory

We continue our study of the Lorentz-invariant field theory based on the equations _jk;l ⁱ =0 and g_ij;k=0. To first order in a perturbation expansion, we find _jk;l ⁱ =0 reduces to the wave equation. In orders higher than the first, we find that _jk;l ⁱ =0 cannot be linearized. We also find that the simple wave-type equation g^ij2g/xⁱx^j=0 is contained in the theory when an appropriate choice is made for the parameters at the origin point.     

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.     

The magnetic behavior of CeB6: Comparison between elastic and inelastic neutron scattering,initial susceptibility and high-field magnetization

We report measurements of the elastic and inelastic neutron scattering, initial susceptibility and high-field magnetization on thoroughly prepared poly- and single crystalline samples of CeB₆. Part of these experiments have been performed at temperatures down to 60 mK and magnetic fields up to 70 kØe. Our neutron-diffraction data provide the first proof that CeB₆ is an antiferromagnet belowT _N2K as has been suggested by previous bulk experiments. The reduced value of the low-temperature magnetic moment both below and aboveT _N points to the existence of a Kondo effect of the ₇ crystal-field (CF) ground state of Ce³⁺. From the low-temperature width of the quasielastic neutron line, the Kondo temperature is inferred to beT _K3 K. The thermal variation of the initial susceptibility (forT>20K) is semiquantitatively explained invoking, besides the Kondo effect, a ₇- ₈ CF splitting of 70 K and magnetic interactions, which are about 10 times stronger between ₈ states than those between ₇ states. This large ₈- ₈ exchange interaction is also assumed to account for the most striking result of this work, i.e. the lack of any CF-transition peak up to 44 meV in our inelastic neutron-scattering spectra.     

Estimating the strength of chaos from the power spectrum

It is rigorously proved that for nonlinear dynamical systems whose time dependence is described by one dimensional, everywhere expanding maps, the width of broadband noise in the power spectrum is bounded by the generalized entropiesK ₂ andK ₃, which measure the strength of chaos in this system asK ₂2K ₃.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Gravitation and universal Fermi coupling in general relativity

The generally covariant Lagrangian densityG = + 2K _matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg _ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form _kl ⁱ = _kl ⁱ for the coefficients _kl ⁱ of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , g_ik, and the coefficients _kl ⁱ . Then the _kl ⁱ are determined by the Palatini equations. From these equations and from the symmetry _kl ⁱ = _lk ⁱ for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10^–81erg cm³     

Cubic nonlinear tensor of a ferromagnet

The nonlinear properties of a ferromagnet are studied. Many-time retarded Green's functions are used to obtain an expression for the cubic nonlinearity tensor with allowance for spatial dispersion of a uniaxial ferromagnet. The components due to the dipole-dipole interaction of the spins and also due to the anisotropy energy are found. A comparative analysis is made of the different components of the cubic nonlinearity tensor in both the nonresonance case and for various resonances, in particular when ₀, 3 2w₀, 2 ₀, 3 ₀ for the case in tripling of the frequency. Here, is the frequency of the incident wave and ₀ is the frequency of uniform precession. It is shown that in the non-resonance case the largest components are those that are nonvanishing when no allowance is made for spatial dispersion; in the resonance cases the largest components are those due to the dipole-dipole interaction of the ferromagnetism spins.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 53–58, December, 1973.