Small perturbations ofC*-dynamical systems

It is shown that if is the generator of a strongly continuous oneparameter group of *-automorphisms of aC*-algebraA and is an unbounded *-derivation ofA with the same domain as , then + is also a generator for all sufficiently small real numbers .     

Surface tension,step free energy,and facets in the equilibrium crystal

Some aspects of the microscopic theory of interfaces in classical lattice systems are developed. The problem of the appearance of facets in the (Wulff) equilibrium crystal shape is discussed, together with its relation to the discontinuities of the derivatives of the surface tension (n) (with respect to the components of the surface normaln) and the role of the step free energy ^step(m) (associated with a step orthogonal tom on a rigid interface). Among the results are, in the case of the Ising model at low enough temperatures, the existence of ^step(m) in the thermodynamic limit, the expression of this quantity by means of a convergent cluster expansion, and the fact that 2^step(m) is equal to the value of the jump of the derivative / (when varies) at the point =0 [withn=(m ₁ sin ,m ₂ sin , cos )]. Finally, using this fact, it is shown that the facet shape is determined by the function ^step(m).     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Structural Transformations in a Bi2O3 Crystal and in Bi2O3‐Based Solid Solutions in the Temperature Interval 25–750°C

The Raman scattering spectra of isostructural Bi₂O₃ and Bi_1.8Tm_0.2O₃ in the course of heating have been investigated. It is shown that the sequences of structural changes with increase in temperature differ: and ^* , respectively. In the hightemperature region, the structure takes the form of a disordered cube irrespective of the previous history of specimens.     

Second-harmonic generation at periodic second-order susceptibility gratings with self-phase and cross-phase modulation

Quasi-phase-matched second-harmonic generation at periodic quadratic susceptibility gratings with self-phase and cross-phase modulation owing to Kerr nonlinearities is investigated. A model of interaction of monochromatic plane travelling waves is considered. The solution assumes a nondepleted pump and results for a numerical computation of second-harmonic conversion efficiency for a highly efficient process are presented. It is shown that for high spatial-frequency gratings the efficiency of second-harmonic generation depends on the reduced detuning and the Kerr-nonlinearity coefficient only. In some cases, if the signs of and are opposite, the Kerr nonlinearity can enhance the second-harmonic conversion efficiency due to the compensation of the phase mismatch attained in the below-half-conversion stage by the reversed phase mismatch in the above-half-conversion stage of the process. The computed maximum conversion efficiencies for various values of and are plotted in a contour map on the - plane.     

A possible test of quantum electrodynamics by means of polarization effects in electron-nucleon scattering

The differential cross-section is given for the electromagnetic scattering of polarized relativistic electrons on polarized nucleons. The finite size of each particle is taken into account by means of two form-factors. The effect of the possible non-punctiform structure of the electron on the polarization effects in scattering is discussed. It is shown that the internal structure of the anomalous magnetic moment of the electron would show itself in the cross-section by terms depending on the transversal polarization of the incident electrons.

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Summary of results of a diploma-thesis for the degree of graduate physicist.

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In conclusion the author wishes to express his sincere gratitude to prof. V. Votruba and J. Kvasnica for suggesting this problem, for helpful discussions and valuable advice.     

Inhomogeneity correlations in dirty superconductors,I

It is shown that fluctuations around the impurity averaged superconducting order parameter can be large due to interplay of disorder and (decoupled) interaction. Correlations () ² exceeding a critical value render superconductors with nonmagnetic impurities gapless. In addition to a mixed phase, 0 andM 0, a superconducting glass phase with =0 andM 0 is derived. In general, correlations () ² emerge from nonperturbative, saddle point solutions of a replicated matrix field theory. Replica symmetry, soft modes, and other order parameters are discussed.This work was supported by the Sonderforschungsbereich 123 of the Deutsche Forschungsgemeinschaft     

Change in primary extinction during decomposition of supersaturated solid solution II. Al-Cu 4% alloy-formation of G.P. zones

The change in integrated intensity of the (200) reflections of a solid solution during the formation of G.P. zones was measured and compared with the change in the character of the diffuse streaks corresponding to them. It was found that the. formation of G.P. zones does not lead to a decrease in primary extinction despite the great changes in the distribution of the copper atoms. It was shown that the formation of a precipitate accompanied by the formation of crystallographically incoherent boundaries greatly decreases the primary extinction.

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. II. 1-u 4%: [. . ]

(200) . . , . , . . , . , , , .

