Ground State and Spin-Glass Phase of the Large-N Infinite-Range Spin Glass via Supersymmetry

The large-N infinite-range spin glass is considered, in particular, the number of spin components k needed to form the ground state and the sample-to-sample fluctuations in the Lagrange multiplier field on each site. The physical significance of k for the correlation functions is discussed. The difference between the large-N and spherical spin glass is emphasized; a slight difference between the average Lagrange multiplier of the large-N and spherical spin glasses is derived, leading to a slight increase in the energy of the ground state compared to the naive expectation. Further, there is a change in the low-energy density of excitations in the large-N system. A form of level repulsion, similar to that found in random matrix theory, is found to exist in this system, surviving interactions. Even though the system is an interacting one, a supersymmetric formalism is developed to deal with the problem of averaging over disorder.     

Diffusion approximations for the scattering of resonance-line photons: Interior and boundary layer solutions

Resonance-line scattering in static low density media with large optical thickness has a diffusive behavior in both space and frequency because photons belonging to the Lorentzian wings of the line may be scattered almost monochromatically a very large number of times. This diffusive behavior holds on frequency scales and spatial scales, χ_c and τ_c, much larger than the scales associated with one elementary scattering of a wing-photon.A method developed for diffusion approximations in neutron transport theory, suitably generalized to handle diffusion in frequency space, is applied to the case of conservative scattering in a bounded medium with interior sources and zero incoming radiation. The method is to separate the line radiation field into an interior part and a boundary layer part which goes to zero in the interior. Each part is expanded in terms of a small parameter ?, which is the ratio of the mean free-path at frequency χ_c to the characteristic spatial scale τ_c.It is shown that the leading term in the interior asymptotic expansion is isotropic, zero on the boundary, and obeys a space and frequency diffusion equation. In the boundary-layer expansion, the leading term is of order ? and is a solution to a monochromatic transfer equation in a semi-infinite, plane-parallel medium. The emergent radiation field is shown to be of order ? and proportional to the gradient of the interior solution at the boundary. Its angular dependence, in the case of isotropic scattering in the atom frame, is given by the Ambartsoumian H-function. A comparison is presented between numerical solutions of the full transfer equation and asymptotic solutions. Non-conservative scattering and time-dependent problems are briefly discussed.     

Fractal modelling of turbulent mixing

The aim of this work is to propose a new model for turbulent flows, called the fractal model (FM), applicable both in a Reynolds averaged Navier–Stokes (RANS) and a large-eddy simulation (LES) formulation, with the ultimate goal of applying it to simulate turbulent combustion irrelevant of its mode (premixed or non-premixed). The model is able to turn itself off in the laminar zones of the flow, and in particular near walls. It is based on the fractal theory. It describes the physics of the smaller spatial scales and therefore represents a small-scales model.

FM describes the physics of the small scales of turbulence based on the phenomenological concept of vortex cascade and on the self-similar behaviour of turbulence in the inertial range. Such a model is used in each cell of a numerical calculation. A characteristic length Δ is associated to each cell, and the local energy u ³ _Δ/Δ is distributed over a certain number of eddies, which depends on the local Reynolds number Re _Δ. Each vortex of the cascade generates N _c vortices; the recursive process of vortex generation terminates at the dissipative scale level, i.e. when the eddy Reynolds number is equal to one. FM is also able to estimate the volume fraction occupied by the dissipative fine structures of turbulence; this quantity is critical in reactive turbulent flows.

The physics of small scales is summarized by a turbulent ‘viscosity’ μ_t, to be added to the molecular one. μ_t is zero where the flow is laminar and, in particular, goes to zero at solid walls. Assuming μ_t to be isotropic, FM is applicable in a RANS formulation (IFM, isotropic fractal model). The model can be extended to the anisotropic case (AFM, anisotropic fractal model) and therefore used to close the transport equations in an LES approach. In the present paper, the model (IFM) is used in a RANS approach and is validated through a test case studied experimentally by Johnson and Bennett, and numerically (with LES) by Akselvoll and Moin. The results obtained are in good agreement both with the experimental and the numerical ones. Other tests are being performed.     

Spin-dependent rectification in the C 59 N molecule

Coherent spin-dependent electron transport is investigated in three conditions: (1) a C₆₀ molecule is connected to two ferromagnetic (FM) electrodes symmetrically, (2) a C₅₉N molecule is connected to two FM electrodes symmetrically and (3) a C₅₉N molecule is connected to two FM electrodes asymmetrically. This work is based on a single-band tight-binding model Hamiltonian and the Green’s function approach with the Landauer–Buttiker formalism. Electrodes used in this study are semi-infinite FM electrodes with finite cross-section. Obvious rectification effect is observed in the C₅₉N molecule which is connected to the FMelectrodes asymmetrically. This effect is more in the P alignment of FM electrodes than in AP alignment of FM electrodes. This study indicates that the rectification behaviour is due to the asymmetry in molecule and junctions. Also in this investigation tunnel magnetoresistance (TMR) is calculated for these molecules. Asymmetry is observed in TMR of C₅₉N which is coupled to the electrodes asymmetrically due to asymmetric junctions, but TMR of C₆₀ is symmetric.     

