On the spectral problem for anyons

We consider the spectral problem resulting from the Schrödinger equation for a quantum system ofn2 indistinguishable, spinless, hard-core particles on a domain in two dimensional Euclidian space. For particles obeying fractional statistics, and interacting via a repulsive hard core potential, we provide a rigorous framework for analysing the spectral problem with its multi-valued wave functions.Partially supported by the Mathematical Sciences Research Institute, Berkeley California, under NSF Grant # DMS 8505550Partially supported under NSF Grant no. DMR-9101542     

A simple pseudomolecular fluid in contact with a wall: Exact and approximate local densities

A simple model mimicking a molecular fluid, introduced by Labik, Nezbeda and Smith (J. Chem. Phys.80 (1984) 5219] is applied to calculations of density profiles of a molecular fluid in contact with a hard wall. This model provides a useful means of investigating many of the quantitative features of more realistic fluid-wall models. In this work we have computed the spherical harmonic coefficients both of the local densities and of the one-particle background correlation functions and have examined the rate of convergence of these expansions. Moreover, we have used this model to test the accuracy of the zeroth-order RAM perturbational theory for the local densityThis work was supported by CPBP, under the Grant No. 01.08.E 2.     

Remote Preparation of a Two-Particle Entangled State via Two Tripartite <Emphasis Type="Italic">W</Emphasis> Entangled States

We present a scheme for remotely preparing a general two-particle entangled state via two tripartite W entangled states of different amplitudes. In this scheme one sender and two remote receivers are involved. The sender can help either one of the receivers to remotely reconstruct the original state with the aid of the other receiver’s two single-particle orthogonal measurements. It is shown that by means of the method of the positive operator-valued measurement, our remote state preparation scheme can be achieved probabilistically. This project supported by the National Key Basic Research and Development Program of China under Grant No. 2006CB921604 and the National Natural Science Foundation of China under Grant Nos. 60578050 and 10434060.     

δ/γ transformation in non-equilibrium solidified peritectic Fe-Ni alloy

Through phase transformation kinetic analysis and experimental observation, the δ/γ transformation occurring in the non-equilibrium peritectic Fe-4.33at.%Ni alloys was systematically investigated. According to JMA solid-state transformation kinetic theory, the Time-Temperature-Transformation (TTT) curves of the δ/γ transformation in peritectic Fe-Ni alloy were calculated. On this basis, the physical correlation between the δ/γ transformation and the initial undercooling of melt (△T) was elucidated. The results indicate that the change of △T can alter not only the overall δ/γ transformation pathways but also the transformation fraction with respect to each transformation mechanism.     

Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime

Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.     

On the statistics of a three-dimensional gas of long thin rods

A gas of long thin rods undergoes an order-disorder phase transition as a function of rod concentration. We have evaluated the critical concentration at which this first-order transition occurs using Onsager's hard-core interaction model. We obtain the nematic angular distribution function of rods in the ordered phase expanded in a series of Legendre polynomials.This work was partially supported by the National Science Foundation through Grant No. GP-10536.     

Absence of the efimov effect in a homogeneous magnetic field

A system of three identical particles in a homogeneous magnetic field is studied. It is shown that the Hamiltonian of this system with short-range potentials after the separation of the center of mass motion has a finite discrete spectrum for each fixed type m of the rotational (SO(2)) symmetry.Supported by the Erwin Schrödinger Institute, Austria, International Science Foundation Grant No. 9400 and Russian Grant of the State Committee for High Education RF-94-27-1022.     

<Emphasis Type="Italic">In situ</Emphasis> X-ray diffraction study of structural evaluation in Fe<Subscript>73</Subscript>Cu<Subscript>1.5</Subscript>Nd<Subscript>3</Subscript>Si<Subscript>13.5</Subscript>B<Subscript>9</Subscript> amorphous alloy at high temperature

The thermodynamics structural relaxation of Fe₇₃Cu_1.5Nd₃Si_13.5B₉ amorphous alloy from room temperature to 400°C has been investigated by measuring the structure factor with in situ X-ray diffraction. The structural information of the atomic configuration such as radial distribution function (RDF) and neighbor atomic distance was gained by Fourier transformation. The research result shows that the amorphous structure remains stable in the temperature range of 30 to 400°C but exhibits distinct changes in local atomic configuration with the increase of temperature. The quantitative determination of the neighbor atomic distance suggests that the degree of short-range order changes by the temperature altering the second nearest neighbor local atomic configuration of the amorphous when structural relaxation occurs. Supported by the Natural Science Foundation of Hebei Province of China (Grant No. A2007000296), the National Natural Science Foundation of China (Grant No. 50731005), SKPBRC (Grant Nos. 2007CB616915 and 2006CB605201), and PCSIRT (Grant No. IRT0650)     

