On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

Inequivalent quantizations for non-linear σ model

We compute the homotopy groups ₀ and ₁ of the classical configuration space of anO(3) invariant field theory on ×, where is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications.     

Non-Markovian reversible Chapman-Kolmogorov measures on subshifts of finite type

We consider shift-invariant probability measures on subshift dynamical systems with a transition matrixA which satisfies the Chapman-Kolmogorov equation for some stochastic matrix compatible withA. We call them Chapman-Kolmogorov measures. A nonequilibrium entropy is associated to this class of dynamical systems. We show that ifA is irreducible and aperiodic, then there are Chapman-Kolmogorov measures distinct from the Markov chain associated with and its invariant row probability vectorq. If, moreover, (q, ) is a reversible chain, then we construct reversible Chapman-Kolmogorov measures on the subshift which are distinct from (q, ).     

Interfacial properties in solid-stabilized emulsions

We prepared concentrated monodisperse oil-in-water emulsions stabilized by solid particles. The osmotic resistance, , of the emulsions was measured for different oil volume fractions above the random close packing ( ). The dimensionless osmotic resistance, /(/R) ( being the interfacial tension and R being the undeformed drop radius), was always substantially higher than the corresponding values obtained for surfactant-stabilized emulsions. It can be concluded that droplet deformation in solid-stabilized emulsions is not controlled by the capillary pressure, /R, of the non-deformed droplets but rather by 0/R, 0 being a parameter characterizing the rigidity of the droplets surfaces. The data can be interpreted considering that the interfacial layers are elastic at small deformations and exhibit plasticity at intermediate deformations. 0 corresponds to the surface yield stress, i.e. the transition between elastic and plastic regimes. We discuss the origin of the surface behavior considering the strong lateral interactions that exist between the adsorbed solid particles. We propose an independent measurement of 0 based on the critical bulk stress that produces droplet fragmentation in dilute emulsions submitted to shear. Finally, the bulk shear elastic modulus was measured as a function of and confirms many of the features revealed by the osmotic resistance.     

Grassmann-Cartan algebra and Klein-Gordon equations

Given a Riemannian structure (M, g), a hypothesis is investigated that if= _p=0 ⁿ _p (M) is submitted to the differential condition (g++)=0, =mc/—which implies that each component of fulfills the Klein-Gordon equation (- ²) _p =0, ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex admits the interpretation in the sense of first quantization with (M) being a convex set of states, with the structure of a Hilbert space over . The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.     

Local energy flux and the refined similarity hypothesis

In this paper we demonstrate the locality of energy transport for incompressible Euler equations both in space and in scale. The key to the proof is the proper definition of a local subscale flux, _t (r), which is supposed to be a measure of energy transfer to length scales <l at the space point r. Kraichnan suggested that for such a quantity the refined similarity hypothesis will hold, which Kolmogorov originally assumed to hold instead for volume-averaged dissipation. We derive a local energy-balance relation for the large-scale motions which yields a natural definition of such a subscale flux. For this definition a precise form of the refined similarity hypothesis is rigorously proved as a big-O bound. The established estimate is _t (r)=O(l _3h-1) in terms of the local Hölder exponenth at the point r, which is also the estimate assumed in the Parisi-Frisch multifractal model. Our method not only establishes locality of energy transfer, but it also clarifies the physical reason that convection effects, which naively violate locality, do not contribute to the subscale flux. In fact, we show that, as a consequence of incompressibility, such effects enter into the local energy balance only as the divergence of a spatial current. Therefore, they describe motion of energy in space and cancel in the integration over volume. We also discuss theorems of Onsager, Eyink, and Constantinet al. on energy conservation for Euler dynamics, particularly to explain their relation with the Parisi-Frisch model. The Constantinet al. proof may be interpreted as giving a bound on the total flux, _t =d ^d r _t (r), of the form _t (r)=O(l _z3h-1), wherez ₃ is the third-order scaling exponent (or Besov index), in agreement with the multifractal model. Finally, we discuss how the local estimates are related to the results of Caffarelli-Kohn-Nirenberg on partial regularity for solutions of Navier-Stokes equations. They provide some heuristic support to a scenario proposed recently by Pumir and Siggia for singularities in the solutions of Navier-Stokes with small enough viscosity.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Investigation of the excitation of nitrogen molecules in the positive column of a discharge in a mixture of CO2 and N2

