Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Positron annihilation anomaly in the high-temperature superconductor YBa2Cu3O7−x

We have measured the ac susceptibility of a wire with a Nb core (1.27 mm diam.) and a Cu cladding (0.37 mm thickness) atT50 K andB0.1 mG. Due to its proximity to Nb, the Cu becomes fully superconducting. From the data we find a breakdown fieldH _b =1.2 (mG) and a coherence length =2.2T ^–1/2 (m) for the Cu, as well as a field penetration depth -34T ^1/2 (m) at the Cu/Nb interface.     

Acoustomagnetoelectric effects at meso-ultrasonic frequencies in anisotropic semiconductors in arbitrary (classical) magnetic fields

Anisotropic acoustomagnetoelectric (AME) effects at meso-ultrasonic frequencies are calculated analytically in semiconductors with an anisotropic mobility () in arbitrary classical magnetic fields. For Bq(q is the ultrasonic wave vector) and an arbitrary direction of q two transverse components of the AME field (E ^B q E _y ^B ) occur in the crystal, and the longitudinal acoustoelectric field changes under the action of a longitudinal magnetic field (E _q ^B =E _q ^B -E _q ⁰ ),E ^B is even, and E ^B is odd in B; for B 1 the component E _y ^B E ^B /B, andE ^B and E _q ^B are independent of B and can be commensurate with the zero-field acoustoelectric field E _q ⁰ if the anisotropy of is large (hexagonal ZnS and ZnO or n-Ge highly compressed along [111]). The transverse AME field E _st ^B is calculated in the configuration E _st ^B qBE _st ^B (standard AMEeffect). For B >> 1 the field B 1E _st ^B B ^–3, so thatE ^B , E _y ^B , and _q ^B can be greater than E _st ^B here. The acoustoelectric analog of the Grabner effect (E _G ^B ), i.e., the component of the AME field along a transverse magnetic field (E _G ^B Bq) is also calculated. For pB > 1 the componentE _G ^B B ^–3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 93–97, June, 1989.     

Nonlocal Monte Carlo algorithm for self-avoiding walks with fixed endpoints

We study a new Monte Carlo algorithm for generating self-avoiding walks with variable length (controlled by a fugacity) and fixed endpoints. The algorithm is a hybrid of local (BFACF) and nonlocal (cut-and-paste) moves. We find that the critical slowing-down, measured in units of computer time, is reduced compared to the pure BFACF algorithm: _CPU N^2.3 versus N^3.0. We also prove some rigorous bounds on the autocorrelation time for these and related Monte Carlo algorithms.     

Hamilton Spaces of Order k ≥ 1

A suitable dual for the k-acceleration bundle(T ^k M, ^k ,M) is the fiberedbundle (T ^k–1 M× _M T*M). The mentioned bundle carries a canonicalpresymplectic structure and k canonical Poisson structures. By means of thisdual we define the notion of Hamilton spaces of orderk, whose total spaceconsists of points x of the configuration spaceM, accelerations of order 1,...,k – 1, y ⁽¹⁾,...,y ^(k–1), and momenta p. Some remarkable Hamiltonian systemsare pointed out. There exists a Legendre mapping from the Lagrange spaces oforder k to the Hamilton space of order k.     

TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (J) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-<1/8 of the ratio of these couplings and in a collinear state for 1/8<<1. The order parameter and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-<<1/8. It appears that the SW theory is still valid for the simple triangular HAF (=0) although the sublattice magnetisation is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at 1/8.     

Retrieval Properties of Bidirectional Associative Memories

We study a two-layer neural network made of N and M(N) neurons, producing a two-way association search for a family of p(N) patterns, where each pattern is a pair of two independent sub-categories of information having respectively N and M(N) components. In terms of the ratio =lim _N M(N)/N, we study the retrieval capability of this network and show that there exists, at least, three regimes of association for which we determine the evolution of the threshold _c () of the storage capacity =lim _N p(N)/N.     

Logical independence in quantum logic

The projection latticesP(₁),P(₂) of two von Neumann subalgebras ₁, ₂ of the von Neumann algebra are defined to be logically independent if A B0 for any 0AP(₁), 0BP(₂). After motivating this notion in independence, it is shown thatP(₁),P(₂) are logically independent if ₁ is a subfactor in a finite factor andP(₁),P(₂ commute. Also, logical independence is related to the statistical independence conditions called C^*-independence W^*-independence, and strict locality. Logical independence ofP(₁,P(₂ turns out to be equivalent to the C^*-independence of (₁,₂) for mutually commuting ₁,₂ and it is shown that if (₁,₂) is a pair of (not necessarily commuting) von Neumann subalgebras, thenP(₁,P(₂ are logically independent in the following cases: is a finite-dimensional full-matrix algebra and ₁,₂ are C^*-independent; (₁,₂) is a W^*-independent pair; ₁,₂ have the property of strict locality.     

Microstructure of fiber-like SiC/Si3N4 composite particulate

The microstructure of fiber-like SiC/Si₃N₄ composite particulate was investigated using high-resolution transmission electron microscopy techniques. The SiC/Si₃N₄ composite particulate consisted of a-SiC core and a -Si₃N₄ outer shell. Two kinds of composite particulate were distinguished when the observed orientation of the SiC core was <110>. In one type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC | (102) -Si₃N₄ and (111)-SiC (114) -Si₃N₄ was identified; in the other type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC (001) -Si₃N₄, and (111)-SiC (101) -Si₃N₄ was observed.     

