Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

On the Effect of Increasing the Radiative-Transition Rate Near a Nanosize Point

A short review of theoretical and experimental studies concerning the photoexcited florescence and Raman scattering of light for a substance in a space containing small material bodies is presented. Calculations of the radiativetransition probability for atoms (molecules) in the vicinity of bodies with a size much smaller than the light wavelength are performed. The probabilities of the singlephoton and doublephoton transitions are shown to increase by factors of 9 and 81 in the vicinity of a nanosize sphere with dielectric constant ||\ 1. The probability of a radiative transition in the vicinity of the vertex of a conic needle bearing up against a plane (both with || 1) increases by factors of (/R _in)² and (/R _in)⁴ for singlephoton and doublephoton transitions, respectively (R _in is the curvature radius for the needle vertex). This theoretical result is suggested as an explanation of the effect of increasing the radiation process intensity in the experiments carried out in the studies cited below.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk

The pivot algorithm is a dynamic Monte Carlo algorithm, first invented by Lal, which generates self-avoiding walks (SAWs) in a canonical (fixed-N) ensemble with free endpoints (hereN is the number of steps in the walk). We find that the pivot algorithm is extraordinarily efficient: one effectively independent sample can be produced in a computer time of orderN. This paper is a comprehensive study of the pivot algorithm, including: a heuristic and numerical analysis of the acceptance fraction and autocorrelation time; an exact analysis of the pivot algorithm for ordinary random walk; a discussion of data structures and computational complexity; a rigorous proof of ergodicity; and numerical results on self-avoiding walks in two and three dimensions. Our estimates for critical exponents are=0.7496±0.0007 ind=2 and= 0.592±0.003 ind=3 (95% confidence limits), based on SAWs of lengths 200N10000 and 200N 3000, respectively.     

Thermodynamic formalism and localization in Lorentz gases and hopping models

The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure (). The inverse-temperature-like variable allows one to scan the structure of the probability distributin in the dynamic phase space. This formalism is applied here to a lorentz lattice gas. where a particle moving on a lattice of sizeL ^d collides with fixed scatterers placed at random locations. Here we give rigorous arguments that the Ruelle pressure in the limit of infinite systems has two branches joining with a slope discontinuity at =1. The low- and high- branches correspond to localization of trajectories on respectively the most chaotic (highest density) region and the most deterministic (lowest density) region, i.e. () is completely controlled by rare fluctuations in the distribution of scatterers on the lattice. and it dose not carry and information on the global structure of the static disorder. As approaches unity from either side, a localization-delocalization transition leads to a state where trajectories are extended and carry information on transprot properties. At finiteL the narrow region around =1 where the trajectories are extended scales as (InL)^–2. where depends on the sign of 1–, ifd>1, and as (L InL)^–1 ifd=1. This result appears to be general for diffusive systems with static disorder, such as random walks in random environments or for the continuous Lorentz gas. Other models of random walks on disordered lattices, showing the same phenomenon, are discussed.     

Cooperative plasticity due to the motion of disorientation and phase separation boundaries

Conclusions As has already been noted above, the theory of planar defects organically includes the mechanics of twinning, grain boundaries, Somigliani dislocations, translational dislocations, disclination, and dispiration. The fundamental propositions of the theory and methods of giving the tensor T are listed in Table 4. The mathematical formalism remains the same throughout, and it is applicable to both discrete objects (it is then necessary to conserve the -function apparatus), and to a continuous (then appropriate smoothing is needed, which usually reduces to replacement of the multiplication procedure by the normal n or by the direction , to operations of finding the gradient, divergence, and curl of regular expressions, and discarding the -functional), In particular, the problem of thermoelasticity is formulated successfully by such a method in the terminology of the present theory.In a broad sence of the word, the development of the theory should be perceived as an extension of the concept of imperfection to defects of sufficiently arbitrary origin. A completely developed formalism was worked out earlier for just linear defects; in the symbols used here, for the case b=b₀ + X (r – r₀) for constant b₀,, and r₀, and without taking account of processes on the boundary S if the linear defect contained such a feature. Let us emphasize that to describe three-dimensional defects occurring because of homogeneous distortion = (V)., it is sufficient to use the apparatus of just the theory of planar defects since the fundamental phenomena are associated with precisely the presence of boundaries and in a formal plane, with the spatial derivatives of , they are always expressed in terms of the functional (S), while in the case of finite surface gradients in terms of (L). The time derivatives of the distortion T, i.e., is written down in the developed representations in terms of the form with all the resulting consequences.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 83–102, June, 1981.     

Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities

The eight-vertex model is equivalent to a solid-on-solid (SOS) model, in which an integer heightl _i is associated with each sitei of the square lattice. The Boltzmann weights of the model are expressed in terms of elliptic functions of period 2K, and involve a variable parameter . Here we begin by showing that the hard hexagon model is a special case of this eight-vertex SOS model, in which =K/5 and the heights are restricted to the range 1l _i4. We remark that the calculation of the sublattice densities of the hard hexagon model involves the Rogers-Ramanujan and related identities. We then go on to consider a more general eight-vertex SOS model, with =K/r (r an integer) and 1l _ir–1. We evaluate the local height probabilities (which are the analogs of the sublattice densities) of this model, and are automatically led to generalizations of the Rogers-Ramanujan and similar identities. The results are put into a form suitable for examining critical behavior, and exponents, , are obtained.Supported by the Guggenheim Foundation and in part by the National Science Foundation, grant MCS 8201733.     

Correlation inequalities for multicomponent rotators

A recent approach to G.H.S. and Lebowitz inequalities is used to prove Griffiths' second inequality for 3 and 4 component models (e.g. Classical Heisenberg model, ||⁴ Euclidean fields). Applications include monotonicity of the mass gap in the external field, and two-sided inequalities between parallel and transverse correlations.     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

КРУЧЕНИЕ ПРИЗМАТИЧЕ СКИХ СТЕРЖНЕЙ ШВЕЛЛЕ РНОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

- [3], [4], U(x, y) . - U(x, y) -, . B § 10 - . , - , - D, . - .     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

On the equivalence of different order parameters for Ising ferromagnets

In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the triplet order parameter _{i j k} are the same as those of the magnetization _i . Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperatureT _c , defined as the temperature below which there is a spontaneous magnetization, is for fixed even spin interactionsJ _e independent of the way in which the odd interactionsJ _o approach zero from above. This is achieved by using only the simplest, Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.Research supported in part by NSF Grant #MPS 75-20638.     

Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

Les absorbants de son resonants

Résumé Dans la présente étude, on trouve un bref résumé des travaux de l'auteur, de ses collègues et collaborateurs, concernant l'utilisation des résonateurs dans l'acoustique architecturale. On explique tout d'abord le problème de l'inpluence des résonateurs sur la durée de la réverbération des salles. Se basant sur des considérations théoriques, l'auteur déduit le critère de l'emplacement le plus favorable des matières absorbant le son dans le résonateur même et discute la possibilité de l'absorption totale du son par le résonateur. Dans le cas des systèmes de résonateurs pareils disposés régulièrement sur les murs, le diapason pouvant être obtenu d'une importante absorption est relativement faible. En se servant de systèmes résonants d'absorption comportant plusieurs couches de résonateurs, reliés en série, le diapason de l'absorption importante peut être notablement élargi. L'auteur explique la corrélation du coefficient d'absorption et de l'angle d'incidence de l'onde sonore. En conclusion, on mentionne des exemples de l'utilisation pratique des résonateurs d'absorption les plus simples pour obtenir la caractéristique de l'absorption de fréquence exigée. On discute aussi le problème de l'influence des vibrations simultanées de la paroi extérieure du système de résonance sur la caractéristique de l'absorption du son.

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. . . , , . , , . . ; .

     

Nonstationary Markov chains and convergence of the annealing algorithm

We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t ₀) ast+, with a computable constantC andt ₀ the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t^–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly.     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

РАДИАЦИОННЫЙ ЗАХВАТ НЕЙТРОНА ЯДРАМИ Sc,Fe, Cu,Mo, Cd и La

, . 20–1000 keV Sc, Fe, Cu, Mo, Cd La.

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The radiative capture of a neutron on Sc, Fe, Cu, Mo, Cd and La nuclei

The energies and intensities of the transitions of a compound nucleus, produced by the capture of a neutron, were measured by means of a single-crystal scintillation spectrometer. The region of energies 20–1000 keV was measured on Sc, Fe, Cu, Mo, Cd and L a nuclei.