The absolute populations of the electron states of the nitrogen molecule C³_u and B³_g in the positive column of a discharge in a mixture of CO₂ and N₂ at an overall pressure of 2.5 mm Hg, a ratio of the components of 11, and a current of 60 mA, are determined. An estimate is made of the possibility of exciting the electron state C³_u by direct electron collision and by multistage excitation from the electron state B³_g. It is suggested that the most probable process by which the electron state C³_u is excited is multistage excitation from vibrational levels of the electron state B³_g.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 49–52, October, 1972.     

Spin manifolds,killing spinors and universality of the Hijazi inequality

In terms of the Dirac operator P, we introduce on any field a first-order operator D and show that the operator (–) on the spinors (=(n/4(n–1))R; dim W=n) is positive. By means of a universal formula, we show that, on a compact spin manifold of dimension 3, the Hijazi inequality [8] holds for every spinor field such that (P, P) = ²(, ) (=const.). In the limiting case, the manifold admits a Killing spinor which can be evaluated in terms of . Different properties of spin manifolds admitting Killing spinors are proved. D is nothing but the twistor operator.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

A theory of the weakly pinned Fröhlich mode

Extending earlier work of Littlewood (1987) a theory for the collective mode (Fröhlich mode) response of weakly pinned charge density waves (CDW) is given. Long range Coulomb interaction is incorporated in both a proper definition of the measured ac conductivity _CDW() and in the Fukuyama-Lee-Rice treatment of phason dynamics. The frequency and wave number dependent quasi particle resistivity is shown to appear only in the internal phason lines in the perturbation expansion of the impurity averaged phason propagatorD _ren. Quantitative results for _CDW() are evaluated within the self-consistent Born approximation toD _ren in three spatial dimensions taking anisotropy into account. Besides the low frequency relaxation mode we find a significant effect of the longitudinal optical phason _LO on the Fröhlich mode pinning frequency when descreening sets in at low temperatures. This is yet another manifestation of selection rule breaking by inhomogeneous pinning and establishes the special role that _LO plays in the dynamics of CDW. An explicit analytical formula for _CDW() is given and discussed in some detail including the important analyticity properties. Available measurements of the linear ac response in a wide range of frequencies and conductivities are compared with the theory and found to agree with the theoretical predictions supporting the concept of weak pinning in CDW.     

High-resolution laser spectroscopy of theQ v(0) transitions in solid parahydrogen

Our recent high-resolution laser spectroscopy of theQ _v(0) (=0,J=00) transitions in solid parahydrogen is discussed. The systems studied include the fundamental vibrational bands of impurity D₂ and HD, the first and second overtones of parahydrogen, and the charge-induced spectrum of-ray irradiated parahydrogen. Additionally, Stark and stimulated Raman-gain spectroscopies are applied to the solid. The linewidths are as sharp as 2 MHz HWHM, which is highly unusual for a solid. Our spectra demonstrate a variety of physical phenomena, particularly thek = 0 selection rule, as well asJ = 1/J = 0 pair intermolecular interactions.     

