Kikuchi ultrafast nanodiffraction in four-dimensional electron microscopy

Coherent atomic motions in materials can be revealed using time-resolved X-ray and electron Bragg diffraction. Because of the size of the beam used, typically on the micron scale, the detection of nanoscale propagating waves in extended structures hitherto has not been reported. For elastic waves of complex motions, Bragg intensities contain all polarizations and they are not straightforward to disentangle. Here, we introduce Kikuchi diffraction dynamics, using convergent-beam geometry in an ultrafast electron microscope, to selectively probe propagating transverse elastic waves with nanoscale resolution. It is shown that Kikuchi band shifts, which are sensitive only to the tilting of atomic planes, reveal the resonance oscillations, unit cell angular amplitudes, and the polarization directions. For silicon, the observed wave packet temporal envelope (resonance frequency of 33 GHz), the out-of-phase temporal behavior of Kikuchi's edges, and the magnitude of angular amplitude (0.3 mrad) and polarization [011] elucidate the nature of the motion: one that preserves the mass density (i.e., no compression or expansion) but leads to sliding of planes in the antisymmetric shear eigenmode of the elastic waveguide. As such, the method of Kikuchi diffraction dynamics, which is unique to electron imaging, can be used to characterize the atomic motions of propagating waves and their interactions with interfaces, defects, and grain boundaries at the nanoscale

Composition-induced structural transitions in mixed rare-gas clusters

The low-energy structures of mixed Ar--Xe and Kr--Xe Lennard-Jones clusters are investigated using a newly developed parallel Monte Carlo minimization algorithm with specific exchange moves between particles or trajectories. Tests on the 13- and 19- atom clusters show a significant improvement over the conventional basin-hopping method, the average search length being reduced by more than one order of magnitude. The method is applied to the more difficult case of the 38-atom cluster, for which the homogeneous clusters have a truncated octahedral shape. It is found that alloys of dissimilar elements (Ar--Xe) favor polytetrahedral geometries over octahedra due to the reduced strain penalty. Conversely, octahedra are even more stable in Kr--Xe alloys than in Kr_38 or Xe_38, and they show a core-surface phase separation behavior. These trends are indeed also observed and further analysed on the 55-atom cluster. Finally, we correlate the relative stability of cubic structures in these clusters to the glassforming character of the bulk mixtures.Comment: 14 pages, 8 figures, 5 tables PRB vol 70, in pres

Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved spacetime are the canonical commutation relations, imposed on the field operators evaluated at a global Cauchy surface. In the algebraic formulation of linear quantum field theory, the canonical commutation relations are restated in terms of a well-defined symplectic structure on the space of smooth solutions, and the local field algebra is constructed as the Weyl algebra associated to this symplectic vector space. When spacetime is not globally hyperbolic, e.g. when it contains naked singularities or closed timelike curves, a global Cauchy surface does not exist, and there is no obvious way to formulate the canonical commutation relations, hence no obvious way to construct the field algebra. In a paper submitted elsewhere, we report on a generalization of the algebraic framework for quantum field theory to arbitrary topological spaces which do not necessarily have a spacetime metric defined on them at the outset. Taking this generalization as a starting point, in this paper we give a prescription for constructing the field algebra of a (massless or massive) Klein-Gordon field on an arbitrary background spacetime. When spacetime is globally hyperbolic, the theory defined by our construction coincides with the ordinary Klein-Gordon field theory on aComment: 21 pages, UCSBTH-92-4

Entangled Nanoparticles: Discovery by Visualization in 4D Electron Microscopy

Particle interactions are fundamental to our understanding of nanomaterials and biological assemblies. Here, we report on the visualization of entangled particles, separated by as large as 70 nm, and the discovery of channels in their near-fields. For silver nanoparticles, the induced field of each particle extends to 50–100 nm, but when particles are brought close in separation we observe channels as narrow as 6 nm, a width that is 2 orders of magnitude smaller than the incident field wavelength. The channels’ directions can be controlled by the polarization of the incident field, particle size, and separation. For this direct visualization of these nanoscopic near-fields, the high spatial, temporal, and energy resolutions needed were hitherto not possible without the methodology given here. This methodology, we anticipate, paves the way for further fundamental studies of particle entanglement and for possible applications spanning materials and macromolecular assemblies

