Erratum: "Explicit pure-state density operator structure for quantum tomography" [

A one-to-one mapping between the one-particle densities and a particular set of n-particle ensembles is constructed. The construction entails simultaneous minimization of the energy and minimization of the L2-norm over the set of ensembles which yield a given density. Differences between the present approach to density functional theory and other approaches, such as Kohn–Sham theory (Ref. 12) and Thomas–Fermi–Dirac–Weizsacker theory (Ref.13) are emphasized. The Levy density functional may be decomposed into kinetic and electron–electron interaction components.

Defect accumulation is the principal factor leading to the swelling and embrittlement of materials during irradiation. It is commonly assumed that, once defect clusters nucleate, their structure remains essentially constant while they grow in size. Here, we describe a new mechanism, discovered during accelerated molecular dynamics simulations of vacancy clusters in fcc metals, that involves the direct transformation of a vacancy void to a stacking fault tetrahedron (SFT) through a series of 3D structures. This mechanism is in contrast with the collapse to a 2D Frank loop which then transforms to an SFT. The kinetics of this mechanism are characterized by an extremely large rate prefactor, tens of orders of magnitude larger than is typical of atomic processes in fcc metals.

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We develop two new modified embedded-atom method (MEAM) potentials for elemental iron, intended to reproduce the experimental phase stability with respect to both temperature and pressure. These simple interatomic potentials are fitted to a wide variety of material properties of bcc iron in close agreement with experiments. Numerous defect properties of bcc iron and bulk properties of the two close-packed structures calculated with these models are in reasonable agreement with the available first-principles calculations and experiments. Performance at finite temperatures of these models has also been examined using Monte Carlo simulations. We attempt to reproduce the experimental iron polymorphism at finite temperature by means of free energy computations, similar to the procedure previously pursued by Müller et al (2007 J. Phys.: Condens. Matter 19 326220), and re-examine the adequacy of the conclusion drawn in the study by addressing two critical aspects missing in their analysis: (i) the stability of the hcp structure relative to the bcc and fcc structures and (ii) the compatibility between the temperature and pressure dependences of the phase stability. Using two MEAM potentials, we are able to represent all of the observed structural phase transitions in iron. We discuss that the correct reproductions of the phase stability among three crystal structures of iron with respect to both temperature and pressure are incompatible with each other due to the lack of magnetic effects in this class of empirical interatomic potential models. The MEAM potentials developed in this study correctly predict, in the bcc structure, the self-interstitial in the (110) orientation to be the most stable configuration, and the screw dislocation to have a non-degenerate core structure, in contrast to many embedded-atom method potentials for bcc iron in the literature.