Microstructure and composition analysis of group III nitrides by X-ray scattering

The importance of Group III-nitride structures for both light-emitting devices and high-power field effect transistors is well known (J.W. Orton, C.T. Foxon, Rep. Prog. Phys. 61 (1998) 1). In both cases, different alloy composition and doping levels or type are utilised and the device performance also depends critically on the interface quality and defect density. We have used high resolution X-ray scattering to measure the state of strain in the individual layers on an absolute scale to derive the alloy composition, i.e. we have avoided the conventional method of using the substrate as an internal reference since it could be strained. The composition and individual layer thickness are derived through simulation of the profile with this additional strain information and the best-fit profile is obtained with an automatic procedure. These structures are laterally inhomogeneous arising from defects breaking up the structure into narrow vertical columns of nearly perfect material and this produces significant broadening of the diffraction pattern. This broadening in the diffraction pattern has been modelled using an extended dynamical scattering model (P.F. Fewster, X-Ray Scattering from Semiconductors, Imperial College Press, World Scientific, Singapore, 2000) to yield the size distribution of perfect crystal regions. The measurement of the rotation about an axis defined by the growth direction of the GaN with respect to the sapphire is determined and is found to be small. However, a poor quality sample indicates that a large range of rotations is possible in these structures.     

Quantum Inequalities in Quantum Mechanics

We study a phenomenon occurring in various areas of quantum physics, in which an observable density (such as an energy density) which is classically pointwise non-negative may assume arbitrarily negative expectation values after quantization, even though the spatially integrated density remains non-negative. Two prominent examples which have previously been studied are the energy density (in quantum field theory) and the probability flux of rightwards-moving particles (in quantum mechanics). However, in the quantum field context, it has been shown that the magnitude and space-time extension of negative energy densities are not arbitrary, but restricted by relations which have come to be known as quantum inequalities. In the present work, we explore the extent to which such quantum inequalities hold for typical quantum mechanical systems. We derive quantum inequalities of two types. The first are kinematical quantum inequalities where spatially averaged densities are shown to be bounded below. Specifically, we obtain such kinematical quantum inequalities for the current density in one spatial dimension (imposing constraints on the backflow phenomenon) and for the densities arising in Weyl–Wigner quantization. The latter quantum inequalities are direct consequences of sharp Gårding inequalities. The second type are dynamical quantum inequalities where one obtains bounds from below on temporally averaged densities. We derive such quantum inequalities in the case of the energy density in general quantum mechanical systems having suitable decay properties on the negative spectral axis of the total energy.Furthermore, we obtain explicit numerical values for the quantum inequalities on the one-dimensional current density, using various spatial averaging weight functions. We also improve the numerical value of the related backflow constant previously investigated by Bracken and Melloy. In many cases our numerical results are controlled by rigorous error estimates.submitted 27/01/04, accepted 05/05/04     

Implantation of ytterbium ions into group II-VI compounds

50 keV ytterbium ions have been implanted into ZnS, CdS, ZnSe, CdTe, CdSe and ZnTe and, after subsequent annealing treatments of varying degree, the cathodoluminescence emission spectra produced by 10 keV or 100 keV electron excitation have been studied.     

Probability distributions for the stress tensor in conformal field theories

The vacuum state—or any other state of finite energy—is not an eigenstate of any smeared (averaged) local quantum field. The outcomes (spectral values) of repeated measurements of that averaged local quantum field are therefore distributed according to a non-trivial probability distribution. In this paper, we study probability distributions for the smeared stress tensor in two-dimensional conformal quantum field theory. We first provide a new general method for this task based on the famous conformal welding problem in complex analysis. Secondly, we extend the known moment generating function method of Fewster, Ford and Roman. Our analysis provides new explicit probability distributions for the smeared stress tensor in the vacuum for various infinite classes of smearing functions. All of these turn out to be given in the end by a shifted Gamma distribution, pointing, perhaps, at a distinguished role of this distribution in the problem at hand.

     

Dynamical Locality and Covariance: What Makes a Physical Theory the Same in all Spacetimes?

