Baryon decays and gamma-spectroscopy of hypernuclei

The applicability of (K ^–,^–) - and (K ^–,^– N)-reactions on^13,14C and^14,15N nuclei to the study of -transitions in primary and daughter -hypernuclei is discussed. The intensity of -deexcitation of ¹³C state |S ¹²C(15·11 MeV; 1⁺1): 1/2⁺ has been shown to be comparable with the intensity of baryon decay. Isospin selection rules are used to distinguish excitation energy ranges of primary hypernuclei, where the identification of the secondary -lines is probable.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Hydrogen sulphide doping of GaAs and AlxGa1−xAs grown by molecular beam epitaxy (MBE)

H₂S gas has been used during molecular beam epitaxy (MBE) growth of GaAs and Al _x Ga_1–x As as sulphur vector forn-type doping. Doping efficiencies are less than 10^–3 at usual growth temperatures, and are limited by an incorporation competitive surface process, probably 2Ga+H₂SGa₂S+H₂. In Al_xGa_1–x As forx0.2 the doping efficiency is further reduced by carrier freeze-out at deep levels. Measured thermal activation energies depend on growth conditions and remain relatively low even up to the direct-indirect bandgap crossover for substrate temperatures in the 585–645 C range.     

Mössbauer study of mixed valent silicides Eu(Ir1−x Pd x )2Si2

The solid solutions Eu(Ir_1–x Pd _x )₂Si₂, which exist for 0x0.125 and 0.75x1. cristallize with the tetragonal ThCr₂Si₂-type structure. The variation of the europium valence with composition has been thoroughly studied at temperatures 4.2T293 K by¹⁵¹Eu Mössbauer resonance. For 0x0.125 the europium valence at room temperature decreases asx increases. For 0.75x1 the valence transition temperature Eu³⁺Eu²⁺ increases asx increases.     

Scaling of the surface tension of phase-separated polymer solutions

The tension of the interface between the equilibrium phases of a phase-separated polymer solution is obtained in the simplest mean-field approximation from the functional equation for the composition profile of the interface. For temperaturesT near the critical solution temperatureT _c, i.e., for Flory parameter near _c, and for high degrees of polymerizationN, the profile and tension scale with=N ^1/2(– _c), just as do the compositions of the coexisting phases in mean-field approximation. The surface tension in the asymptotic limitN, _c at fixedx, is found to be given bya ²/kT _c (2c'/c)^1/2 N ^-5/4(x), wherea is the lattice spacing of an underlying lattice (or, roughly, the length of a monomer),c andc are the vertical and total coordination numbers of the lattice, and(x) is a scaling function, known for allx, with the asymptotic behavior asx0 and asx. The latter implies that becomes independent ofN asN at fixedT nearT _c; the former implies that becomes proportional toN ^–1/2(1–T/T _c)^3/2 asTT _c at fixedN1, as found previously.     

Positron annihilation in ionic media and an optical model of the positron

It is proposed that positron motion in quasiatomic positron + anion systems formed in anionic media can be described by a potential of the form V_eff(r) = Z_eff/r²-/r, where Z_eff is the effective charge of the nucleus, and n is the effective charge of the anion. It is shown that the positron wave function of the ground state of the quasiatomic positron + anion system in the field of such a potential is _X(r) = l/4·A_nx·r^X·e^–ar. Thus the validity of selecting a test variation positron wave function (r) = l/4·A·r·e^–ar is demonstrated for the potential V_eff = at r = 0 and V_eff = –/r for r > 0 (Gol'danskii-Prokop'ev optical positron model, Fiz. Tverd. Tela,8, 515 (1966)), belonging to the class of functions _X(r). Having the wave function _X(r) and Slater wave functions _ns,p(r) of the electrons, annihilation photon angular distribution (APAD) curves are calculated, together with halfwidths of the APAD curves and positron lifetimes _ns,p.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 52–56, May, 1990.     

