Generalized large number hypothesis and cosmological constant

By generalizing Dirac's large number hypothesis we infer that the cosmological constant varies witht ^–2, as expected from earlier studies.     

Gamma-ray spectroscopy of nuclei with large deformations

The large multidetector gamma-ray arrays (such as GAMMASPHERE, EUROBALL, and GASP) have played a central role in nuclear-structure studies during the past decade. In this paper I will discuss recent results from experiments on nuclei with very large deformations, including: the measurement of the spins, parities, and excitation energies of superdeformed bands in ¹⁵²Dy; the observation of extreme deformations in ¹⁰⁸Cd and the evidence for hyper-intruder states; the study of superdeformed nuclei around , which provide an opportunity to test our microscopic understanding of collective excitations; and lifetimes of strongly deformed triaxial bands in ¹⁶³Lu. I will conclude with a brief discussion on the next generation gamma-ray detector array, GRETA.Received: 9 December 2002, Published online: 17 February 2004PACS: 21.10.Re Collective levels - 23.20.Lv transitions and level energies - 21.10.Tg Lifetimes - 29.30.Kv X- and -ray spectroscopy     

Scaling function for the energy density correlation at large momentum

The static energy-density correlation function S ²(0)S ²(x)–S ²² is calculated in the critical region for theS ⁴ Ginzburg-Landau-Wilson model at short distances and for nonzero field. Short distance expansion is used and its structure for more complex vertex functions is given. Goldstone mode singularities present at the magnetization curve are taken into account. The main application is given in the theory of polymer solutions. Here, S ²(0)S ²(x)–S ²² becomes the Fourier transform of the densitydensity correlation.     

Highly mobile Einstein spaces in the large

We consider an Einstein spaceV of the Petrov type II or III admitting a group of motionsG of high order. First we calculate the composition law and topological structure ofG. ThenV (or its submanifolds of transitivity) is represented as the homogeneous spaceG/H ofG,H being a subgroup ofG, and the actionG onV and the topology ofV are determined. The topologies of the spacesV are as follows: ⁴ (spaceT*₂), ⁴ of ³ T¹ (spaceT ₂), ⁴ (spaceT*₃), ³ (submanifolds of transitivity in spaceT ₃).In two cases (spacesT ₂ andT ₃) we have obtained metrics free of singularities.     

Level I theory of large deviations in the ideal gas

LetX ₁,X ₂,... be i.i.d. random elements (the states of the particles 1,2,...). Letf be an ^d-valued, measurable function (an observable) and letB R^dbe a convex Borel set. DenoteS _n=f(X₁)+f(X₂)+...+f(X_n). Using large-deviation theory, it may be shown that, under certain regularity conditions, there exists a point _B (the dominating point of B) so that, givenS _n/n B, actually S_n/n _B in probability as n. Having this conditional weak law of large numbers as our starting point, we consider physical systems of independent particles, especially the ideal gas. Given an observed energy level, we derive convergence results for empirical means, empirical distributions, and microcanonical distributions. Results are obtained for a closed system with a fixed number of particles as well as for an open particle system in the space (a Poisson random field). Our approach is elementary in the sense that we need not refer to the abstract level II theory of large deviations. However, the treatment is not restricted to the so-called discrete ideal gas, but we consider the continuous ideal gas.     

Cluster hull algorithms for large systems with small memory requirement

Improved hull walking algorithms for two-dimensional percolation are proposed. In these algorithms a walker explores the external perimeter of percolation clusters. With our modifications very large systems (sizeL) can be studied with finite and small memory requirement and in computation time L ^7/4. Applications in determining spanning probabilities, continuum percolation, and percolation with nonuniform occupation probability are pointed out.     

