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Displaced Path Integral Formulation for the Momentum Distribution of Quantum Particles

Physical Review Letters 2010年第11期105卷 110602-110602页

作者： Lin Lin Joseph A. Morrone Roberto Car Michele Parrinello Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Computational Science Department of Chemistry and Applied Biosciences ETH Zurich USI Campus Via Giuseppe Buffi 12 CH-6900 Lugano Switzerland

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems.

关键词： Statistical mechanics

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Jammed hard-particle packings: From Kepler to Bernal and beyond

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Reviews of Modern physics 2010年第3期82卷 2633-2633页

作者： S. Torquato F. H. Stillinger []Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute of Advanced Study Princeton New Jersey 08540 USA

Understanding the characteristics of jammed particle packings provides basic insights into the structure and bulk properties of crystals, glasses, and granular media and into selected aspects of biological systems. This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature of that diversity is the necessity to classify individual jammed configurations according to whether they are locally, collectively, or strictly jammed. Each of these categories contains a multitude of jammed configurations spanning a wide and (in the large system limit) continuous range of intensive properties, including packing fraction ϕ, mean contact number Z, and several scalar order metrics. Application of these analytical tools to spheres in three dimensions (an analog to the venerable Ising model) covers a myriad of jammed states, including maximally dense packings (as Kepler conjectured), low-density strictly jammed tunneled crystals, and a substantial family of amorphous packings. With respect to the last of these, the current approach displaces the historically prominent but ambiguous idea of “random close packing” with the precise concept of “maximally random jamming.” Both laboratory procedures and numerical simulation protocols can and, frequently, have been used for creation of ensembles of jammed states. But while the resulting distributions of intensive properties may individually approach narrow distributions in the large system limit, the distinguishing varieties of possible operational details in these procedures and protocols lead to substantial variability among the resulting distributions, some examples of which are presented here. This review also covers recent advances in understanding jammed packings of polydisperse sphere mixtures, as well as convex nonspherical particles, e.g., ellipsoids, “

关键词： Spheres Euclidean space laboratory procedure jammed state Kepler

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Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming

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Physical Review E 2010年第6期82卷 061302-061302页

作者： S. Torquato Y. Jiao Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive-shrinking cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in d-dimensional Euclidean space Rd, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential-linear-programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in Rd for d=2, 3, 4, 5, and 6 with a diversity of disorder and densities up to the respective maximal densities. A novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures (locally maximally dense and mechanically stable packings), besides the usual disordered ones (such as the maximally random jammed state), with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere. For example, in three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range [0.6, 0.7408…], where π/18=0.7408… corresponds to the density of the densest packing. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for d=2, 4, 5, and 6. Our jammed sphere packings are characterized and compared to the corresponding packings generated by the well-known Lubachevsky-Stillinger (LS) molecular-dynamics packing algorithm. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust an

关键词： Packing

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Densest local sphere-packing diversity: General concepts and application to two dimensions

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Physical Review E 2010年第4期81卷 041305-041305页

作者： Adam B. Hopkins Frank H. Stillinger Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of configuration space. The knowledge of Rmin(N) in d-dimensional Euclidean space Rd allows for the construction both of a realizability condition for pair-correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings in Rd. In this paper, we focus on the two-dimensional circular disk problem. We find and present the putative densest packings and corresponding Rmin(N) for selected values of N up to N=348 and use this knowledge to construct such a realizability condition and an upper bound. We additionally analyze the properties and characteristics of the maximally dense packings, finding significant variability in their symmetries and contact networks, and that the vast majority differ substantially from the triangular lattice even for large N. Our work has implications for packaging problems, nucleation theory, and surface physics.

关键词： Spheres

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Growth and characteristics of GaInN/GaInN multiple quantum well light-emitting diodes

Growth and characteristics of GaInN/GaInN multiple quantum w...