Intensity dependence of multiphoton dissociation in formaldehyde

A new intensity-dependent measurement of multiple-photon dissociation (MPD) in H₂CO, HDCO, and D₂CO gases by the use of an intense pulsed CO₂TEA laser is reported. In this measurement the energy and duration of the laser pulses are kept constant, and the intensity is varied by irradiating the sample using concave mirrors of different focal lengths. A model calculation is used to analyze and fit the present and previous experimental MPD data of HDCO and D₂CO. In this model it is assumed that dissociation is obtained by a repeated mechanism in which coherent multiphoton excitation (CME) of the molecule to high vibration-rotation states |v, J〉 is followed by intramolecular transfer of the excitation energy (ITEE) to the other modes of the molecule. In the calculations the CME is described in the framework of the density matrix formalism with relaxations, and is used to calculate absorption from the ground state as well as absorption from excited states reached by the energy redistribution in the molecule. The ITEE process is assumed to be intensity independent and to cause a random energy distribution in each transferring process. It is found that the experimental results are consistent with the absorption of 14±4 and 17±5 photons per molecule for HDCO and D₂CO, respectively, and this is sufficient to cause their dissociation.     

A study of 't Hooft and Wilson loops

An investigation is undertaken for 't Hooft loop operators in four-dimensional gauge theories. For the first time, a perimeter law is shown to be their behavior in weak coupling Wilson lattice (and continuum) non-abelian SU(N) gauge theories for all N. However, it is also argued that this perimeter law is poor criterion for quark confinement. Rather, it is suggested that non-leading long-distance behavior is what is crucial and relevant in distinguishing non-abelian from abelian (and hence confining from non-confining) theories. A new object, “the 't Hooft line”, is introduced to measure this non-leading behavior and is computed in strong coupling on the lattice. There, one finds magnetic screening characterized by a magnetic screening mass, m_s. It is shown to all orders in strong coupling that m_s is the glueball mass, a result which is expected to persist in weak coupling and in the continuum. Two further consequences of this work are that pure non-abelian gauge theories cannot be in a Higgs phase and that in such models that absence of massless physical particles implies confinement.Finally, non-leading behavior in Wilson loops is examined. The present picture of confinement suggests the absence of van der Waals forces in Yang-Mills theories.     

Defect clusters of variable composition as an origin of coloration of oxide crystals under thermal treatment and irradiation

The dominant role of inclusions of tungsten oxides with variable composition due to variable tungsten valence in the sensitivity of optical absorption of ${\mathrm{PbWO}}_4$ (PWO) scintillation crystals to thermal treatment and irradiation is demonstrated. A model for processes in the inclusions, which lead to crystal coloration and recovery of initial transparency, is discussed. The deteriorating influence of inclusions containing oxides of variable-valence ions on the radiation hardness of PWO is also illustrated by studying PWO single crystals intentionally doped with niobium. To extend the model to other oxide crystals, annealing of ${\mathrm{LiNbO}}_3$ single crystals in atmospheres of poor and rich in oxygen was performed, and a reversible coloration of the crystal due to the change of niobium valence in niobium oxide inclusions is demonstrated.     

Bottlenecking of indirect g shifts of local moments in metals

The indirect g shift in the electron spin resonance of local moments in metals is examined using the Bloch-Hasegawa equations. The g shift is found to have three components. First the usual Hasegawa term that decreases as the bottleneck increases, and second, a temperature dependent indirect shift that is unaffected by the bottleneck. The third term becomes unobservable in the unbottlenecked limit; it is proportional to the ratio of the non S-state local moment susceptibility to the S-state local moment susceptibility. The width of the resonance is found to be proportional to T — θ, where θ is the ordering temperature, and not to temperature T, thereby providing an explanation for the “negative” residual linewidth frequently observed in magnetically concentrated systems.     

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

A model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid- paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength N_s, magnetic number M₁ Darcy number Da and the non-linearity of magnetization parameter M₃ is to hasten, while increase in the ratio of viscosities Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of ferroconvection. Further, increase in Bi, Da⁻¹ and N_s and decrease in Λ, M₁ and M₃ is to diminish the dimension of convection cells.     