Second order large deviation estimates for ferromagnetic systems in the phase coexistence region

We consider thed-dimensional Ising model with ferromagnetic nearest neighbor interaction at inverse temperature . Let be the magnetization inside ad-dimensional hyper cube , ₊ be the+Gibbs state andm*() be the spontaneous magnetization. For such thatm*()>0 we find a sufficient condition (easily verified to hold for large ) for ₊({M [a,b]}) to decay exponentially with ||^(d–1)/d when –m*<b<m*, –1a<b. Ford=2 this sufficient condition is the exponential decay of a connectivity function. We also prove a partial converse to this result, obtain a sharper result for the magnetization ond–1 dimensional cross sections of the model and prove a similar result ford=2, –m*<a<b<m*, and large, when free boundary conditions are chosen outside .Work partly supported by the U.S. Army Research Office     

Finite-state neural networks. A step toward the simulation of very large systems

Neural networks composed of neurons withQ _N states and synapses withQ states are studied analytically and numerically. Analytically it is shown that these finite-state networks are much more efficient at information storage than networks with continuous synapses. In order to take the utmost advantage of networks with finite-state elements, a multineuron and multisynapse coding scheme is introduced which allows the simulation of networks having 1.0×10⁹ couplings at a speed of 7.1×10⁹ coupling evaluations per second on asingle processor of the Cray-YMP. A local learning algorithm is also introduced which allows for the efficient training of large networks with finite-state elements.     

Localization at large disorder and at extreme energies: An elementary derivations

The work presents a short proof of localization under the conditions of either strong disorder ( > ₀) or extreme energies for a wide class of self adjoint operators with random matrix elements, acting inl ² spaces. A prototypical example is the discrete Schrödinger operatorH=–+U ₀(x)+V _x onZ ^d ,d1, withU ₀(x) a specified background potential and {V _x } generated as random variables. The general results apply to operators with – replaced by a non-local self adjoint operatorT whose matrix elements satisfy: _y |T _x,y | ^S Const., uniformly inx, for somes<1. Localization means here that within a specified energy range the spectrum ofH is of the pure-point type, or equivalently — the wave functions do not spread indefinitely under the unitary time evolution generated byH. The effect is produced by strong disorder in either the potential or in the off-diagonal matrix elementsT _{x, y} . Under rapid decay ofT _{x, y} , the corresponding eigenfunctions are also proven to decay exponentially. The method is based on resolvent techniques. The central technical ideas include the use of low moments of the resolvent kernel, i.e. <|G _E (x, y)| ^s > withs small enough (<1) to avoid the divergence caused by the distribution's Cauchy tails, and an effective use of the simple form of the dependence ofG _E (x, y) on the individual matrix elements ofH in elucidating the implications of the fundamental equation (H–E)G _E (x,x ₀)= _x,x0 . This approach simplifies previous derivations of localization results, avoiding the small denominator difficulties which have been hitherto encountered in the subject. It also yields some new results which include localization under the following sets of conditions: i) potentials with an inhomogeneous non-random partU ₀ (x), ii) the Bethe lattice, iii) operators with very slow decay in the off-diagonal terms (T x,y1/|x–y|^(d+)), and iv) localization produced by disordered boundary conditions.Work supported in part by NSF Grants PHY-8912067 and PHY-9214654 (MA), and ONR Grant N00014-91-J-1526 (SM)     

Lattice instantons in the large dimension limit

We give a lattice construction of the discretizations of the topologically nontrivial maps S ^2n–1S ⁿ . For n=1, 2, 4, 8, these are the Hopf maps. The construction, based on Barnes-Wall lattices, Reed-Muller error-correcting codes, and Hadamard matrices, generalizes to n=2 ⁱ for i any integer. Manton's result for the cases n=2 and 4 (i.e., the monopole and instanton) are included. We argue that discrete harmonic analysis will be exact in the infinite dimension limit.Work supported in part by the DOE contract #DE-ACO2-87ER-40325.B.Department of Energy Outstanding Junior Investigator supported in part by DOE contract number DE-FGO5-85ER-40226.     

Vicious random walkers in the limit of a large number of walkers

The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP _t ^(p) ) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP _t ^(p) in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limittp.     