Thermal fluctuations and ac response of weakly pinned charge density waves

The Fukuyama-Lee theory for the ac response () of weakly pinned charge density waves is extended to include thermal fluctuations. The equation of motion for the local phase includes an extrinsic damping and a distinction is made between static and dynamic parameters in it. It is split into static, thermally fluctuating and response contributions to the phase, respectively. The static problem is treated using a result from Feigel'man's theory which provides a revised value for the weak pinning constant. The impurity averaging of the response equation is performed using the simplifying statistical properties of the stochastic pinning force following Bleher's recent work. The main emphasis is on the treatment of the thermal fluctuations via a thermal field _th. The non-linear Langevin equation for _th is linearized and further simplified by an RPA type approximation which eliminates the impurity fluctuations from _th. The resulting equation is solved exactly. It is shown that the correlation function of the thermal field decays initially with a short time constant. This allows to treat the thermal fluctuations on an equal footing with the impurity fluctuations in the self-consistent Born approximation. The main contribution of the thermal fluctuations results in powers of a thermal factor exp(- _th ² /2) to the first and second order self energies of the phason Green's function. Numerical results due to these modifications are given for (,T). It is found that the absorption peak in Re () broadens and shifts to lower frequencies when the temperature is raised. The corresponding treatment for three spatial dimensional is indicated. The thermal factor is evaluated for this case and differences to Maki's result are noted. The questions of analyticity and conductivity sum rule are also dealt with.Dedicated to Professor Helmut Reik on the occasion of his 60th birthday     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

A continuum analogue of the lattice gas

We construct a Hilbert space , spanned by vectors , where is a bounded measurable set in ^v (=dimension of space), and interpret as at state where all pointsx are occupied by an incompressible fluid, andx unoccupied. is generated by applying unitary filling operatorsU( ) to a cyclic vector |, the completely unoccupied state. The operatorsU( ) generate a commutativec*-algebra, of which the hermitian elements are interpreted as the observables of the theory.All the -divisible representations of the symmetric group of order 2 are found. We give a generalization to a theory with any number of particle types.     

The surfboard Schrödinger equations

We study the large time behavior of solutions of time dependent Schrödinger equationsiu/t=–(1/2)u+t V(x/t)u with bounded potentialV(x). We show that (1) if>–1, all solutions are asymptotically free ast, (2) if–1 a solution becomes asymptotically free if and only if it has the momentum support outside of suppV for large time, (3) if –1 <0 all solutions are still asymptotically modified free ast and that (4) if 0 <2, for each local minimumx ₀ ofV(x), there exist solutions which are asymptotically Gaussians centered atx=tx ₀ and spreading slowly ast.     

Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models

Results from percolation theory are used to study phase transitions in one-dimensional Ising andq-state Potts models with couplings of the asymptotic formJ _x,y const/¦x–y¦². For translation-invariant systems with well-defined lim _x x ² J _x =J ⁺ (possibly 0 or ) we establish: (1) There is no long-range order at inverse temperatures withJ ⁺1. (2) IfJ ⁺>q, then by sufficiently increasingJ ₁ the spontaneous magnetizationM is made positive. (3) In models with 0<J ⁺< the magnetization is discontinuous at the transition point (as originally predicted by Thouless), and obeysM( _c )1/( _c J ⁺)^1/2. (4) For Ising (q=2) models withJ ⁺<, it is noted that the correlation function decays as xy()c()/|x–y|² whenever< _c . Points 1–3 are deduced from previous percolation results by utilizing the Fortuin-Kasteleyn representation, which also yields other results of independent interest relating Potts models with different values ofq.     

Exponential decay in the stark effect

LetH=–+V+Fx ₁ withV(x ₁,x ) analytic in the first variable andV(x ₁+ia, x ) bounded and decreasing to zero asx for eacha . Let be an eigenvector of –+V with negative eigenvalue. Among our results we show that forF0, (,e ^–H ) decays exponentially at a rate governed by the positions of the resonances ofH. This exponential decay is in marked contrast to conventional atomic resonances for which power law decay is the rule.Research supported by NSF Grant No. MCS 78-00101.     

