Weak density of states

Let L be a quantum logic, here an orthoalgebra, and let be a convex set of states on L. Then generates a base-normed space, and the dual-order unit-normed space contains a canonically constructed homomorphic copy of L, denoted by e(L). A convex set of states on L is said to be ample provided that every state on L is obtained by restricting an element of the base of the bi-dual order unit-normed space to e(L). For a quantum logic L we show that a convex set of states is ample if and only if is weakly dense in the convex set of all states on L. The notion of ampleness is then discussed in the context of Gleason-type theorems for W^* algebras and JBW algebras and also in the context of classical logics.Dedicated to Prof. Peter Mittelstaedt on the occasion of his sixtieth birthday. Research supported by the Swiss National Science Foundation.     

High-temperature series expansion for the relaxation times of the two dimensional Ising model

We derive the high temperature series expansions for the two relaxation times of the single spin-flip kinetic Ising model on the square lattice. The series for the linear relaxation time _l is obtained with 20 non-trivial terms, and the analysis yields 2.183±0.005 as the value of the critical exponent _l , which is equal to the dynamical critical exponentz in the two-dimensional case. For the non-linear relaxation time we obtain 15 non-trivial terms, and the analysis leads to the results _nl = 2.08 ± 0.07. The scaling relation _l – _nl = ( being the exponent of the order parameter) seems to be fulfilled, though the error bars of _nl are still quite substantial. In addition, we obtain the series expansion of the linear relaxation time on the honeycomb lattice with 22 non-trivial terms. The result for the critical exponent is close to the value obtained on the square lattice, which is expected from universality.     

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.     

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.     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

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     

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.     

Symmetry transformations in Batalin-Vilkovisky formalism

Let us suppose that the functionalS on an odd symplectic manifold satisfies the quantum master equation e ^s = 0. We prove that in some sense every quantum observable (i.e. every functionH obeying _p (He ^s) = 0) determines a symmetry of the theory with the action functionalS. Research supported in part by NSF grant No. DMS-9201366.     

On the decay width of multiply measured unstable state

In the case of multiple measurements we have found that there is nonzero decay width () (even for bound states) and that, for relatively long time intervals separating successive measurements, () tends like ^–k (k 1 according to the investigated model) to the asymptotic value _o for unstable states and to zero for bound states. We have shown that the detector efficiencyZ 1 is responsible for this effect and that the evolution operator acting in the considered subspace of states should be renormalized to avoid this effect. As an illustration we have considered electromagnetic levels in the Coulomb field as an example of unstable states.     

Ferromagnetic resonance in media with an inhomogeneous saturation magnetization

The method of transition probabilities is used to calculate the line width of ferromagnetic resonance in a medium with an inhomogeneous saturation magnetization. It is shown that in addition to linear (with respect to the Fourier components of the function describing inhomogeneities) terms, the perturbation Hamiltonian must include also quadratic terms. The frequency dependence of the contribution of the porosity to H is fundamentally different from the frequency dependence of the magnetic anisotropy contribution. This anisotropy contribution H_a() decreases on increase in the frequency and has a maximum at = (2/3)_M, whereas the porosity contribution H_p increases on increase in the frequency and vanishes at = (2/3)_M.deceasedTranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp.48–52, December, 1980.     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

Energy-Momentum Properties and the Spin of Short-Lived Particles

The space–time translation property of a stable particle is characterized by a time-like Lorentz vector (E, _k ). We show in this contribution that unstable particles are, in addition, characterized by a space-like Lorentz 4-vector of uncertainties, or spreads, ( E, k). This is true for unstable states created in formation-, in production-, and in decay-experiments. The space-like nature of the spread vector causes a nonzero momentum spread to be present in all Lorentz frames so that there is no Lorentz frame in which the unstable particle is entirely at rest. With the space-like spreadvector ( E, k) in addition to the time-like (E, _k ), also the rotation property of an unstable particle is affected, and unstable states have an uncertainty in their spin. This means neighboring spin states are occupied in addition to the original spin. Experiments are discussed that show a principal limitation of the accuracy of spin measurement from finite lifetimes. Wave functions for unstable particles are discussed, and we show in the example of a short-lived spin-0 state that the appearance of a spin neighbor in the amplitude is proportional to the inverse lifetime.     

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.     

