Calculation of quasi-stationary state parameters within the algebraic version of the resonating-group method

The dynamical equations of the algebraic version of the resonatinggroup method are used to determine the positionsE _res,l and the widths _l of quasi-stationary states or, what is equivalent, to find the polesE _l =E _resl –i _l /2 of theS-matrix in the fourth quadrant of thek-plane. Concrete calculations are performed for the -decay of⁸Be. A comparison with the results of other authors and with experiment is made.     

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.     

Correlations in two-component log-gas systems

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a zero-density Kosterlitz-Thouless-type transition as the dimensionless coupling :=q ²/kT is varied through =2. In the charge-ordered system we use a perturbation technique to establish anO(1/r ⁴) decay of the two-body correlations in the high-temperature limit. For 2⁺, the low-fugacity expansion of the asymptotic charge-charge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations. In the system without charge ordering the two-body correlations exhibit anO(1/r ²) decay in the high-temperature limit, with a universal amplitude for the charge-charge correlation which is associated with the state being conductive. Low-fugacity expansions establish anO(1/r ) decay of the two-body correlations for 2<<4 and anO(1/r ⁴) decay for >4. For both systems we derive sum rules which relate the long-wavelength behaviour of the Fourier transform of the charge correlations to the dipole carried by the screening cloud surrounding two opposite internal charges. These sum rules are checked for specific solvable models. Our predictions for the Kosterlitz-Thouless transition and the large-distance behavior of the correlations should be valid at low densities. At higher densities, both systems might undergo a first-order liquid-gas transition analogous to the two-dimensional case.     

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.     

Monte Carlo simulation of phase separation and clustering in the ABV model

As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump rates _A and _B, respectively. For a small concentration of vacancies (c _v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk ₁(t),k ₂ ² (t) is studied during the early stages of phase separation, for several choices of concentrationc _B of B atoms. Forc _B=0.18 also the time evolution of the cluster size distribution is studied. Apart from very early times, the mean cluster sizel(t) as well as the moments of the structure function depend on timet and the ratio of the jump rates (= _B/ _A) only via a scaled timet/(). Qualitatively, the behavior is very similar to the direct exchange model containing no vacancies. Consequences for phase separation of real alloys are briefly discussed.     

Estimates of general Mayer graphs. II. Long-range behavior of graphs with two root points occurring in the theory of ionized systems

We find the asymptotic behavior of general Mayer 2-graphs (Mayer graphs with two root points), which occur in the theory of ionized systems. This problem arises when one wants to compute corrections to the Debye length for large values of the plasma parameter. For a given 2-graph (r) with Debye-Hückel linese ^– /r, we prove the inequalitiesC _m r ^– e ^– (r) (r ₀)C_Mr^3k–l e ^– , for anyrr ₀, and whereC _m andC _M are positive and finite constants which depend only on . These bounds are finite whenever (r) is not infinite everywhere. The integersl, k, and denote, respectively, the number of lines of the graph , its number of field points, and its local line connectivity (the maximum number of chains linking the root points, which have no line in common). From this result, we deduce that the simple irreducible 2-graphs dominant at large distances decay exponentially likee ^– and have an isthmus between the root points (an isthmus is a line whose deletion separates the graph into two disjoint components, each one containing a root point). We prove also that 2-graphs that have a number of linesl > 3k+ are infinite. We exhibit simple, irreducible prototypes satisfying this condition, for anyk 6. This implies that the Abe-Meeron theory of ionized gases as applied to a classical plasma is not free from divergences. Finally, we extend the preceding results to 2-graphs with lines F_L=(e ^– /r)^k L, withk _L real positive. We prove that they still decay exponentially likee ^– , where is now the maximal flow in a network associated to by assigning the capacityk _L to each lineL.     

Low-temperature properties of Samarium monopnictides

SmP, SmAs, SmSb and SmBi order antiferromagnetically at Néel temperatures of 1.6, 1.8, 2.1 and 9 K, respectively. The crystal-field splittings _5/2 between the ₇ doublet and the ₈ quartet of theJ=5/2 ground state of the Sm³⁺ ion have been derived from caloric and magnetic measurements in the paramagnetic temperature range.     

