First-order phase transitions in finite-size strips with interfaces

Finite-size rounding of the magnetization discontinuity at the magnetic phase transition atH=0 (T<T _c ) in 2d Ising-type strips of sizeL ×L , with ± boundary conditions alongL inducing an interface of lengthL , is studied by phenomenological considerations and transfer matrix techniques. Scaling expressions are derived forL =O(L ) and also in the infinite strip limitL . Most of the results can be extended to the 3d case.     

Norm inequalities for fractional powers of positive operators

It is shown that ifA, B andX are operators on a Hilbert space such thatA andB are positive andX belongs to a norm ideal associated with some unitarily invariant norm |·|, then for 0 r 1 we have |A ^r XB ^r | |X|^1-r |AXB| ^r . This is an extension of the classical Heinz-Kato inequality which was originally proved for the usual operator norm. Other related inequalities are also discussed.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Anisotropy of infrared optical absorption in layered superconductors

We analyze the problem of infrared optical absorption in a clean layered London superconductor in the vicinity of the gap =2. We conclude that absorption of light with wave vectorqc is enhanced over ordinary Drude absorption (qc) due to resonance absorption (Landau damping). Experimental absorption studies with qc might therefore improve chances to observe a superconducting gap in the high-T _c superconductors.     

Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations

Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ,v : uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL in the special direction and linear dimensionsL in all other directions. The related shape effects forL L but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv +(d–1)v =+2 does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.Visiting Supercomputer Senior Scientist at Rutgers University.     

a-b plane anisotropy of single-domain crystals of Bi2Sr2CaCu2O8

The polarized reflectance of thea-b plane of single-domain Bi₂Sr₂CaCu₂O₈ crystals is anisotropic above and belowT _c . The normal-state infrared conductivity is higher forEa whereas the high-frequency conductivity is higher alongb, particularly for transitions associated with the Bi–O layers. BelowT _c there is a definite anisotropy to the far-infrared absorption, with a finite absorption forEb down to 20 meV. This anisotropy of thea-b plane could be due either to anisotropy of the superconducting gap or to anisotropy of the midinfrared component to the conductivity.     

Expectations and entropy inequalities for finite quantum systems

We prove that the relative entropy is decreasing under a trace-preserving expectation inB(K ¹), and we show the connection between this theorem and the strong subadditivity of the entropy. It is also proved that a linear, positive, trace-preserving map ofB(K) into itself such that 1 decreases the value of any convex trace function.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

Entropy,the central limit theorem and the algebra of the canonical commutation relation

The central limit theorem of Cushen and Hudson is reformulated on the algebra of the CCR. Namely, for a gauge invariant state , the weighted convolutions _n of the central limit tend to the quasi-free reduction _Q of pointwise. It is proved that if the initial relative entropy S(, _Q ) is finite, then S( _n , _Q ) goes to 0 and so _n – _Q 0. No restriction on the dimension of the test function space is made.     

Flux diffusion in high-T c superconductors

In type-II superconductors in the flux flow (J J _c ), flux creep (J _c J _c ), and thermally activated flux flow (TAFF) (J J _c ) regimes the inductionB(r,t), averaged over several penetration depths , in general follows from a nonlinear equation of motion into which enter the nonlinear resistivities (B, J ,T) caused by flux motion and (B, J ,T) caused by other dissipative processes.J andJ are the current densities perpendicular and parallel toB,B=|B|, andT is the temperature. For flux flow and TAFF in isotropic superconductors with weak relative spatial variation ofB, this equation reduces to the diffusion equation plus a correction term which vanishes whenJ =0 (this means B××B=0) or when – = 0 (isotropic normal conductor). When this diffusion equation holds the material anisotropy may be accounted for by a tensorial . The response of a superconductor to an applied current or to a change of the applied magnetic field is considered for various geometries. Such perturbations affect only a surface layer of thickness where a shielding current flows which pulls at the flux lines; the resulting deformation of the vortex lattice diffuses into the interior until a new equilibrium or a new stationary state is reached. The a.c. response, in particular the frequency with maximum damping, depends thus on the geometry and size of the superconductor.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Microwave relaxation and phenomenological damping in thin films

The relation between relaxation timeT, frequency swept resonance linewidth , and phenomenological damping is given by =2/T=(_x+_y), where _x,y = (H ₀+(N _x,y –N _z ) 4M _s ).N _x,y,z are sample demagnetizing factors,H ₀ is the effectivez-directed static field, 4M _s is the saturation induction, and is the gyromagnetic ratio. This fairly simple but general relation shows that the numerical relation between damping and relaxation at a given frequency can be quite different for in-plane and normally magnetized thin films. For thesame loss processes, so thatT andT are equal, is larger than . For permalloy films at 1 GHz, =15 . In addition, the conventional field swept linewidth, H=/, is simply related to only forN _x =N _y . Both and H are geometry dependent and do not provide an intrinsic measure of the relaxation. These results are confirmed by both resonance and transient response experiments. The large values of for large angle switching may also be partially explained by this analysis because the relevant magnetization motion is due to a demagnetizing field normal to the film plane.Visiting scientist on leave fromRaytheon Company, U.S.A. Supported by the Japan Society for the Promotion of Science.     