     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

Energy criterion in the interpretation of dielectric relaxation

The universal fractional-power-law frequency dependence of relaxation seen in most solid dielectrics has the unique property that the ratio of macroscopic energy lost per radian to energy stored is independent of frequency. In a recent publication we have shown that this energy criterion is satisfied if the energy loss in every microscopic dipolar reversal is independent of the rate of reversals. The present paper derives for the first time a quantitative relationship between the macroscopic energy loss per radian and the microscopic loss , thus providing a justification of the energy criterion approach. The relationship between this new frequency-domain interpretation of relaxation processes and the currently accepted theories of universal behaviour is discussed.     

Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

A lower bound for the memory capacity in the Potts-Hopfield model

We consider Potts-Hopfield networks of sizeN. We prove the result: _c >0 such that for all 0<< _c we can find, >0 in such a way that, whenN, we can store N patterns, all of them being sorrounded by -energy barriers at distance.     

Continuous quantum measurements and the action uncertainty principle

The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral in finite limits). With the help of the measurement amplitude, maximum deviation of measurement outputs from the classical one can be easily determined. The aim of the present paper is to express this variance in a simpler and transparent form of a specific uncertainty principle (called the action uncertainty principle, AUP). The most simple (but weak) form of AUP is S, whereS is the action functional. It can be applied for simple derivation of the Bohr-Rosenfeld inequality for measurability of gravitational field. A stronger (and having wider application) form of AUP (for ideal measurements performed in the quantum regime) is | ^t (S[q]/q(t))q(t)dt|, where the paths [q] and [q] stand correspondingly for the measurement output and for the measurement error. It can also be presented in symbolic form as (Equation) (Path) . This means that deviation of the observed (measured) motion from that obeying the classical equation of motion is reciprocally proportional to the uncertainty in a path (the latter uncertainty resulting from the measurement error). The consequence of AUP is that improving the measurement precision beyond the threshold of the quantum regime leads to decreasing information resulting from the measurement.     

Mosaic Structure of (001)YBa2Cu3O7-δ/(10.2)Al2O3 Epitaxial Films and Millimeter Waveband Properties of Microstrip Resonators

The c-axis single-phase YBa₂Cu₃O_7- films ( = 0-0.15) on sapphire substrates prepared by the laser ablation technique and the band-pass stripline resonators for 34 GHz-range have been investigated. Increasing disorientation of mosaic block structure of YBa₂Cu₃O_7- films is related to increasing surface resistance R_s at 135 GHz-range and decreasing unloaded quality factor Q_o of linear stripline resonators. The linear dependence between the YBa₂Cu₃O_7- film mosaicity (M) and half-width B₁ of 00.13 reflecting component is determined. The reflection spreading is due to microstrains resulted mainly from the coherent adjustment of the YBa₂Cu₃O_7- film lattice to GdBa₂Cu₃O_7- sub-layer and sapphire substrate. Increasing number of the block characterized by a weak radial lattice adjustment () is demonstrated by spreading of 00.13 reflection. It is found out that depends on the Bragg angle of reflection due to inhomogenity of YBa₂Cu₃O_7- mosaic structure, which resulted from the gradual mosaicity decreasing with the depth.     

Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

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     

Electric field gradients in amorphous metals

The⁵⁷Fe-Mössbauer spectroscopy has been used in order to study the quadrupole splitting E_Q at the Fe-site and its dependence on temperature in Fe_85–XCr_XB₁₅ and Fe_80–XMo_XB₂₀ amorphous alloys. In all investigated compositions the local symmetry was lower than cubic with room temperature values of E_Q in the range of 0.4–0.5 mm/s. In all cases relatively broad distributions of E_Q and therefore of the EFG have been obtained. The EFG of the investigated compounds changes reversibly with temperature up to about 650 K according to the relation E_Q (T)=E_Q (O)·(1-BTV^3/2) as in the case of crystalline noncubic metals. Assuming that the same dependence of B on the Debye temperature as in crystalline non-cubic metals holds for amorphous alloys, values of have been obtained in good agreement with those determined from the temperature dependence of the Mössbauer f-factor.     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

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.     

Determination of parameters in equation for ferromagnetic resonance of ferrites

The paper describes a new method for determining the parameters in the equation for ferromagnetic resonance — the internal effective field, the spectroscopic splitting factor and the saturation magnetization in polycrystalline magnetically isotropic ferrites. Relations are derived for calculating these parameters by means of the values of the resonance external static fields, which are obtained by measuring on samples having different geometrical shapes and differently arranged static and microwave magnetic fields. The advantages and disadvantages of the method and remarks on the experimental method are given. The paper ends with an example of measurement.

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The determination of the saturation magnetization of ferrites by the method described here was reported on at the Seminary on Ferrites in Microwave Technique, held by the Institute of Technical Physics, Czechoslovak Academy of Sciences, and the Research Institute of Communications Engineering of A. S. Popov, on November 25, 1959.