On laplace integrals and transfer operators in large dimension: Examples in the nonconvex case

This Letter gives detailed proofs concerning the analysis of the pair correlations for a nonconvex model. Using the transfer matrix approach, the problem is reduced to the analysis of the spectral properties of this transfer operator. Although the problem is similar to the semiclassical study of the Kac operator presented in a paper with M. Brunaud, which was devoted to the study of exp-(v/2) exp h ² exp-(v/2) for h small, new features appear for the model exp-(v/2h) exp h exp-(v/2h). Our principal results concern the splitting of this operator between the two largest eigenvalues. We give an upper and a lower bound for this splitting in the semi-classical regime. As a corollary, we get good control of the decay of the pair correlation. Some of the results were announced in a previous paper. Related WKB constructions will be developed in a later paper.Inspired by papers by M. Kac [15, 16].     

Measurement of one and two bond N–C couplings in large proteins by TROSY-based J-modulation experiments

Residual dipolar couplings (RDCs) between NC′ and NC^α atoms in polypeptide backbones of proteins contain information on the orientation of bond vectors that is complementary to that contained in NH RDCs. The ¹J_NC^α and ²J_NC^α scalar couplings between these atoms also display a Karplus relation with the backbone torsion angles and report on secondary structure. However, these N–C couplings tend to be small and they are frequently unresolvable in frequency domain spectra having the broad lines characteristic of large proteins. Here a TROSY-based J-modulated approach for the measurement of small ¹⁵N–¹³C couplings in large proteins is described. The cross-correlation interference effects inherent in TROSY methods improve resolution and signal to noise ratios for large proteins, and the use of J-modulation to encode couplings eliminates the need to remove frequency distortions from overlapping peaks during data analysis. The utility of the method is demonstrated by measurement of ¹J_NC′, ¹J_NC^α, and ²J_NC^α scalar couplings and ¹D_NC′ and ¹D_NC^α residual dipolar couplings for the myristoylated yeast ARF1·GTPγs protein bound to small lipid bicelles, a system with an effective molecule weight of 70 kDa.     

Hierarchical matrices in the see-saw mechanism,large neutrino mixing and leptogenesis

We consider the see-saw mechanism for hierarchical Dirac and Majorana neutrino mass matrices m _D and M _R, including the CP violating phases. Simple arguments about the structure of the neutrino mass matrix and the requirement of successful leptogenesis lead to the situation that one of the right-handed Majorana neutrinos is much heavier than the other two, which in turn display a rather mild hierarchy. It is investigated how for the neutrino mixing one small and two large mixing angles are generated. The mixing matrix element |U _e3|² is larger than 10^-3 and a characteristic ratio between the branching ratios of lepton flavor violating charged lepton decays is found. Successful leptogenesis implies sizable CP violation in oscillation experiments. As in the original minimal see-saw model, the signs of the baryon asymmetry of the universe and of the CP asymmetry in neutrino oscillations are equal and there is no connection between the leptogenesis phase and the effective mass as measurable in neutrinoless double beta decay.Received: 28 May 2003, Revised: 13 September 2003, Published online: 26 November 2003     

Shears band with a large dynamic moment of inertia in 197Bi

High-spin states in ¹⁹⁷Bi were studied with the AFRODITE γ-ray array at iThemba LABS using the ¹⁸¹Ta( ²²Ne, 6n) reaction at a beam energy of 125 MeV. A new shears band was found and linked to the low-lying states in ¹⁹⁷Bi. Its dynamic moment of inertia, , is considerably larger than the of the shears bands in the neighbouring Pb isotopes. This is probably a result of the involvement of an additional high-K h_9/2 proton orbital.     

Dirac's large numbers hypothesis in Einstein's theory of gravitation

A method is given for incorporating Dirac's Large Numbers hypothesis into Einstein's standard theory of general relativity. The method involves the assumption that at each point in space there exist two types of clocks, a cosmological clock measuring ephemeris time and an atomic clock measuring atomic timet _A . Newton's law of universal gravitation is formulated relativistically in terms of these two times and the proper distance determined by measuring rods between simultaneous events, and a method is given for operationally identifyingG. The Large Numbers hypothesis requirement thatG _A 1/t _A is then used to establish the relationship between the two times. Alternative derivations of the time relationship not involving a time-varying gravitational constant are obtained by intercomparison of various large numbers. It is shown that the resulting relationship betweent _A and gives agreement with the observed natural microwave radiations. Also, the Large Numbers hypothesis leads to a time formed from the fundamental constants of Nature that is comparable to the age of the Universe.     

