Random aggregation and random-walking center of mass

Two random aggregation models are used in demonstrating the properties of the random displacementsr _i of the center of mass of aggregating particles. It is found that r _i is a randomly decreasing sequence that scales with the cluster size (steps)s and _i ^=1/s r _i s ^1/D , whereD is the fractal dimension. The center-of-mass random walk is a consistent representation of the dynamics of aggregation.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

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).     

Correlation functionals of infinite volume quantum spin systems

The existence and analyticity of the correlation functionals of a quantum lattice in the infinite volume limit is proved. The result is valid at sufficiently high temperatures and for a large class of interactions. Our method estimates the kernelK for a set of Kirkwood-Salzburg equations. While a naive estimate would indicate that K =, we take into account cancellations between different contributions toK in order to show that for sufficiently high temperatures K <1, and this estimate is independent of the volume of the system.Supported in part by the Air Force Office of Scientific Research.     

On the global behaviour of symmetric Skyrmions

It is shown that the chiral angle, (r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, (r) is strictly convex or concave. As r, (r) and (r) approach their limit values at the rate Or ^- for any (0,2).     

Infrared and Raman study of Si2Te3

Results of ir and Raman investigations on trigonal layer-structured Si₂Te₃ single crystals are reported. The ir reflection spectrum withEc exhibits seven reststrahl-like bands, whereas the corresponding spectrum withEc shows only one very small bump. Values for ₀ and are given. The Raman spectra are very rich in structure and can only be interpreted qualitatively as being a mixture of single phonon lines and one- and two-phonon density-of-states contributions. One-phonon density-of-states effects are disorder-induced owing to the statistical occurrence of the Si atoms within the regular hexagonal Te sublattice.     

The Optical Spectra of the Arsenic Triselenide Crystal in the Range from 1 to 10 eV

Full complexes of fundamental optical functions of the As₂Se₃ single crystal in the region from 1 to 10 eV are calculated at 10 K (1–5.5 eV) and 77 K (5.5–10 eV) for three light polarizations (E a, E b, and E c). Their main characteristic features are established. The experimental reflection spectra and the spectra of other optical functions calculated on their basis are compared with the known literature data.     

On the Existence of a Maximizer for the Strichartz Inequality

It is shown that a maximizing function u _*L ² does exist for the Strichartz inequality e ^it _x ² u _L ⁶ _t (L ⁶ _x )Su _L ², with S>0 being the sharp constant.     

The S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

Renormalization group equations with several length scales and crossover scaling functions for axial anisotropy

The critical behaviour of axially anisotropicn-vector models is characterized by two distinct length scales, the correlation lengths and for the easy and hard axes. In order to handle the full range of anisotropics from to partial differential renormalization group equations are derived, depending on and . The anisotropicX-Y model is studied in detail near four dimensions. The crossover scaling functions for the susceptibilities are calculated to first order in=4–d. Two distinct crossover regions are found for weak and dominant anisotropy, respectively.     

Numerical simulation of heavy hole cyclotron resonance NEMAG inp-Ge

The cyclotron resonance of heavy holes in germanium underE ₀B ₀[001] fields is simulated by the numerical Monte-Carlo technique. Linear and non-linear regimes of hot hole interaction with high-frequency transverse electric field E [0 0 1] are considered. A new procedure for the calculation of components of the gyrotropic part of the hot hole differential mobility tensor is proposed. We concentrate mainly on negative transverse effective mass hot holes.     

Trace norm convergence of exponential product formula

LetH andK be lower-bounded self-adjoint operators whose form sum is denoted byH K. We show the norm inequality (e^–rH/2 e^–rK e^–rH/2)^1/r forr > 0 and any symmetric norm . WhenH +K is essentially self-adjoint and e^–K is of trace class, we prove that (e^–rH/2e^–rK e^–rH/2)^1/r converges asr 0 to e^–(H+K) in the trace norm.     

On log-Sobolev inequalities for infinite lattice systems

For a system on an infinite lattice, we show that a Gibbs measure for a smooth local specification ={E } satisfying the Dobrushin uniqueness theorem also satisfies log-Sobolev inequality, provided it is satisfied for one-dimensional measures E _l .     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

Three-photon absorption and its limitation of third-order nonlinear optical effects in rutile

Three-photon absorption and three-photon-induced excited-state absorption of rutile are studied by transmission measurements using picosecond pulses of a mode-locked Nd: glass laser. The nonlinear absorption limits efficient stimulated Raman scattering. It reduces the efficiency of two-photon absorption of a picosecond probe continuum. Three-photon absorption coefficients, excited-state absorption cross sections, a Raman gain factor, and two-photon absorption cross-section spectra are determined. The arrangementsEc andE c are considered.     

Directed paths on percolation clusters

We consider a variant of the problem of directed polymers on a disordered lattice, in which the disorder is geometrical in nature. In particular, we allow a finite probability for each bond to be absent from the lattice. We show, through the use of numerical and scaling arguments on both Euclidean and hierarchical lattices, that the model has two distinct scaling behaviors, depending upon whether the concentration of bonds on the lattice is at or above the directed percolation threshold. We are particularly interested in the exponents and, defined by ft and xt , describing the free-energy and transverse fluctuations, respectively. Above the percolation threshold, the scaling behavior is governed by the standard random energy exponents (=1/3 and =2/3 in 1+1 dimensions). At the percolation threshold, we predict (and verify numerically in 1+1 dimensions) the exponents=1/2 and =v/v, where v and v are the directed percolation exponents. In addition, we predict the absence of a free phase in any dimension at the percolation threshold.     

Some properties of a collision term of a kinetic equation in a magnetic field

The collision term of a Fokker-Planck type kinetic equation is derived for the case of a two component magnetized plasma. It is shown that the collision processes are fully described by one symmetric two-dimensional dyadicQ. The collision term is modified for the case in which the distribution function of the field particles is Maxwellian.Conditions under which the magnetic Rosenbluth potentials can be introduced are studied. It is shown, in case that the distribution function of the field particles is Maxwellian, that the coefficients of friction and diffusion are expressible in terms of two scalar potentials only if _a = 0 or if the components D and D of the difusion coefficient are constant with respect to _a , for arbitrary _b of the field particles.     

Multiatom interactions,order and stability in binary transition metal alloys

Interface delocalization or depinning transitions such as wetting or surface induced disorder are considered. At these transitions, the correlation length for transverse correlations parallel to the surface diverges. These correlations are studied in the framework of Landau theory. It is shown the t^–1/2 at all types of transitions for systems with short-range forces wheret measures the distance from bulk coexistence.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.