Local decay of scattering solutions to Schrödinger's equation

The main theorem asserts that ifH=+gV is a Schrödinger Hamiltonian with short rangeV, L _compact ² (IR³), andR>0, then exp(iHt) _{S L} ² _(|x|<R)=O(t ^–1/2), ast where _S is projection onto the orthogonal complement of the real eigenvectors ofH. For all but a discrete set ofg,O(t ^–1/2) may be replaced byO(t ^–3/2).Research supported by the National Science Foundation under grants NSF GP 34260 and MCS 72-05055 A04     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Gravitation and universal Fermi coupling in general relativity

The generally covariant Lagrangian densityG = + 2K _matter of the Hamiltonian principle in general relativity, formulated by Einstein and Hilbert, can be interpreted as a functional of the potentialsg _ikand of the gravitational and matter fields. In this general relativistic interpretation, the Riemann-Christoffel form _kl ⁱ = _kl ⁱ for the coefficients _kl ⁱ of the affine connections is postulated a priori. Alternatively, we can interpret the LagrangianG as a functional of , g_ik, and the coefficients _kl ⁱ . Then the _kl ⁱ are determined by the Palatini equations. From these equations and from the symmetry _kl ⁱ = _lk ⁱ for all matter fields with /=0 the Christoffel symbols again result. However, for Dirac's bispinor fields, / becomes dependent on the Dirac current, essentially with a coupling factor Khc. In this case, the Palatini equations define a new transport rule for the spinor fields, according to which a second universal interaction results for the Dirac spinors, besides Einstein's gravitation. The generally covariant Dirac wave equations become the general relativistic nonlinear Heisenberg wave equations, and the second universal interaction is given by a Fermi-like interaction term of the V-A type. The geometrically induced Fermi constant is, however, very small and of the order 10^–81erg cm³     

Interpretation of measurements of π0-meson photoproduction partial cross sections on a6Li nucleus with O+ level excitation

The anomalously large measured values of the cross section of the reaction +⁶Li ⁰ +⁶Li^* (3.56 MeV), which were obtained in two different laboratories, 260–450 MeV -rays, are discussed. It is shown that the disagreement between theory and experiment is due to the background reaction +⁷Li ⁰ + n +⁶Li^* (3.56 MeV), which became possible as a result of the poor isotropic purity of the target. This background reaction is discussed with respect to obtaining data on ⁰-meson photoproduction on neutrons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, 92–96, November, 1991.     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Adiabatic Models of the Cosmological Radiative Era

We consider a generalization of the Lemaitre-Tolman-Bondi (LTB) solutions by keeping the LTB metric but replacing its dust matter source by an imperfect fluid with anisotropic pressure _ab . Assuming that total matter-energy density is the sum of a rest mass term, ^(m), plus a radiation ^(r) = 3p density where p is the isotropic pressure, Einstein's equations are fully integrated without having to place any previous assumption on the form of _ab . Three particular cases of interest are contained: the usual LTB dust solutions (the dust limit), a class of FLRW cosmologies (the homogeneous limit) and of the Vaydia solution (the vacuum limit). Initial conditions are provided in terms of suitable averages and contrast functions of the initial densities of ^(m), ^(r) and the 3-dimensional Ricci scalar along an arbitrary initial surface t = t _i . We consider the source of the models as an interactive radiation-matter mixture in local thermal equilibrium that must be consistent with causal Extended Irreversible Thermodynamics (hence _ab is shear viscosity). Assuming near equilibrium conditions associated with small initial density and curvature contrasts, the evolution of the models is qualitatively similar to that of adiabatic perturbations on a matter plus radiation FLRW background. We show that initial conditions exist that lead to thermodynamically consistent models, but only for the full transport equation of Extended Irreversible Thermodynamics. These interactive mixtures provide a reasonable approximation to a dissipative tight coupling characteristic of radiation-matter mixtures in the radiative pre-decoupling era.     

Generalized Bargmann potentials

Conditions are found for the coefficient functions of a linear ordinary differential equation of the kth order ^(k)+u₁^(k-2)+...+u_k-1=^k, when its solution has the following analytical dependence on the parameter: =exp(z _i=1 ⁿ (+a_i)(a_ja_j(Z)). The problem is closely related to the finding of n-soliton solutions of the simplest form for the periodic Toda system, corresponding to A _nand C _nseries.