Combined effect of demagnetizing field and induced magnetic anisotropy on the magnetic properties of manganese-zinc ferrite composites

This work is devoted to the analysis of factors responsible for the high-frequency shift of the complex permeability (μ^?) dispersion region in polymer composites of manganese-zinc (MnZn) ferrite, as well as to the increase in their thermomagnetic stability. The magnetic spectra of the ferrite and its composites with polyurethane (MnZn-PU) and polyaniline (MnZn-PANI) are measured in the frequency range from 1 MHz to 3 GHz in a longitudinal magnetization field of up to 700 Ое and in the temperature interval from −20 °С to +150 °С. The approximation of the magnetic spectra by a model, which takes into account the role of domain wall motion and magnetization rotation, allows one to determine the specific contribution of resonance processes associated with domain wall motion and the natural ferromagnetic resonance to the μ^?. It is established that, at high frequencies, the μ^? of the MnZn ferrite is determined solely by magnetization rotation, which occurs in the region of natural ferromagnetic resonance when the ferrite is in the “single domain” state. In the polymer composites of the MnZn ferrite, the high-frequency permeability is also determined mainly by the magnetization rotation; however, up to high values of magnetizing fields, there is a contribution of domain wall motion, thus the “single domain” state in ferrite is not reached. The frequency and temperature dependence of μ^? in polymer composites are governed by demagnetizing field and the induced magnetic anisotropy. The contribution of the induced magnetic anisotropy is crucial for MnZn-PANI. It is attributed to the elastic stresses that arise due to the domain wall pinning by a polyaniline film adsorbed on the surface of the ferrite during in-situ polymerization.     

Photo-modification and synthesis of semiconductor nanocrystals

Both photo-oxidation and photosynthesis manifest a strong interaction between nanoparticles and photons due to the large surface area-to-volume ratio. The final sizes of the semiconductor nanocrystals are determined by the photon energy during these phenomena. The photosynthesis is demonstrated in a Si-rich oxide and is similar to thermal synthesis, which involves the decomposition of SiO_x into Si and SiO₂, that is well known and often employed to form Si or Ge nanocrystals embedded in SiO₂ by annealing SiO_x at high temperature. However, photosynthesis is much faster, and allows the low-temperature growth of Si nanocrystals and is found to be pronounced in the SiO nanopowder, which is made by thermal CVD using SiH₄ and O₂. The minimum laser power required for the photosynthesis in the SiO nanopowder is much lower than in the Si-rich oxide formed by the co-sputtering of Si and SiO₂. This is attributed to the weak bond strength of Si-Si and Si-O in the SiO nanopowder. Photosynthesis, which can control the size and position of Si nanocrystals, is a novel nanofabrication technique making the best use of the strong interaction between photons and nanoparticles.     

Asymmetric d-wave superconducting topological insulator in proximity with a magnetic order

In the framework of the Dirac–Bogoliubov–de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet d-wave symmetry. The asymmetric role of this gap respect to the electron–hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of d-wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$ and orbital rotated angle α of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid structures.     

On exact equilibrium states in external gravitational fields of heated,self-gravitating gas clouds cooling by conducting and radiation

We present exact analytic solutions describing the equilibrium states available to a one-dimensional, self-gravitating cloud of gas subject to an external constant gravitational acceleration due to a plane of “stars”. The gas is taken to be heated at a rate proportional to the local gas density and is cooling by both radiation and conduction. The solutions are valid for a thermal conductivity which is an arbitrary function of gas temperature, T, and for radiative cooling which is proportional to the local gas density, ?, multiplied by an arbitrary function of gas pressure, ?. Illustrations of the general spatial dependence are given for the cases where the radiative cooling is proportional to ?²T, and in which the thermal conductivity is either constant, or proportional to T^a(a > 0) in the limits of T tending zero or infinity, respectively.We show that the phenomenon of density “inversion”, reported earlier, is indeed ameliorated by the radiative cooling term, as we had speculated it might be, but is not removed. This indicates that the phenomenon of density inversion is of rugged quality, persisting under a wide variety of conditions and, therefore, of general astrophysical import. We also show that, depending on the ratios of various parameters entering the problem, there is a new phenomenon possible in which the gas temperature has a local minimum at some non-central location so that a wedge of cool gas is in equilibrium surrounded by a hot medium.We have done these calculations as an aid to understanding the complicated behavior of interstellar gas clouds in particular, and the general physical interplay between force balance and energy balance in models of gas clouds more realistic than those heretofore available.     

Contrasting magnetic behavior of fine particles of some Kondo lattices

We have investigated the magnetic behavior of ball-milled fine particles of well-known Kondo lattices, CeAu₂Si₂, CePd₂Si₂ and CeAl₂, by magnetization and heat-capacity studies in order to understand the magnetic behavior when the particle size is reduced. These compounds have been known to order antiferromagnetically in the bulk form near ($T_N=$) 10, 10 and 3.8 K respectively. We find that the features due to magnetic ordering get suppressed to temperatures below 1.8 K in the case of fine particles of ternary alloys, though trivalence of Ce as inferred from the effective moment remains unchanged. In contrast to this, in CeAl₂, there appears to be a marginal enhancement of $T_N$, when the particle size is reduced to less than a micron. These results can be consistently understood by proposing that these compounds move toward left in the Doniach magnetic phase-diagram, for instance, due to relatively more 4f-localization, as the particle size is reduced.     