The shape resonance

For a class of Schrödinger operatorsH:=–(²/2m)+V onL ²( ⁿ ), with potentials having minima embedded in the continuum of the spectrum and non-trapping tails, we show the existence of shape resonances exponentially close to the real axis as 0. The resonant energies are given by a convergent perturbation expansion in powers of a parameter exhibiting the expected exponentially small behaviour for tunneling.     

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].     

The sl2 Loop Algebra Symmetry of the Six-Vertex Model at Roots of Unity

We demonstrate that the six vertex model (XXZ spin chain) with =(q+q^-1)/2 and q^2N=1 has an invariance under the loop algebra of sl₂ which produces a special set of degenerate eigenvalues. For =0 we compute the multiplicity of the degeneracies using Jordan–Wigner techniques.     

Neutron scattering from spatio-temporal patterns in thermal convection

We have investigated the thermal convection of a nematic liquid crystal in a two-dimensional, vertical slab container with long edgesa (horizontal) andb (vertical). Using a real-time and real-space neutron scattering technique, we find that the frequencies of oscillatory convection is given by a formula whose geometrical part is ² (h ² +k ²/b ²). For the Fourier indices (h,k) we find the selection rule(h+k)=2n withn=1,2 ... The variation of ² with the vertical temperature difference T, as T approaches the convection threshold T _c , is found to be surprisingly well fitted by the two-dimensional, critical Ising index .     

Metallic Nanocrystallites-Coated Piezoelectric Quartz for Applications in Gas Sensing

This article reports the gas-sensing capability of nanocrystalline (NC) transition metal-coated piezoelectric quartz crystal (PQC). NC transition metal particles of Pd and Ag with particles size of 10–15 nm, while Pt and Au are 20–25 nm are used. The NC particles deposited on the quartz substrate adsorbs gaseous pollutants, thereby increasing the weight of the quartz substrate and decreasing its vibration frequency. We have found that transition metals, Pd, Pt, Au, and Ag in particular, show good sensitivity for NH₃-detection; the maximum frequency change occurs at 150°C for Pd and Pt and at 100°C for Au and Ag. The NC Pd- and NC Pt-coated PQC also show good sensitivity for CO₂-detection at 150°C. Likewise, the NC Au-coated PQC shows very good sensitivity for NO₂-detection but at a higher temperature (180^°C). The frequency change as a function of the pollutant gas concentration ( f-curve) follows the Langmuir adsorption isotherm (unimolecular adsorption) except in the case of NC Pd-coated PQC under NH₃ and NC Au-coated PQC under NO₂. The f-curve for the NC Pd-coated PQC is convex with respect to the NH₃ concentration axis. The f-curve for the NC Au-coated PQC is convex in the low NO₂ concentration region, and concave in the high NO₂ concentration region. Both curves indicate multi-molecular adsorption, Type III and Type V adsorption, respectively. Therefore, the good sensitivity and stability of these gas sensors can be attributed to physical adsorption of the pollutant gases as a result of van der Waals attraction.     

Relationship between field shift and phase constant change in two-dimensional three-layered dielectric or hollow waveguides due to uniform bends

It is shown theoretically that the field shift x and phase constant change in two-dimensional three-layered dielectric or hollow waveguides bent uniformly with large bending radiusR are related by x = 2R/ ₀, where ₀ is the axial phase constant. The relationship predicts that the field distributions of the TE₀ or TM₀ mode shift toward the outward direction of bending, whereas those of other TE _n or TM _n (n=1,2,...) modes shift inward in a hollow waveguide. Characteristic features in dielectric waveguides are also described.     

Group actions on C*-algebras, 3-cocycles and quantum field theory

We study group extensions , where acts on a C^*-algebraA. Given a twisted covariant representation ,V of the pairA, we construct 3-cocycles on with values in the centre of the group generated byV(). These 3-cocycles are obstructions to the existence of an extension of byV() which acts onA compatibly with . The main theorems of the paper introduce a subsidiary invariant which classifies actions of onV() and in terms of which a necessary and sufficient condition for the the cohomology class of the 3-cocycle to be non-trivial may be formulated. Examples are provided which show how non-trivial 3-cocycles may be realised. The framework we choose to exhibit these essentially mathematical results is influenced by anomalous gauge field theories. We show how to interpret our results in that setting in two ways, one motivated by an algebraic approach to constrained dynamics and the other by the descent equation approach to constructing cocycles on gauge groups. In order to make comparisons with the usual approach to cohomology in gauge theory we conclude with a Lie algebra version of the invariant and the 3-cocycle.