Pairwise entanglement and local polarization of Heisenberg model

The characteristics of pairwise entanglement and local polarization (LP) are discussed by studying the ground state (states) of the Heisenberg XX model. The results show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2 for odd qubit); LP and the probability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412 (for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough. Supported by the National Natural Science Foundation of China (Grant Nos. 10547008, 90403034, 90403019, 90406017 and 60525417), the National Key Basic Research Special Foundation of China (Grant Nos. 2005CB724508 and 2006CB921400), the Foundation of Xi’an Institute of Post and Telecommunications (Grant No. 105-0414), and the Natural Science Foundation of Shanxi Province (Grant No. 2004A15)     

Transition prediction of a hypersonic boundary layer over a cone at small angle of attack—with the improvement of e<Superscript><Emphasis Type="Italic">N</Emphasis></Superscript> method

The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5°, and the angle of attack is 1°. The conventional e ^N method is used, but the transition location so obtained is obviously incorrect. The reason is that in the conventional method, only the amplifying waves are taken into account, while in fact, for different meridians the decay processes of the disturbances before they begin to grow are different. Based on our own previous work, new interpretation and essential improvement for the e ^N method are proposed. Not only the amplification process but also the decay process is considered. The location, where by linear stability theory, the amplitude of disturbance wave is amplified from its initial small value to 1%, is considered to be the transition location. The new result for transition prediction thus obtained is found to be fairly satisfactory. It is also indicated that for the calculation of base flow, boundary layer equations can be used for a small angle of attack. Its computational cost is much smaller than those for DNS. Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 90716007), the Special Foundation for the Authors of National Excellent Doctoral Dissertations (Grant No. 200328), and the Foundation of Liu-Hui Center of Applied Mathematics of Nankai University and Tianjin University     

An Elementary Proof of Lyapunov Exponent Pairing for Hard-Sphere Systems at Constant Kinetic Energy

The conjugate pairing of Lyapunov exponents for a field-driven system with smooth inter-particle interaction at constant total kinetic energy was first proved by Dettmann and Morriss [Phys. Rev. E 53:R5545 (1996)] using simple methods of geometry. Their proof was extended to systems interacting via hard-core inter-particle potentials by Wojtkowski and Liverani [Comm. Math. Phys. 194:47 (1998)], using more sophisticated methods. Another, and somewhat more direct version of the proof for hard-sphere systems has been provided by Ruelle [J. Stat. Phys. 95:393 (1999)]. However, these approaches for hard-sphere systems are somewhat difficult to follow. In this paper, a proof of the pairing of Lyapunov exponents for hard-sphere systems at constant kinetic energy is presented, based on a very simple explicit geometric construction, similar to that of Ruelle. Generalizations of this construction to higher dimensions and arbitrary shapes of scatterers or particles are trivial. This construction also works for hard-sphere systems in an external field with a Nosé–Hoover thermostat. However, there are situations of physical interest, where these proofs of conjugate pairing rule for systems interacting via hard-core inter-particle potentials break down.     

Fabrication of metal oxide nanostructures based on Atomic Force Microscopy lithography

Atomic Force Microscopy (AFM) mechanical lithography is a simple but significant method for nanofabrication. In this work, we used this method to construct nanostructures on Pt/Cu bilayer metal electrodes under ambient conditions in air. The influence of various scratch parameters, such as the applied force, scan velocity and circle times, on the lithography patterns was investigated. The Pt-Cu-Cu _x O-Cu-Pt nanostructure was constructed by choosing suitable scratch parameters and oxidation at room temperature. The properties of the scratched regions were also investigated by friction force microscopy and conductive AFM (C-AFM). The I–V curves show symmetric and linear properties, and Ohmic contacts were formed. These results indicate that AFM mechanical lithography is a powerful tool for fabricating novel metal-semiconductor nanoelectronic devices. Supported by the National Natural Science Foundation of China (Grant No. 90306010), the Program for New Century Excellent Talents in University of China (Grant No. NCET-04-0653), the National Basic Research Program of China (Grant No. 2007CB616911), and the Science and Technology Department of Henan Province (Grant No. 072300420100)     

Uniqueness of one-dimensional continuum Gibbs states

We investigate one-dimensional continuum grandcanonical Gibbs states corresponding to finite range superstable many-body potentials. Absence of phase transitions in the sense of uniqueness of the tempered Gibbs state is proved for potentials without hard-core by first proving uniqueness of the Gibbs measures for related hard-core potentials and then taking an appropriate limit of those Gibbs measures.     