Evaluation of Mössbauer line diffusion broadening by exponential fit

The Mössbauer line broadening measured by R.Lindsey in -iron stabilized with vanadium is evaluated by an exponential fit described in the APPENDIX of this paper. By this procedure the low temperature Mössbauer line width _m ⁰ , the diffusion frequency factorD ₀ and the activation enthalpyH are computed.Knauer's andSørensen-Trumpy's definitions of the time correlation factorf _t , necessary for theD ₀ calculation from Mössbauer line broadening, are applied to the Fe-V diluted BCC solid solutions.     

Exact results for correlations in a two-component log-gas

A study of the one-dimensional lattice gas of positive and negative charges interacting via the logarithmic potential is continued. The two-particle distribution functions are evaluated exactly at the couplings=2 and 4. It is proved that the=4 isotherm exhibits an insulator-conductor phase transition at the reduced density 1/2, and the scaling behavior of the correlations near this critical point is given. Similarities of the conjectured phase diagram with that of a one-dimensional one-component log-gas in a periodic potential are noted.     

jj-Type of coupling in the scheme to construct the energy levels of a shallow acceptor in semiconductors

There is examined the classification of shallow acceptor energy levels by jj-type coupling, whose wave functions are converted by sets of irreducible representations by one of the subgroupsD _4h ^/ ,D _3d ^/ ,D _2h ^/ of the group o _h ^/ . The representations ₅ ⁺ of the groupD _4h ^/ are obtained in the one-function approximation by using a variational method, and systems of eight radical second-order differential equations are solved for two functions ₅ ⁺ in the case of a shallow acceptor in germanium by the method of orthogonal differential factorization. A comparison is made of the two low levels found and their radial functions for each of the functions ₅ ⁺ with the computed levels and the functions of LS-type coupling.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 103–107, September, 1981.The authors are grateful to N. P. Konyukhova for great assistance in the numerical solution of the system of radial equations.     

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.     

A Sum Rule for the Two-Dimensional Two-Component Plasma

In a two-dimensional, two-component plasma, the second moment of the density correlation function has the simple value {12[1–(/4)]²}^–1, where is the dimensionless coupling constant. This result is derived by using analogies with critical systems.     

Structural and magnetic phase transitions in Pr2NiO4

Neutron powder diffraction and magnetization measurements have been performed in stoichiometric Pr₂NiO₄₊(0), which at room temperature (RT) is orthorhombic (Bmab). Ni²⁺ becomes three dimensionally (3D) antiferromagnetically ordered atT _N 325K, with a propagation vectork=[100], and spins oriented along thea axis (parallel to the propagation vector). The magnetic structure belongs to the _7g (––+)-representation (g _x mode, Shubnikov groupB _pmab') ofBmab, and a magnetic moment of 1.5 _B is measured at 155K. This compound undergoes two different structural phase transitions. First, going down in temperature, Pr₂NiO₄ transforms by a first order phase transition from orthorhombic (Bmab) to tetragonal (P4₂/ncm) atT _c1115K. At high temperature, we can predict a transformation from orthorhombic (Bmab) to tetragonal (I4/mmm) in a continuous way. The extrapolated temperature for this second structural transition isT _c21500±100K. The low temperature structural transformation allows a change in the magnetic structure which forT<T _c1 is better described in the orthorhombic symmetry. Just belowT _c1 the magnetic structure is described by the: _3g (–+)-representation ofPccn(g_xc_yf_z mode, Shubnikov groupPccn), this magnetic phase begins to disappear going down in temperature and at the same time a new magnetic phase grows. This new magnetic structure is described by the _1g ofPccn (c _xg_ya_z mode, Shubnikov groupPccn). Both magnetic structures coexist in a certain temperature range. At 1.5 K thec _xg_ya_z mode represents the total of the magnetic ordering. To reproduce the observed magnetic intensities we are forced to consider that Pr³⁺ is polarized below 40 K, with a magnetic structure which is coupled to the Ni sublattices (i.e. _1g and _3g ). The magnetic moment at low temperature for Pr is about 1.28 _B .     

The theory of pure operations

This paper continues the study started in [13] where classes of operations were investigated in the partially ordered vector space approach to the theory of statistical physical systems. In this approach the set of states is represented by a norm closed generating coneK in a complete base norm space (V, K, B) and the set of operations is represented by the setP of positive norm non-increasing linear operators onV. In actual physical experiments it is usually the case that only certain subsets ofK are available and it is supposed that the set (K) of such subsets is the set of split faces ofK. The properties of two important classes of operation are examined. The first classP of strong operations has the property that each member leaves every element of (K) invariant and therefore can be measured in every restricted situation. The second classP _P of pure operations has the property above and also sends pure states into pure states. A study is made, in terms of the structure of (K), of when such operations are physically relevant. The paper ends with an examination of (K),P, P _P in the Von Neumann algebra model.     