Study ofA+A→0 with probability of reaction and diffusion in one dimension and in fractal substrata

We present Monte Carlo simulations of annihilation reactionA+A0 in one dimensional lattice and in three different fractal substrata. In the model, the particles diffuse independently and when two of them attempt to occupy the same substratum site, they react with a probabilityp. For different kinds of initial distributions and in the short an intermediate time regimes, the results for 0<p1 show that the density ofA particles approximately behaves as (t)=(t=0)f(t/t ₀), with the scaling functionf(x)1 forx1,f(x)x ^–y forx1. The crossover timet ₀, behaves ast _{0 0eff} ^–1y where theeffective initial density _0eff depends on (t=0) and on the kind of initial distribution. For a given substratum of spreading dimensiond _s, the exponenty(d _s/2<y<1) depends only onp and its value increases asp decreases (y1 whenp0). In the very long time regime it is expected thatp(t)t ^–ds/2 independently ofp.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

A relationship between future and past null infinity

By the addition of a single pointi at space-like infinity, null infinity,I =I ⁺ I ^-, may be regarded as the null cone with vertexi. We show that, given suitable regularity conditions ati, there exist natural Bondi scalings on the whole ofI which may be used to relate quantities onI ⁺ andI ^-. In particular, we show that, in terms of such a scaling, the mass aspect ₂ ^o onI satisfies lim _x°,xI+ ₂ ^° = lim _x°,xI- ₂ ^° where the limits are taken along the same generator ofI.     

On the pointwise behavior of semi-classical measures

In this paper we concern ourselves with the small asymptotics of the inner products of the eigenfunctions of a Schrödinger-type operator with a coherent state. More precisely, let _j and E _j denote the eigenfunctions and eigenvalues of a Schrödinger-type operator H with discrete spectrum. Let _(x,) be a coherent state centered at the point (x, ) in phase space. We estimate as 0 the averages of the squares of the inner products ( _a ^(x,) , _j ) over an energy interval of size around a fixed energy, E. This follows from asymptotic expansions of the form for certain test function and Schwartz amplitudes a of the coherent state. We compute the leading coefficient in the expansion, which depends on whether the classical trajectory through (x, ) is periodic or not. In the periodic case the iterates of the trajectory contribute to the leading coefficient. We also discuss the case of the Laplacian on a compact Riemannian manifold.Research supported in part by NSF grant DMS-9303778     

Scaling relationships for anisotropic random walks

Aspects of transport in a highly multiple-scattering environment are investigated by examining random walkers moving in media having anisotropic angular scattering cross sections (turn-angle distributions). A general expression is obtained for the mean square displacement x² of a random walker executing ann-step walk in an infinite homogeneous material, and results are used to predict scaling relations for the probability() that a walker returns to the planar surface of a semi-infinite medium at a distance from the point of its insertion.     

Phase Transformations α → β → γ → δ → ε in Titanium Hydride TiH x with Increase in Hydrogen Concentration

Structural phase transformations of the hcp bcc fct fcc fct ( ) type in titanium hydrides TiH _x experimentally found to occur with increase in the hydrogen concentration x are studied theoretically. Free energy phases are statistically calculated, and their concentration dependence is determined. Phase transformation temperatures are found from intersection points of free energy curves and from points of common tangents to the curves. The energy parameters of the system are estimated. The calculation results are compared with the experimental data.     

On the asymptotic behavior of the solutions of the Caldirola-Kanai equation

We study in this Letter the asymptotic behavior, as t+, of the solutions of the one-dimensional Caldirola-Kanai equation for a large class of potentials satisfying the condition V(x)+ as |x|. We show, first of all, that if I is a closed interval containing no critical points of V, then the probability P _t (t) of finding the particle inside I tends to zero as t+. On the other hand, when I contains critical points of V in its interior, we prove that P _t (t) does not oscillate indefinitely, but tends to a limit as t+. In particular, when the potential has only isolated critical points x ₁, ..., x _N our results imply that the probability density of the particle tends to in the sense of distributions.Supported by Fulbright-MEC grant 85-07391.     

Variance calculations and the Bessel kernel

In the Laguerre ensembleof n xN Hermitian matrices, it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic, denoted var_N f, asN . Furthermore, this statistic often contains an additional parameter a for which the limit is most interesting and most difficult to compute numerically. We derive exact expressions for both lim_N var_N f and lim , lim_N var_N f.