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     

Uncertainties and an interpretation of nonrelativistic quantum theory

We propose an interpretation of nonrelativistic quantum theory which can be considered a generalized Copenhagen interpretation. The uncertainties (i.e., q and p) in Heisenberg's uncertainty relation q · p/2 can be characterized as (average) errors in an approximate simultaneous measurement if the interpretation proposed here is accepted in nonrelativistic quantum mechanics. Under this interpretation, the (discrete) trajectory of a particle (like Wilson chamber) is significant enough. We propose to analyze this trajectory numerically.     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Dynamical property of YFeMnO4

In order to interpret abrupt changes of distributions of orientations andmagnitudes of hyperfine fields in Mössbauer measurements of⁵⁷Fe in YFeMnO₄, a model is proposed. The origin is assumed to be not static but dynamic. Fluctuating fields are caused by spins in a fully frustrated spin system, namely, a Heisenberg spin system on a triangular lattice in a two-dimensional antiferromagnet. Extending the stochastic theory for the fluctuation between two states to that among many states with a Gaussian distribution, we fit the spectra with three parameters, hyperfine fieldH _hf, correlation time _c, andwidth of fluctuating field , within a limited condition of =_c=1. Obtained results represent the characteristic features of Mössbauer spectra well, in spite of a simplified model.     

Pulsed NMRON oscillatory free induction decay signals in the angular distribution of gamma radiation from plated60CoFe

Results for an inhomogeneously broadened⁶⁰CoFe NMRON sample have been obtained for gamma detected single pulse (nutation) and two pulse (free induction decay) experiments in the region of intermediate-to-lowR(=₁/). Here ₁ is the angular frequency measure of the strength of the ferromagnetically enhanced RF field at the nucleus and is the HWHM of the inhomogeneously broadened line. Comparisons of the oscillatory FID signals obtained are made with the theoretical predictions of the following paper [6].     

Symmetry properties of nonlinear barrier coefficients

This paper concerns the properties of a symmetric barrier between two reservoirs. The barrier can passK conserved quantities. The current of theith quantity is assumed to satisfy the nonlinear relationJ _i=A _ijj+B_ijkljkl where the _i's are the affinity differences across the barrier andA _ij andB _ijkl are functions of the average affinities of the reserviors. It is shown thatB _ijkl is symmetric in all indices.     

Spatio-temporal Fourier components and soft modes in thermal convection: A neutron scattering study

In a nematic liquid crystal subjected to a vertical temperature difference T in a vertical slab container, we find, using real-time and real-space neutron scattering, that the spatiotemporal pattern can be indexed on a two-dimensional lattice with selection rule (h+k)=2n. Higher index modes are sequentially activated as T increases from the convection threshold T _c . The frequency softening as TT _c and asTT ₀, the super-cooling limit of the nematic, is discussed.     

Experimental Test of a Time-Temperature Formulation of the Uncertainty Principle Via Nanoparticle Fluorescence

No Heading The uncertainty in the measured fluorescence decay lifetimes of 30 nm particles of YAG:Cc was used to evaluate the predictions of a novel form of the Heisenberg uncertainty principle suggested by de Sabbata and Sivaram, T t h/k. The worst-case uncertainty in temperature of 4.5 °K (as derived from the relationship between temperature and lifetime) and the measured uncertainty in decay lifetime, 0.45 ns, yielded an internal estimate of T t = 2.0 × 10^–9 °K s, which is 263 times larger than /k = 7.6 × 10^–12 °K s. An external estimate of T t = 4.5 × 10¹¹ °K s (which is = 6 times /k) is derived from the independently measured uncertainty in the temperature of the sample and the experimentally determined uncertainty in lifetime. These results could be low by a factor of 5.6 if signal averaging must be taken into account. If valid, the findings are consistent with the predictions of this version of the uncertainty principle and they imply the existence of a type of thermal quantum limit.     

Mates toE=mc 2 and to the Heisenberg uncertainty relations

E=mc ² is found to be a special case ofE= ^±1cⁿ, where is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,t time dilation, andl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(l)/1=(t)/t. Then(E)/E=5 (t)/2t=±()/. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws for particles are proposed.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Jauch-Piron system of imprimitivities for phonons. I. Localizability in discrete space

This paper is devoted to a discussion of the notion of localizability for phonons, i.e., quasiparticles arising from the harmonic vibrations of a system ofn atoms bound to one another by elastic forces. The natural tools for the analysis of localizability are the projection operatorsÊ() acting on the Hilbert space of one-phonon states, where is an arbitrary subset of the set that consists ofn vectors specifying the equilibrium positions ofn atoms. The expectation value ofÊ() is the probability that the phonon belongs to the atoms whose equilibrium positions are characterized by the elements of . For a strongly localizable phonon all of the projection operatorsÊ() commute with one another, whereas in the case of a weakly localizable phonon the operatorsÊ(₁) andÊ(₂) do not commute when ₁ and ₂ overlap. With the aid of the Jauch-Piron quantum theory of localization in space, the present paper describes the method of obtainingÊ() and also shows that if in the system ofn atoms there exist normal modes of zero frequency, then the phonon is only weakly localizable. Given the explicit expression forÊ(), one can define the number-of-phonons operator as well as the quasiparticle analogue (given in a companion paper) of the Wigner distribution function.     