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

The averaged null energy condition for general quantum field theories in two dimensions

It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and possesses an energy-momentum tensor. The latter is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur

Averaged Energy Conditions and Evaporating Black Holes

In this paper the averaged weak (AWEC) and averaged null (ANEC) energy conditions, together with uncertainty principle-type restrictions on negative energy (``quantum inequalities''), are examined in the context of evaporating black hole backgrounds in both two and four dimensions. In particular, integrals over only half-geodesics are studied. We determine the regions of the spacetime in which the averaged energy conditions are violated. In all cases where these conditions fail, there appear to be quantum inequalities which bound the magnitude and extent of the negative energy, and hence the degree of the violation. The possible relevance of these results for the validity of singularity theorems in evaporating black hole spacetimes is discussed.Comment: Sections 2.1 and 2.2 have been revised and some erroneous statements corrected. The main conclusions and the figures are unchanged. 27 pp, plain Latex, 3 figures available upon reques

Quantum field theory and time machines

We analyze the "F-locality condition" (proposed by Kay to be a mathematical implementation of a philosophical bias related to the equivalence principle, we call it the "GH-equivalence principle"), which is often used to build a generalization of quantum field theory to non-globally hyperbolic spacetimes. In particular we argue that the theorem proved by Kay, Radzikowski, and Wald to the effect that time machines with compactly generated Cauchy horizons are incompatible with the F-locality condition actually does not support the "chronology protection conjecture", but rather testifies that the F-locality condition must be modified or abandoned. We also show that this condition imposes a severe restriction on the geometry of the world (it is just this restriction that comes into conflict with the existence of a time machine), which does not follow from the above mentioned philosophical bias. So, one need not sacrifice the GH-equivalence principle to "emend" the F-locality condition. As an example we consider a particular modification, the "MF-locality condition". The theory obtained by replacing the F-locality condition with the MF-locality condition possesses a few attractive features. One of them is that it is consistent with both locality and the existence of time machines.Comment: Revtex, 14 pages, 1 .ps figure. To appear in Phys. Rev. D More detailed discussion is given on the MF-locality condition. Minor corrections in terminolog

Graphene-layered steps and their fields visualized by 4D electron microscopy

Enhanced image contrast has been seen at graphene-layered steps a few nanometers in height by means of photon-induced near-field electron microscopy (PINEM) using synchronous femtosecond pulses of light and electrons. The observed steps are formed by the edges of graphene strips lying on the surface of a graphene substrate, where the strips are hundreds of nanometers in width and many micrometers in length. PINEM measurements reflect the interaction of imaging electrons and induced (near) electric fields at the steps, and this leads to a much higher contrast than that achieved in bright-field transmission electron microscopy imaging of the same strips. Theory and numerical simulations support the experimental PINEM findings and elucidate the nature of the electric field at the steps formed by the graphene layers. These results extend the range of applications of the experimental PINEM methodology, which has previously been demonstrated for spherical, cylindrical, and triangular nanostructures, to shapes of high aspect ratio (rectangular strips), as well as into the regime of atomic layer thicknesses

Restrictions on negative energy density in a curved spacetime

Recently a restriction ("quantum inequality-type relation") on the (renormalized) energy density measured by a static observer in a "globally static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for the minimally coupled scalar field, in the extension of quantum inequality-type relation on flat spacetime of Ford and Roman. They found negative lower bounds for the line integrals of energy density multiplied by a sampling (weighting) function, and explicitly evaluate them for some specific spacetimes. In this paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are compact and without boundary. In the short "sampling time" limit, the bound has asymptotic expansion. Although the expansion can not be represented by locally invariant quantities in general due to the nonlocal nature of the integral, we explicitly evaluate the dominant terms in the limit in terms of the invariant quantities. We also make an estimate for the bound in the long sampling time limit.Comment: LaTex, 23 Page