Shape transformation transitions in a model of fixed-connectivity surfaces supported by skeletons

A compartmentalized surface model of Nambu and Goto is studied on triangulated spherical surfaces by using the canonical Monte Carlo simulation technique. One-dimensional bending energy is defined on the skeletons and at the junctions, and the mechanical strength of the surface is supplied by the one-dimensional bending energy defined on the skeletons and junctions. The compartment size is characterized by the total number L^′ of bonds between the two-neighboring junctions and is assumed to have values in the range from L^′ = 2 to L^′ = 8 in the simulations, while that of the previously reported model is characterized by L^′ = 1, where all vertices of the triangulated surface are the junctions. Therefore, the model in this paper is considered to be an extension of the previous model in the sense that the previous model is obtained from the model in this paper in the limit of L^′↦1. The model in this paper is identical to the Nambu-Goto surface model without curvature energies in the limit of L^′↦∞ and hence is expected to be ill-defined at sufficiently large L^′. One remarkable result obtained in this paper is that the model has a well-defined smooth phase even at relatively large L^′ just as the previous model of L^′↦ 1. It is also remarkable that the fluctuations of surface in the smooth phase are crucially dependent on L^′; we can see no surface fluctuation when L^′≤ 2, while relatively large fluctuations are seen when L^′≥ 3.     

Asymptotic analysis of wall modes in a flexible tube

The stability of wall modes in a flexible tube of radius R surrounded by a viscoelastic material in the region R < r < H R in the high Reynolds number limit is studied using asymptotic techniques. The fluid is a Newtonian fluid, while the wall material is modeled as an incompressible visco-elastic solid. In the limit of high Reynolds number, the vorticity of the wall modes is confined to a region of thickness in the fluid near the wall of the tube, where the small parameter , and the Reynolds number is , and are the fluid density and viscosity, and V is the maximum fluid velocity. The regime is considered in the asymptotic analysis, where G is the shear modulus of the wall material. In this limit, the ratio of the normal stress and normal displacement in the wall, , is only a function of H and scaled wave number . There are multiple solutions for the growth rate which depend on the parameter .In the limit , which is equivalent to using a zero normal stress boundary condition for the fluid, all the roots have negative real parts, indicating that the wall modes are stable. In the limit , which corresponds to the flow in a rigid tube, the stable roots of previous studies on the flow in a rigid tube are recovered. In addition, there is one root in the limit which does not reduce to any of the rigid tube solutions determined previously. The decay rate of this solution decreases proportional to in the limit , and the frequency increases proportional to . Received: 5 November 1997 / Revised: 10 March 1998 / Accepted: 29 April 1998     

On size corrections to the diamagnetic susceptibility of a free electron gas

The magnetic behavior of spinless electrons confined in a cylinder of radiusR by a harmonic oscillator potential is calculated over the entire range of sizesR/r _H, wherer _H is the radius of the classical electron orbit due to a constant magnetic fieldH. The magnetic moment is shown to be large and positive in the small size limitR/r _H?1 in agreement with recent experimental work, while in the usual large size limitR/r _H?1 the Landau susceptibility is obtained. The model is compared with a similar calculation in which a periodic boundary condition is applied in order to show explicitly how qualitative differences arise in the small size limit, and the relevance of the results to calculations for rectangular and spherical geometries with hard wall boundary conditions is examined.     

Radiative corrections to positronium decay

In this work a method for calculating radiative corrections to positronium decay is presented that is direct, and allows for a systematic extension applicable to the calculation of corrections beyond the first [o(α)] correction. An expression for the decay amplitude in terms of the Bethe-Salpeter wavefunction is employed. The Bethe-Salpeter wavefunction is evaluated perturbatively in a scheme having a lowest-order bound state equation that is exactly soluble. The decay amplitude is evaluated in Coulomb gauge, without the introduction of a photon mass. One-loop renormalization in Coulomb gauge is shown to be consistent. Using this method the known analytic result for the o(α) correction to the parapositronium decay rate is obtained. The same method is applied to orthopositronium, and the existing theoretical discrepancy in the value of the o(α) correction to the decay rate is resolved. This o(α) correction is obtained with an error which corresponds to an uncertainty in the total rate much smaller than α²Γ_LO (where Γ_LO is the lowest-order rate). Also, the o(α) correction to the differential decay rate is computed for the first time.