The affine geometry of the Lanczos H-tensor formalism

We identify the fiber-bundle-with-connection structure that underlies the Lanczos H-tensor formulation of Riemannian geometrical structure. We consider linear connections to be type (1,2) affine tensor fields, and we sketch the structure of the appropriate fiber bundle that is needed to describe the differential geometry of such affine tensors, namely the affine frame bundleA ₁ ² M with structure groupA ₁ ² (4) =GL(4) T ₁ ^{2 4} over spacetimeM. Generalized affine connections on this bundle are in 1-1 correspondence with pairs(, K) onM, where thegl(4)-component denotes a linear connection and the T ₁ ^{2 4}-componentK is a type (1,3) tensor field onM. We show that the Lanczos H-tensor arises from a gauge fixing condition on this geometrical structure. The resulting translation gauge, theLanczos gauge, is invariant under the transformations found earlier by Lanczos. The other Lanczos variablesQ _mandq are constructed in terms of the translational component of the generalized affine connection in the Lanczos gauge. To complete the geometric reformulation we reconstruct the Lanczos Lagrangian completely in terms of affine invariant quantities. The essential field equations derived from ourA ₁ ² (4)-invariant Lagrangian are the Bianchi and Bach-Lanczos identities for four-dimensional Riemannian geometry.     

The Weyl-Cartan Space Problem in Purely Affine Theory

According to Poincaré, only the epistemological sum of geometry and physics is measurable. Of course, there are requirements of measurement to be imposed on geometry because otherwise the theory resting on this geometry cannot be physically interpreted. In particular, the Weyl-Cartan space problem must be solved, i.e., it must be guaranteed that the comparison of distances is compatible with the Levi-Civita transport. In the present paper, we discuss these requirements of measurement and show that in the (purely affine) Einstein-Schrödinger unified field theory the solution of the Weyl-Cartan space problem simultaneously determines the matter via Einstein's equations. Here the affine field ⁱ _kl represents Poincaré's sum, and the solution of the space problem means its splitting in a metrical space and in matter fields, where the latter are given by the torsion tensor ⁱ _[kl].     

On the classification of simple vertex operator algebras

Inspired by a recent work of Frenkel-Zhu, we study a class of (pre-)vertex operator algebras (voa) associated to the self-dual Lie algebras. Based on a few elementary structural results we propose thatV, the category of Z₊-graded prevoasV in whichV[0] is one-dimensional, is a proper setting in which to study and classify simple objects. The categoryV is organized into what we call the minimalk ^th types. We introduce a functor —which we call the Frenkel-Lepowsky-Meurman functor—that attaches to each object inV a Lie algebra. This is a key idea which leads us to a (relative) classification of thesimple minimal first type. We then study the set of all Virasoro structures on a fixed minimal first typeV, and show that they are in turn classified by the orbits of the automorphism group Aut((V)) in cent((V)). Many new examples of voas are given. Finally, we introduce a generalized Kac-Casimir operator and give a simple proof of the irreducibility of the prolongation modules over the affine Lie algebras.     

Ensemble average of an arbitrary number of pairs of different eigenvalues using Grassmann integration

An identity satisfied by the eigenvalues of a real-symmetric matrix and an integral representation of a determinant using Grassmann variables are used to show that the ensemble average ofS different pairs of eigenvalues of a GOE is given by (–1) ^S 2^{–S –1/2}(S+1/2).     

Band-mapping of InP (100) along the ΓX-line

We have prepared InP (100) surfaces from wafer-material by cycles of argon ion sputtering and gentle annealing. From these samples normal-emission photoelectron spectra were recorded using photons in the energy range 10eV<h<75eV. From the results we derive the initial-state band disperison along the X-line of the 3-dimensional Brillouin zone. Our results are fully consistent with initial-state bands mapped by other authors along the KX-line. From the good agreement we conclude that the quality of the (100)-surfaces as used in our work is at least adequate for bulk band investigations.     

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