Produits tensoriels continus d'espaces et d'algèbres de Banach

The notion of tensor product of a family (A _i ) _i I of Banach algebras is generalized to the case whenI is a topological space; in this case A _i is generated by some elements x _i , the family (x _i ) being subjected to certain conditions: for instance the functioni x _i must be continuous. This notion is applied to Quantum Field Theory in the following sense: certain algebras of observables can be considered as continuous tensor products of simpler ones, namely of algebras of observables with one degree of freedom.     

Gap emission in ultraviolet photoemission experiments

It is shown that the gap emission observed in ultraviolet photoelectron spectra of metals takes place via a wavevector conserving excitation in the surface region localized on bulk Brillouin zone boundaries. Thus gap emission correspond to direct transitions between bulk initial statesE _i(k =k _BZ,k ) and evanescent statesE _f(k =k _BZ,k ) which are made possible by the existence of the surface. This fact can be used to map occupied bulk energy band dispersions. Examples for Silver, Copper, Gold and Platinum are given.     

Anisotropic properties of volume holograms in Bi12SiO20 monocrystals

A theoretical and experimental study is made on light diffraction from holographic diffraction gratings, recorded in cubic photorefractive crystals Bi₁₂SiO₂₀ with (110) cut, for two orientation of the grating wave vector,K [001] andK [110], when an external electric field is applied.     

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.     

Andreev levels of SNS-junctions in weak magnetic fields

Spatial quantization of the energy spectrum of quasiparticles, bound by Andreev scattering in the normal layer of SNS junctions, remains observable in weak constant magnetic fieldsH parallel to the phase boundaries. Quasiparticles, especially in the low lying Andreev states, can traverse thick normal regions many thousand times before they are scattered once by interaction withH . This confirms the expectation that quasiparticle transport phenomena in superconducting heterostructures should be little influenced by magnetic fields as long as the cyclotron radius greatly exceeds the average spatial extension of the unperturbed wave functions normal to the phase boundaries.     

Crossover to tricritical behavior at the nematic to smecticA transition: An x-ray scattering study

We have carried out a comprehensive x-ray scattering study of the nematic to smecticA transition in the alkylbenzoate (nCB) and thiosulfate series. By changing the aliphatic chain lengthn (C _n H_2n+1) in these series, crossovers from critical to tricritical behavior are induced. We observe a smooth progression of effective exponents from the set,y1.5,v 0.80, andv 0.67 toy=1.1,v =0.6, andv =0.5 for the critical and tricritical regions respectively. In both cases the exponents are close to, but in disagreement with, values expected from current theoretical models. We conclude on an empirical basis that the varied exponents reported in the literature for other systems reflect the critical to tricritical crossover.     

Analyticity in Hubbard Models

The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when t is small, or t ²/U is small; here, is the inverse temperature, U the on-site repulsion, and t the hopping coefficient. For more general models with Hamiltonian H=V+T where V involves local terms only, the free energy is analytic when T is small, irrespective of V. There exists a unique Gibbs state showing exponential decay of spatial correlations. These properties are rigorously established in this paper.     

Dual-oriented thin crystals of molybdenum grown under Ar+ ion bombardment

Ar⁺ sputtering of an Cu(111) surface while simultaneously supplying Mo atoms is known to induce an oriented growth of Mo thin crystals, or seed-layers, on evolving conical Cu protrusions. The seed-layers thus formed are shown to be dual-oriented, or bicrystalline, consisting of columnar crystallites grown homo-epitaxially. The orientation relationship between the two types of crystallites was (100)_I (111)_II with [001]_I [110]_II, and this bicrystallinity probably resulted from a non-uniform charge-up of the layers' growth front. As concluded from high-resolution electron microscopy, the Mo(100) stacking is elastically converted into the Mo(111) stacking and vice versa, under the influence of tensile stress. The homo-epitaxy that the seed-layers exhibited is believed to reflect the mutual convertibility of the Mo(100) and (111) stackings.