Steady flux in a continuous-space Sinai chain

We examine the steady-state flux of particles diffusing in a one-dimensional finite chain with Sinai-type disorder, i.e., the system in which in addition to the thermal noise, particles are subject to a stationary random-correlated in space Gaussian force. For this model we calculate the disorder average (over configurations of the random force) flux exactly for arbitrary values of system's parameters, such as chain lengthN, strength of the force, and temperature. We prove that within the limitN1 the average flux decreases withN as J(N)=C/N and thus confirm our recent predictions that the flux in the discrete-space Sinai model is anomalous.     

Nuclear physics with ion traps at ISOLDE: present and future

Nuclear physics experiments with ion traps started at the on-line separator ISOLDE/CERN, Geneva, with the installation of the tandem Penning trap mass spectrometer ISOLTRAP. With this device the massM of a stored ion is determined by measuring its cyclotron frequency _c=(q/M)B in a magnetic fieldB. Mass measurements with a resolving powerR=_c/_c(FWHM)1×10⁶ and accuracies of M/M10^–7 were performed on more than sixty unstable isotopes of the elements Rb, Sr, Cs, Ba, Fr, and Ra.     

On the invariant sets of a family of quadratic maps

The Julia setB for the mappingz (z–)² is considered, where is a complex parameter. For 2 a new upper bound for the Hausdorff dimension is given, and the monic polynomials orthogonal with respect to the equilibrium measure onB are introduced. A method for calculating all of the polynomials is provided, and certain identities which obtain among coefficients of the three-term recurrence relations are given. A unifying theme is the relationship betweenB and -chains ± (± (± ...), which is explored for –1/42 and for with ||1/4, with the aid of the Böttcher equation. ThenB is shown to be a Hölder continuous curve for ||<1/4.Supported by NSF Grant MCS-8104862Supported by NSF Grant MCS-8002731     

Exponential convergence to equilibrium for a class of random-walk models

We prove exponential convergence to equilibrium (L ² geometric ergodicity) for a random walk with inward drift on a sub-Cayley rooted tree. This randomwalk model generalizes a Monte Carlo algorithm for the self-avoiding walk proposed by Berretti and Sokal. If the number of vertices of levelN in the tree grows asC _N ~ ^N N ^–1 , we prove that the autocorrelation time satisfies N² N¹⁺     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Thermodynamics of the re-entrant regime of type II two-dimensional superconductivity in a strong transverse magnetic field

The thermodynamics (including energy gap and critical temperatureT _c ) of a two-dimensional type II BCS superconductor subjected to a strong transverse magnetic fieldH in the re-entrant regime is studied. There are qualitative differences with the re-entrant 3D case; in particularT _c grows unboundedly likeB/lnB asB (filling factor 1) for fixedN. The thermodynamics atT=0 is completely described by the evaluation of the magnetic Gibbs free energy as a function of andH. A first order magnetic phase transition (failure of H/ B>0 for around each lowlying Landau level) found for the normal phase for unbroadened Landau levels, is washed out in the superconducting phase.     

Energy relaxation in aϕ 4 with long range interactions

We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential of ⁴-type and infinite range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions <E _n(t)E _n > of the fluctuations of the one-particle energiesE _n(t) decays exponentially. The corresponding relaxation time is proportional toN and is given by (T, N) =N₀(T). The temperature dependent time scale ₀ can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode coupling approximation and by a perturbative approach. Both results agree in leading order in 1/N. It is speculated that any interaction of range generates a timescale .     

On classical models of Spin

We discuss two classical situations that lead to probabilities characteristic for systems with spin-1/2. (a) Pitowsky model: It is demonstrated that the definition of spin functions does not imply which circle (a parallel or a great circle) on the sphere should be taken as a probability space in calculation of conditional probabilities. Pitowsky's choice of parallels must be formulated as an assumption about the model. It is shown that the model explicitly avoiding this difficulty is possible and no contradiction with the Bell Theorem is found. The modification is based on a new pathological decomposition of the sphere and belongs to a class of hidden variable theories with undetected signals. (b) Aerts model: We show the importance of the polarization effect of the measurements for the sake of obtaining a non-Kolmogorovian probability model. It is also shown that the conditioning by a change of state leads in general to the non-Kolmogorovian probability calculus.2. For example, let _{Cw,z xCw,z}µ_c ({y C _w,z S ₊|(x,y) /2})=µ _c(C _w,z S ₊)= 1/2µ _c(C _w,z). Pitowsky spheres with white points distributed onC _w,z in this way exist. The proof is exactly analogous to this of Theorem 1 in [1]. Then (**) = 1 -/, if one takesC _w,z as the probability space. This example seems very instructive.3. If the chargeq falls down on some point then it clearly has not fallen down on another one. Having given a result of a measurement we cannot, within the model with polarization, talk in a sensible way about its alternative: We can think either aboutsuccessive measurements (then the Bell inequality is not derivable) or ask What would have happened if..., but then we deal with a different problem (in Aerts' terminology [2b] this is anobservation) and obtain again Eq. (8) (there is no complementarity but there is no model of spin either).     

Maximum uniform deformation in tension

An equation is derived for the hyperbola which touches the true stress curve S =f(), where is the contraction of the specimen at the point _p (uniform contraction), S_B (true ultimate strength). With a flat maximum of the tensile force, this hyperbola coincides with the true stress curve at a part corresponding to extension by the maximum force. The use of the tangent hyperbola for determining _p and S_B is demonstrated.It is found that for those metals and alloys which are at present known to have a convex true stress curve in the uniform plasticity range, the uniform contraction _p cannot exceed 0.5, corresponding to a uniform elongation _p 1, while the true (logarithmic) uniform elongation _p 0.693. The limiting values of the hardening modulus and of the ratio S_B/_B are also found.