On the statistical mechanics of classical Coulomb and dipole gases

A detailed, rigorous study of the statistical mechanics-screening- and critical properties, phase diagrams, etc., of classical Coulomb monopole and dipole gases in two or more dimensions is presented. The statistical mechanics of the two-dimensionalXY and Villain models is reconsidered and related to the one of two-dimensional lattice Coulomb gases. At low temperatures and moderate densities those gases behave like dipole gases. The Kosterlitz-Thouless transition is analyzed in that perspective and characterized by an order parameter. Techniques useful for a proof of existence of such a transition in a two-dimensional hard-core Coulomb gas are developed and applied to the study of dipole gases.A Sloan Fellow, and supported in part by NSF grant No. DMR 7904355.     

Scheme for Probabilistic Remotely Preparing a d-Dimensional Equatorial Quantum State

We present a scheme for probabilistic remote preparation of a d-dimensional equatorial quantum state. In the scheme, a bipartite d-dimensional partial entangled state is used as the quantum channel, and the single-qudit projective measurement and appropriate unitary transformation are needed. As a special, the remote preparation in three dimension is studied. The project supported Natural Science Foundation of Education Bureau of Jiangsu Province of China (Grant No 05 KJD 140035 and 06 KJD 520027).     

The unitary pole expansion of the off-shell t-matrix elements for local potentials with hard cores

A convenient separable expansion of the t-matrix, similar to the one developed recently by Harms for local potentials with soft cores, has been obtained in the case of a hard-core potential as well. The unitary pole expansion (UPE), as it is called, is found to be strongly convergent. The UPE values of the off-shell t-matrix elements for a hard-core potential with an exponential shape agree fairly well with those obtained by Laughlin and Scott from the direct solution of the inhomogeneous Lippman-Schwinger equation.     

Modification of Dispersion Relations and Generalization of the Hartree-Fock Method for Hard-Core Interactions in Nuclear Matter

The influence of a hard-core part in the interaction on dispersion relations for the generalized optical potential (mass operator) and the T-matrix of nuclear matter is investigated in the frame-work of the A⁰⁰-approximation. The model is based on the two-nucleon scattering problem in vacuo, for which a hard-core generalization of the Low equation is derived. As a consequence, T-matrix and mass operator are shown to split into a polynomial of the first order in the energy variable and a dispersion integral generalized by a limiting process, so that dispersion relations of the twice subtracted type result. Restriction to a self-consistent calculation of the non-dispersive term of the mass operator leads to a close analogue of the Hartree-Fock equations for non-singular interactions. This simple approximation which avoids the full-nucleon problem is shown to yield a qualitatively correct density dependence of the ground-state energy possibly to be improved by more realistic interactions. A formulation as an eigenvalue problem for finite nuclei is also given.     

Statistical Mechanics of Complex Systems for Pattern Identification

This paper presents a statistical mechanics concept for identification of behavioral patterns in complex systems based on measurements (e.g., time series data) of macroscopically observable parameters and their operational characteristics. The tools of statistical mechanics, which provide a link between the microscopic (i.e., detailed) and macroscopic (i.e., aggregated) properties of a complex system are used to capture the emerging information and to identify the quasi-stationary evolution of behavioral patterns. The underlying theory is built upon thermodynamic formalism of symbol sequences in the setting of a generalized Ising model (GIM) of lattice-spin systems. In this context, transfer matrix analysis facilitates construction of pattern vectors from observed sequences. The proposed concept is experimentally validated on a richly instrumented laboratory apparatus that is operated under oscillating load for identification of evolving microstructural changes in polycrystalline alloys. This work has been supported in part by the U.S. Army Research Office (ARO) under Grant No. W911NF-07-1-0376, by NASA under Cooperative Agreement No. NNX07AK49A, and by the U.S. Office of Naval Research (ONR) under Grant No. N00014-08-1-0380. Any opinions, findings and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsoring agencies.     

Stark effect in multielectron systems: Non-existence of bound states

We prove non-existence of bound states for a class ofN-body systems in homogeneous electric fields. This class includes atoms and Born—Oppenheimer molecules. This result in conjunction with a stability result of [HS] implies existence of resonances for such systems.Research partially supported by NSERC under Grant No. A7901 and NSF under Grant No. DMS8507040     

Universality in the effective pair interaction ofd-shell metals — Compressibility and vacancy formation energy of 3d-liquid metals

Like liquid alkali metalsd-shell liquid metals show scaling behaviour in structure and interaction potentials. A realistic interaction potential model, properly parametrized can reasonably describe the universality in the isothermal compressibility and vacancy formation energy of 3d-liquid metals in electron ion plasma model.