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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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Dependence of the correlated-momentum patterns in double ionization on the carrier-envelope phase and intensity of a few-cycle laser pulse

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Physical Review A 2010年第6期82卷 063423-063423页

作者： G. G. Xin D. F. Ye J. Liu Key Laboratory of Cluster Science and Department of Physics School of Science Beijing Institute of Technology Beijing 100081 China Science and Technology Computation Physics Laboratory Beijing Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Applied Physics and Technology Peking University Beijing 100084 China

In the present paper, we investigate the correlated electron emission of atoms irradiated by a few-cycle laser pulse, with emphasis on the correlated longitudinal momentum spectra. We find that the spectra show clear v-shaped structures, in analogy to what was observed recently in long-pulse experiments. Moreover, the patterns of the spectra depend sensitively on the carrier-envelope phase as well as the laser intensity. The v-shaped structure is more pronounced at lower and higher intensities and becomes obscure at medium intensity. At a lower intensity, upon change of the phase from 0 to π/2, the v-shaped structure shifts from the first quadrant to the third quadrant and the ratios between the double ionization yields in the first and third quadrants are found to increase by a few orders of magnitude. The semiclassical rescattering model is exploited in the preceding calculations and the underlying mechanisms are uncovered by analyzing the subcycle dynamics of classical trajectories.

关键词： Electron emission

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Quantum phase transition in a disordered long-range transverse Ising antiferromagnet

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Physical Review E 2010年第2期81卷 021101-021101页

作者： Anjan Kumar Chandra Jun-ichi Inoue Bikas K. Chakrabarti Centre for Applied Mathematics and Computational Science and Theoretical Condensed Matter Physics Division Saha Institute of Nuclear Physics 1/AF Bidhannagar Kolkata 700064 India Complex Systems Engineering Graduate School of Information Science and Technology Hokkaido University N14-W9 Kita-ku Sapporo 060-0814 Japan

We consider a long-range Ising antiferromagnet put in a transverse field (LRTIAF) with disorder. We have obtained the phase diagrams for both the classical and quantum cases. For the pure case applying quantum Monte Carlo method, we study the variation in order parameter (spin correlation in the Trotter direction), susceptibility, and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We discuss generally the phase diagram for the same LRTIAF model with perturbative Sherrington-Kirkpatrick-type disorder. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the pure LRTIAF system, an infinitesimal SK spin-glass disorder is enough to induce a stable glass order in the LRTIAF. This glass order eventually gets destroyed as the thermal or quantum fluctuations are increased beyond their threshold values and the transition to paramagnetic phase occurs. Analytical studies for the phase transitions are discussed in details in each case. These transitions have been confirmed by applying classical and quantum Monte Carlo methods. We show here that the disordered LRTIAF has a surrogate incubation property of the SK spin glass phase.

关键词： Phase diagrams

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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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Reformulation of the covering and quantizer problems as ground states of interacting particles

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Physical Review E 2010年第5期82卷 056109-056109页

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

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d-dimensional Euclidean space Rd interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in Rd that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the “void” nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their “dual” solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4, depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the q

关键词： Ground state

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Photodetachment of hydrogen negative ions with screened Coulomb interaction

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Physical Review A 2010年第6期81卷 065402-065402页

作者： Song Bin Zhang Jian Guo Wang R. K. Janev Yi Zhi Qu Xiang Jun Chen Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Hefei 230026 People’s Republic of China The Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics PO Box 8009 Beijing 100088 People’s Republic of China Macedonian Academy of Sciences and Arts PO Box 428 1000 Skopje Macedonia College of Material Sciences and Optoelectronic Technology Graduate School of the Chinese Academy of Sciences PO Box 4588 Beijing 100049 People’s Republic of China

The effects of Coulomb interaction screening on photodetachment cross sections of hydrogen negative ions below the n =2 excitation threshold is investigated by using the R-matrix method with pseudostates. The contributions of Feshbach and shape resonances to H− photodetachment cross section are presented when screening length (D) varies from D = ∞ to D = 4.6 a.u. It is found that the interaction screening has dramatic effects on the photodetachment cross sections of hydrogen negative ions in the photoelectron energy region around the n = 2 excitation threshold by strongly affecting the evolution of near-threshold resonances.

关键词： Coulomb interactions

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Exact constructions of a family of dense periodic packings of tetrahedra

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Physical Review E 2010年第4期81卷 041310-041310页

作者： S. Torquato Y. Jiao Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered “dimer” packings of tetrahedra, including the densest known packings with density ϕ=40004671=0.856347…. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.

关键词： constructions family tetrahedra tetrahedrons family Dense Platonic solid

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Phase behavior of colloidal superballs: Shape interpolation from spheres to cubes

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Physical Review E 2010年第6期81卷 061105-061105页

作者： Robert D. Batten Frank H. Stillinger Salvatore Torquato Department of Chemical Engineering 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 Princeton Center for Theoretical Science 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 School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball’s interior is defined by the inequality |x|2q+|y|2q+|z|2q≤1, which provides a versatile family of convex particles (q≥0.5) with cubelike and octahedronlike shapes as well as concave particles (q<0.5) with octahedronlike shapes. Here, we consider the convex case with a deformation parameter q between the sphere point (q=1) and the cube (q=∞). We find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases. Calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low-density equations of state closer to spheres than to cubes. Dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q. Along the ordered, high-density equation of state, superballs with 1

关键词： Spheres

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Stylistic analysis of paintings using wavelets and machine learning

Stylistic analysis of paintings using wavelets and machine l...

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17th European Signal Processing Conference, EUSIPCO 2009

作者： Jafarpour, Sina Polatkan, Güngör Brevdo, Eugene Hughes, Shannon Brasoveanu, Andrei Daubechies, Ingrid Princeton University Departments of Electrical Engineering Computer Science and Mathematics Program in Applied and Computational Mathematics Princeton NJ 08544 United States

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features". © EURASIP, 2009.

关键词： Decision trees

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Dislocation climb strengthening in systems with immobile obstacles: Three-dimensional level-set simulation study

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Physical Review B 2010年第5期81卷 054104-054104页

作者： Zi Chen Kevin T. Chu David J. Srolovitz Jeffrey M. Rickman Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08540 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08540 USA Vitamin D Inc. Menlo Park California 94025 USA Institute of High Performance Computing Singapore Singapore Department of Materials Science and Engineering Lehigh University Bethlehem Pennsylvania 18015 USA Department of Physics Lehigh University Bethlehem Pennsylvania 18015 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08540 USA

We employ a parallel, three-dimensional level-set code to simulate the dynamics of isolated dislocation lines and loops in an obstacle-rich environment. This system serves as a convenient prototype of those in which extended, one-dimensional objects interact with obstacles and the out-of-plane motion of these objects is key to understanding their pinning-depinning behavior. In contrast to earlier models of dislocation motion, we incorporate long-ranged interactions among dislocation segments and obstacles to study the effect of climb on dislocation dynamics in the presence of misfitting penetrable obstacles/solutes, as embodied in an effective climb mobility. Our main observations are as follows. First, increasing climb mobility leads to more effective pinning by the obstacles, implying increased strengthening. Second, decreasing the range of interactions significantly reduces the effect of climb. The dependence of the critical stress on obstacle concentration and misfit strength is also explored and compared with existing models. In particular, our results are shown to be in reasonable agreement with the Friedel-Suzuki theory. Finally, the limitations inherent in the simplified model employed here, including the neglect of some lattice effects and the use of a coarse-grained climb mobility, are discussed.

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