The question of what it means for a theory to describe the same physics on all spacetimes (SPASs) is discussed. As there may be many answers to this question, we isolate a necessary condition, the SPASs property, that should be satisfied by any reasonable notion of SPASs. This requires that if two theories conform to a common notion of SPASs, with one a subtheory of the other, and are isomorphic in some particular spacetime, then they should be isomorphic in all globally hyperbolic spacetimes (of given dimension). The SPASs property is formulated in a functorial setting broad enough to describe general physical theories describing processes in spacetime, subject to very minimal assumptions. By explicit constructions, the full class of locally covariant theories is shown not to satisfy the SPASs property, establishing that there is no notion of SPASs encompassing all such theories. It is also shown that all locally covariant theories obeying the time-slice property possess two local substructures, one kinematical (obtained directly from the functorial structure) and the other dynamical (obtained from a natural form of dynamics, termed relative Cauchy evolution). The covariance properties of relative Cauchy evolution and the kinematic and dynamical substructures are analyzed in detail. Calling local covariant theories dynamically local if their kinematical and dynamical local substructures coincide, it is shown that the class of dynamically local theories fulfills the SPASs property. As an application in quantum field theory, we give a model independent proof of the impossibility of making a covariant choice of preferred state in all spacetimes, for theories obeying dynamical locality together with typical assumptions.     

Dynamical Locality of the Free Scalar Field

Dynamical locality is a condition on a locally covariant physical theory, asserting that kinematic and dynamical notions of local physics agree. This condition was introduced in arXiv:1106.4785, where it was shown to be closely related to the question of what it means for a theory to describe the same physics on different spacetimes. In this paper, we consider in detail the example of the free minimally coupled Klein–Gordon field, both as a classical and quantum theory (using both the Weyl algebra and a smeared field approach). It is shown that the massive theory obeys dynamical locality, both classically and in quantum field theory, in all spacetime dimensions n ≥ 2 and allowing for spacetimes with finitely many connected components. In contrast, the massless theory is shown to violate dynamical locality in any spacetime dimension, in both classical and quantum theory, owing to a rigid gauge symmetry. Taking this into account (equivalently, working with the massless current) dynamical locality is restored in all dimensions n ≥ 2 on connected spacetimes, and in all dimensions n ≥ 3 if disconnected spacetimes are permitted. The results on the quantized theories are obtained using general results giving conditions under which dynamically local classical symplectic theories have dynamically local quantizations.     

Stability of Quantum Systems at Three Scales: Passivity, Quantum Weak Energy Inequalities and the Microlocal Spectrum Condition

Quantum weak energy inequalities have recently been extensively discussed as a condition on the dynamical stability of quantum field states, particularly on curved spacetimes. We formulate the notion of a quantum weak energy inequality for general dynamical systems on static background spacetimes and establish a connection between quantum weak energy inequalities and thermodynamics. Namely, for such a dynamical system, we show that the existence of a class of states satisfying a quantum weak inequality implies that passive states (e.g., mixtures of ground- and thermal equilibrium states) exist for the time-evolution of the system and, therefore, that the second law of thermodynamics holds. As a model system, we consider the free scalar quantum field on a static spacetime. Although the Weyl algebra does not satisfy our general assumptions, our abstract results do apply to a related algebra which we construct, following a general method which we carefully describe, in Hilbert-space representations induced by quasifree Hadamard states. We discuss the problem of reconstructing states on the Weyl algebra from states on the new algebra and give conditions under which this may be accomplished. Previous results for linear quantum fields show that, on one hand, quantum weak energy inequalities follow from the Hadamard condition (or microlocal spectrum condition) imposed on the states, and on the other hand, that the existence of passive states implies that there is a class of states fulfilling the microlocal spectrum condition. Thus, the results of this paper indicate that these three conditions of dynamical stability are essentially equivalent. This observation is significant because the three conditions become effective at different length scales: The microlocal spectrum condition constrains the short-distance behaviour of quantum states (microscopic stability), quantum weak energy inequalities impose conditions at finite distance (mesoscopic stability), and the existence of passive states is a statement on the global thermodynamic stability of the system (macroscopic stability).Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany. verch@mis.mpg.de