Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $\sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability

Locally covariant quantum field theory and the spin–statistics connection

The framework of locally covariant quantum field theory (QFT), an axiomatic approach to QFT in curved spacetime (CST), is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new approach is given, which allows for a more operational description of theories with spin and for the derivation of a more general version of the spin–statistics connection in CSTs than previously available. This part of the text is based on [C. J. Fewster, arXiv:1503.05797.] and a forthcoming publication; the emphasis here is on the fundamental ideas and motivation

X-ray investigation of lateral hetero-structures of inversion domains in LiNbO3, KTiOPO4 and KTiOAsO4

In this paper periodically domain-inverted (PDI) ferroelectric crystals are studied using high-resolution X-ray diffraction. Rocking curves and reciprocal-space maps of the principal symmetric Bragg reflections in LiNbO3 (LN) (Λ = 5μm), KTiOPO4 (KTP) (Λ = 9μm) and KTiOAsO4 (KTA) (Λ = 39μm) are presented. For all the samples strong satellite reflections were observed as a consequence of the PDI structure. Analysis of the satellites showed that they were caused by a combination of coherent and incoherent scattering between the adjacent domains. Whilst the satellites contained phase information regarding the structure of the domain wall, this information could not be rigorously extracted without a priori knowledge of the twinning mechanism. Analysis of the profiles reveals strain distributions of Δd/d = 1.6 × 10-4 and 2.0 × 10-4 perpendicular to domain walls in KTP and LN samples, respectively, and lateral correlation lengths of 63μm (KTP), 194μm (KTA) and 10μm (LN). The decay of crystal truncation rods in LN and KTP was found to support the occurrence of surface corrugations

Self sustained traversable wormholes and the equation of state

We compute the graviton one loop contribution to a classical energy in a \textit{traversable} wormhole background. The form of the shape function considered is obtained by the equation of state $p=\omega\rho$. We investigate the size of the wormhole as a function of the parameter $\omega$. The investigation is evaluated by means of a variational approach with Gaussian trial wave functionals. A zeta function regularization is involved to handle with divergences. A renormalization procedure is introduced and the finite one loop energy is considered as a \textit{self-consistent} source for the traversable wormhole.The case of the phantom region is briefly discussed.Comment: Uses RevTeX 4. 21 pages. Submitted to Classical and Quantum Gravity. Extended version of the talk given at ERE2006 (Palma de Mallorca, September 4-8, 2006) and of the talk given at MG11-GT5, Berlin, 23-29 July, 200

High resolution x-ray characterization of periodically domain-inverted nonlinear optical crystals

A high-resolution triple-axis diffractometer has been used for the structural characterization of periodically domain-inverted nonlinear optical crystals of KTiOPO4 and LNbO3. Striations have been revealed in high strain-sensitivity multiple-crystal topographs of the domain-inverted regions of both these samples and these are dominated by orientation contrast. The combination of high-resolution reciprocal-space mapping and topography has shown that the extended diffraction streak in the q[210] direction for domain-inverted LiNbO3 originates from the "minutely misoriented structure" which is related to the original configuration of dislocations. The reason for the generation of the structural imperfections via the domain-inversion processing is interpreted in terms of the converse piezoelectric effect

Thermal States in Conformal QFT. II

We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on the real line. In the first part we have proved the uniqueness of KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets A in B and A is the fixed point of B w.r.t. a compact gauge group, then any locally normal, primary KMS state on A extends to a locally normal, primary state on B, KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his 90th birthday. The final version is available under Open Access. This paper contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a proof of the same theorem in the book by Bratteli-Robinson). v3: a reference correcte

Local realizations of contact interactions in two- and three-body problems

Mathematically rigorous theory of the two-body contact interaction in three dimension is reviewed. Local potential realizations of this proper contact interaction are given in terms of Poschl-Teller, exponential and square-well potentials. Three body calculation is carried out for the halo nucleus 11Li using adequately represented contact interaction.Comment: submitted to Phys. Rev.

Classical and semi-classical energy conditions

The standard energy conditions of classical general relativity are (mostly) linear in the stress-energy tensor, and have clear physical interpretations in terms of geodesic focussing, but suffer the significant drawback that they are often violated by semi-classical quantum effects. In contrast, it is possible to develop non-standard energy conditions that are intrinsically non-linear in the stress-energy tensor, and which exhibit much better well-controlled behaviour when semi-classical quantum effects are introduced, at the cost of a less direct applicability to geodesic focussing. In this article we will first review the standard energy conditions and their various limitations. (Including the connection to the Hawking--Ellis type I, II, III, and IV classification of stress-energy tensors). We shall then turn to the averaged, nonlinear, and semi-classical energy conditions, and see how much can be done once semi-classical quantum effects are included.Comment: V1: 25 pages. Draft chapter, on which the related chapter of the book "Wormholes, Warp Drives and Energy Conditions" (to be published by Springer), will be based. V2: typos fixed. V3: small typo fixe