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作者： Lee, Wonseok Kim, Min-Ho Zhu, Di Noemaun, Ahmed N. Kim, Jong Kyu Schubert, E.F. Future Chips Constellation and Engineering Science Program Rensselaer Polytechnic Institute Troy NY 12180 United States Samsung LED Suwon 443-743 Korea Republic of Future Chips Constellation Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy NY 12180 United States Future Chips Constellation Department of Electrical Computer and Systems Engineering Rensselaer Polytechnic Institute Troy NY 12180 United States Department of Materials Science and Engineering Pohang University of Science and Technology Pohang 790-784 Korea Republic of

We demonstrate GaInN multiple quantum well (MQW) light-emitting diodes (LEDs) having ternary GaInN quantum barriers (QBs) instead of conventional binary GaN QBs for a reduced polarization mismatch between QWs and QBs and an additional separate confinement of carriers to the MQW active region. In comparison with GaInN LEDs with conventional GaN QBs, the GaInN/GaInN LEDs show a reduced blueshift of the peak wavelength with increasing injection current and a reduced forward voltage. In addition, we investigate the density of pits emerging on top of the MQW layer that are correlated with V-defects and act as a path for the reverse leakage current. The GaInN/GaInN MQW structure has a lower pit density than the GaInN/GaN MQW structure as well as a lower reverse leakage current. Finally, the GaInN/GaInN MQW LEDs show higher light output power and external quantum efficiency at high injection currents compared to the conventional GaInN/GaN MQW LEDs. We attribute these results to the reduced polarization mismatch and the reduced lattice mismatch in the GaInN/GaInN MQW active region. © 2010 American Institute of physics.

关键词： III-V semiconductors

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Adaptation of Pixelated CdZnTe gamma-ray imaging technology for in situ planetary science applications

Adaptation of Pixelated CdZnTe gamma-ray imaging technology ...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： Suzanne Nowicki Julia Bodnarik Larry Evans Min Namkung Ann Parsons Jeffrey Schweitzer Richard Starr Astrochemistry Laboratory NASA Goddard Space Flight Center Greenbelt MD USA Applied Physics Program University of Michigan Ann Arbor MD USA Laboratory for Nuclear Science University of Connecticut Storrs CT USA

It is important for planetary sciences to find a gamma-ray spectrometer that is compact, light and provides good energy resolution in an energy range that varies from ~ 30 keV to 10 MeV. Pixelated CdZnTe detector is a good candidate for this application due to its small volume, light weight and it has demonstrated good energy resolution below ~2-3 MeV. At higher energies, charge sharing effect becomes a problem due to the size of the pixel. In this paper, the electron cloud diameter as a function of energy has been studied using the MCNPX Monte Carlo code. In the energy range studied, the electron cloud size increases linearly with energy. The effect of charge sharing in a 2×2×1.5 cm 3 pixelated CdZnTe detector at 662 keV, 2.614 MeV and 7.631 MeV is shown. The anode is an 11 × 11 pixelated array with 1.72 mm pitch. The simulation reveals that the electron cloud size is about three times the size of the pixel pitch for an 8 MeV event. As the energy of the source increases, charge sharing effect is dominant and the charge cloud is collected by multiple pixels which reduces the spectral performance of the detector.

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Maximal Potential Energy Transport: A Variational Principle for Solidification Problems

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Physical Review Letters 2010年第25期105卷 254502-254502页

作者： A. J. Wells J. S. Wettlaufer S. A. Orszag Department of Geology and Geophysics Yale University New Haven Connecticut 06520 USA Program in Applied Mathematics Yale University New Haven Connecticut 06520 USA Department of Physics Yale University New Haven Connecticut 06520-8109 USA Department of Mathematics Yale University New Haven Connecticut 06520-8283 USA

We analyze numerically the mechanisms controlling the spacing of chimneys—channels devoid of solid—in two-dimensional mushy layers formed by solidifying a binary alloy. Chimneys are the principal conduits through which buoyancy effects material transport out of the mushy layer and into the liquid from which it formed. Experiments show a coarsening of chimney spacing; we pursue the hypothesis that the spacing adjusts to optimize material transport and hence maximize the rate of removal of potential energy stored in the mushy layer. The optimal solute flux increases approximately linearly with the mush Rayleigh number. However, for spacings below a critical value, the chimneys collapse and solute fluxes cease, revealing a hysteresis between chimney convection and no flow. The results are consistent with a variational principle controlling the dynamics of this dissipative system.