Imaging and focusing of an atomic beam with a large period standing light wave

A novel atomic lens scheme is reported. A cylindrical lens potential was created by a large period ( 45 m) standing light wave perpendicular to a beam of metastable He atoms. The lens aperture (25 m) was centered in one antinode of the standing wave; the laser frequency was nearly resonant with the atomic transition 2³ S ₁–2³ P ₂ (=1.083 m) and the interaction time was significantly shorter than the spontaneous lifetime (100 ns) of the excited state. The thickness of the lens was given by the laser beam waist (40 m) in the direction of the atomic beam. Preliminary results are presented, where an atomic beam is focused down to a spot size of 4 m. Also, a microfabricated grating with a period of 8 m was imaged. We discuss the principle limitations of the spatial resolution of the lens given by spherical and chromatic aberrations as well as by diffraction. The fact that this lens is very thin offers new perspectives for deep focusing into the nm range.     

Deposition of high-resolution Carbon/Carbon multilayers on large areas for X-ray optical applications

To synthesize X-ray optical multilayers showing both high resolution and high reflectivity spacer and absorber materials with low absorption coefficients for the desired spectral range are required. Simulations of C/C multilayers with different period thicknesses, d, and single layer densities, , show that a reflectance R([_Cu]K)>80% and a resolving power of about /600 can be achieved for C/C layer stacks with d=3 nm and N=1000 periods.An advanced large area PLD technique was used to deposit C/C single- and multilayers onto Si-substrates up to 6 in diameter. By variation of the laser parameters, we achieved densities of the carbon single layers in the range of _C=2.0...2.7 g/cm³ (measured by XRR) and surface roughnesses _C=0.13...0.19 nm (measured by AFM). Due to the interface intermixing and penetration depth of highly energetic ions, especially during the deposition of the absorber layers, the density contrast of multilayers with period thicknesses lower than 5 nm is noticeably reduced. C/C multilayers with period thicknesses d=1.1...7.0 nm, more than 500 periods and density contrasts of about 0.2 g/cm³ were deposited. PACS 81.15.Fg; 41.50+h; 68.55-a     

Black holes associated with galaxies

A small and a large black hole are naturally associated with a galaxy of total massM and spherical halo radiusR. Also of massM, the large black hole is a spatial contraction of the galaxy down to its Schwarzschild radius,r r, with=2GM/c ²R, whereG/c ²=4.78×10^–17 kpc/M is Newton's gravitational constant divided by the speed of light squared. The small black hole is ther r contraction of the large hole, i.e., the iterated double contraction of the galaxy itself, with the resulting massm=M=2GM ²/c²R. In the case of the Milky Way (M=7.0×10¹¹ M andR=15 kpc) the latter equation for the small black hole mass yieldsm=3.1×10⁶ M , which is close to the observed value for the mass of the black hole at the center of the Milky Way. Black holes of the small type may evolve to the large by mass accretion, perhaps during a quasar phase. Vast regions of the universe may in fact be populated by large black holes—missing mass—which validates the cosmological principle and effects the closure of the universe.     

Retardation of electromagnetic waves by helices of large diameters

This paper is devoted to the study of the wave retardation by helices of large diameters, when the lengthL of one turn of the helix is larger than the vacuum wavelength, i.e.L/>1. The dispersion equation of the tape helix wound up on a dielectric cylinder was derived and the dependence of the phase velocity of slowed-down waves on the diameter of helix was calculated. The theory was verified experimentally at a frequencyf=2·385 GHz. Helices were wound up on polyfoam (=1·04) and plexiglass (=2·55) cylinders of various diameters. For the helix wound up on plexiglass cylinders it was found that the wave retardation depends on the form of conductor from which the helix is made. The retardation of waves is determined by an effective dielectric constant _ef which is equal either ( _i + _e)/2 for the tape helix or ( _{i e}) for the helix made from a wire of the circular cross-section; here _i is the dielectric constant of inner dielectric rod and _e is that of outer space.