Relationship between T c and electronegativity differences in compound superconductors

The electronegativity differences, N, between the anions and the cations in suggested resonating elements of some representative high-temperature superconductors with T _c - 10 K are evaluated adopting Pauling's scale. The relationship between N and T _c was found to separate all the examined high-T _csuperconductors onto two curves: One for the cuprate superconductors having two-dimensional layered structures was a straight line, T _c=29.8+4.1N; the other correlation curve representing the remaining compound superconductors including the doped 113 perovskite and the perovskite-related 214 structures was at lower T _c values but also suggested that increasing electronegativity differences was related to increasing T _c.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Behavior of the electrical resistivity at phase transitions in binary alloys

The excess resistivity of binary alloys is calculated in the Born approximation for the scattering of quasifree electrons from the atomic disorder. can be represented as the convolution of the structure functionS(q) and the fourier transform of the effective potential. The critical anomaly of is derived from scaling expressions forS(q), both for alloys which undergo unmixing and for order-disorder transitions. The variation of with concentration and temperature in the vicinity of a critical point is obtained. The time-dependence of the resistivity of alloys after a sudden quench into the two-phase region is also calculated, using computer simulation data forS(q,t), and a maximum of is found for zones with linear dimension of 8–12 lattice spacings. All these results are in fair agreement with the available experiments. As a further possible application, we obtain the critical exponent for the nonlinear relaxation of the resistivity of an alloy close to the order-disorder transition.     

Spectral behavior of quasi periodic potentials

Spectral properties of Schrödinger operators of the typeH =–+V, where is the Laplacian,V a quasiperiodic potential and a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as is increased.Research supported in part by grant NSF MCS 7900813     

Spannungsverläufe Nach Wechseln der Verformungsgeschwindigkeit an Metalleinkristallen

The theoretical relations between _v and measured stress changes are discussed and compared with experimental results. For instantaneous change in the strain rate, the first deviation of the stress increase from the linearity ( _C ) can be used as a measure of _v for small deformation only. The comparison of _C with the extrapolated value _A enables to reveal the presence of recovery. The comparison of stress changes measured after a given rate change at the same strain on unrecovering (low temperatures) and recovering (higher temperatures) samples enables to differentiate between various types of recovery.     

The influence of compression on the absorption of AgBr single crystals

The influence of compression on the edge of self absorption of AgBr single crystals was studied. The measurements were performed at a temperature of –180°C. The shift of the edge of self absorption was studied both in the field of elastic and plastic deformations. The shift of the absorption edge towards the UV end of the spectrum was determined in the field of elastic deformations and towards the i.r. end in the field of plastic deformations. After the ending of the deformation and after unloading the crystal the return of the absorption edge towards the original position was observed.

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AgBr

AgBr. –180°C. , . , — . .

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The author thanks Prof. Dr. L. Zachoval and K. K. Vacek C. Sc. for their interest in this work and for many comments given during the work.     

Spannungsverläufe Nach Wechseln der Verformungsgeschwindigkeit an Metalleinkristallen II. Auswertung der Spannungsänderungen Nach Wechseln der Abgleitgeschwindigkeit

The general relation between the change in the effective stress on dislocation _v and the extrapolated value _A (linear extrapolation from the region of steady flow over the transient regiona _u) is given under the assumption that the hardening is approximately constant in the strain interval of the magnitude ofa _u ata=const. The effect of recovery on the stress variations after strain rate change is also evaluated. Finally, the equations describing the rate of stress changes in the transient regiona _u are deduced.

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Ke Karlovu 5, Praha 2, Czechoslovakia.     

Unbounded derivations and invariant states

Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(^1/2) equipped with the inner product(|)_#=(|)+(^1/2|^1/2), , D(^1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld     

Matrix field theory for disordered local pairing superconductors with two glass order parameters and spin-flip pairbreaking processes

We derive the exact matrix field theory for a replicated grassmannian representation of a local pairing superconducting disorder ensemble including three superconducting order parameters and the spin-flip pairbreaking mechanism. Disorder is assumed to be gaussian distributed. We find by exactly solving the saddle-point equation the criterion for a vanishing gap ^–1 + ^–1 , where denotes the averaged superconducting order parameter, ^–1 the spin-flip scattering rate, and ^–1 the scattering rate corresponding to correlations of Re(–). Taken at =0, our field theory, which is exact in all orders of ^–1 , contains new terms in addition to those of theO( ^–1 ) model derived by Efetov et al. Our formulation transfers correctly to all orders the invariances of the action into symmetries of the matrix field theory. The saddle point approximation is outlined and it is shown how singular corrections to the saddle point density of states arise atE _F in a gapless superconductor. Finally singular corrections in the two particle propagator, the density correlation function and the conductivity are calculated for =0 in one loop order. It turns out that these corrections can be entirely expressed by those of the single particle density of states.