关键词： Potential energy

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Origin of broad polydispersion in functionalized dendrimers and its effects on cancer-cell binding affinity

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Physical Review E 2010年第3期82卷 036108-036108页

作者： Jack N. Waddell Douglas G. Mullen Bradford G. Orr Mark M. Banaszak Holl Leonard M. Sander Department of Mathematics University of Michigan Ann Arbor Michigan 48109 USA Program in Macromolecular Science and Engineering Ann Arbor Michigan 48109 USA Michigan Nanotechnology Institute for Medicine and Biological Sciences Ann Arbor Michigan 48109 USA Michigan Nanotechnology Institute for Medicine and Biological Sciences University of Michigan Ann Arbor Michigan 48109 USA Program in Applied Physics University of Michigan Ann Arbor Michigan 48109 USA Department of Physics University of Michigan Ann Arbor Michigan 48109 USA Department of Chemistry University of Michigan Ann Arbor Michigan 48109 USA Michigan Center for Theoretical Physics University of Michigan Ann Arbor Michigan 48109 USA

Nanoparticles with multiple ligands have been proposed for use in nanomedicine. The multiple targeting ligands on each nanoparticle can bind to several locations on a cell surface facilitating both drug targeting and uptake. Experiments show that the distribution of conjugated ligands is unexpectedly broad, and the desorption rate appears to depend exponentially upon the mean number of attached ligands. These two findings are explained with a model in which ligands conjugate to the nanoparticle with a positive cooperativity of ≈4 kT, and that nanoparticles bound to a surface by multiple bonds are permanently affixed. This drives new analysis of the data, which confirms that there is only one time constant for desorption, that of a nanoparticle bound to the surface by a single bond.

关键词： Nanoparticles

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Geometrical ambiguity of pair statistics: Point configurations

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Physical Review E 2010年第1期81卷 011105-011105页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Point configurations have been widely used as model systems in condensed-matter physics, materials science, and biology. Statistical descriptors, such as the n-body distribution function gn, are usually employed to characterize point configurations, among which the most extensively used is the pair distribution function g2. An intriguing inverse problem of practical importance that has been receiving considerable attention is the degree to which a point configuration can be reconstructed from the pair distribution function of a target configuration. Although it is known that the pair-distance information contained in g2 is, in general, insufficient to uniquely determine a point configuration, this concept does not seem to be widely appreciated and general claims of uniqueness of the reconstructions using pair information have been made based on numerical studies. In this paper, we present the idea of the distance space called the D space. The pair distances of a specific point configuration are then represented by a single point in the D space. We derive the conditions on the pair distances that can be associated with a point configuration, which are equivalent to the realizability conditions of the pair distribution function g2. Moreover, we derive the conditions on the pair distances that can be assembled into distinct configurations, i.e., with structural degeneracy. These conditions define a bounded region in the D space. By explicitly constructing a variety of degenerate point configurations using the D space, we show that pair information is indeed insufficient to uniquely determine the configuration in general. We also discuss several important problems in statistical physics based on the D space, including the reconstruction of atomic structures from experimentally obtained g2 and a recently proposed “decorrelation” principle. The degenerate configurations have relevance to open questions involving the famous traveling salesman problem.

关键词： Inverse problems

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Streaks to Rings to Vortex Grids: Generic Patterns in Transient Convective Spin Up of an Evaporating Fluid

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Physical Review Letters 2010年第4期105卷 044504-044504页

作者： J.-Q. Zhong M. D. Patterson J. S. Wettlaufer Department of Geology & Geophysics Yale University New Haven Connecticut 06520-8109 USA Faculty of Engineering & Design University of Bath Bath BA2 7AY United Kingdom Department of Physics Yale University New Haven Connecticut 06520-8109 USA Program in Applied Mathematics Yale University New Haven Connecticut 06520-8109 USA

We observe the transient formation of a ringed pattern state during spin up of an evaporating fluid on a time scale of order a few Ekman spin up times. The ringed state is probed using infrared thermometry and particle image velocimetry and it is demonstrated to be a consequence of the transient balance between Coriolis and viscous forces which dominate inertia, each of which are extracted from the measured velocity field. The breakdown of the ringed state is quantified in terms of the antiphasing of these force components which drives a Kelvin-Helmholtz instability and we show that the resulting vortex grid spacing scales with the ring wavelength. This is the fundamental route to quasi-two-dimensional turbulent vortex flow and thus may have implications in astrophysics and geophysics wherein rotating convection is ubiquitous.

关键词： Vortex flow

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