Hydrodynamical limit for a Hamiltonian system with weak noise

Starting from a general hamiltonian system with superstable pairwise potential, we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles. We prolve that, in the scaling limit, the time conserved quantities, energy, momenta and density, satisfy the Euler equation of conservation laws up to a fixed timet provided that the Euler equation has a smooth solution with a given initial data up to timet. The strength of the noise term is chosen to be very small (but nonvanishing) so that it disappears in the scaling limit.Research partially supported by U.S. National Science Foundation grants DMS 89001682, DMS 920-1222 and a grant from ARO, DAAL03-92-G-0317Research partially supported by U.S. National Science Foundation grants DMS-9101196, DMS-9100383, and PHY-9019433-A01, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship     

The smooth cohomology ofN=2 supersymmetric Landau-Ginzburg field theories

We compute the smooth cohomology (both unrestricted and compactly supported) of the supercharge of an ultraviolet cutoffN=2 supersymmetric Landau-Ginzburg field theory.Supported in part by the National Science Foundation under grant DMS-9206936.Supported in part by the Department of Energy under grant DE-FG02-88ER25065.     

Existence of conserved currents in the perturbative sine-Gordon and massive thirring models

The existence of infinitely many conserved currents in the quantized sine-Gordon and massive Thirring models is proved in renormalized perturbation theory.Research supported in part by National Science Foundation Grant No. PHY 74-22218 A03Research supported in part by National Science Foundation Grant No. MP 574-05783 A01     

Effective action and cluster properties of the abelian Higgs model

We continue our program to establish the Higgs mechanism and mass gap for the abelian Higgs model in two and three dimensions. We develop a multiscale cluster expansion for the high frequency modes of the theory, within a framework of iterated renormalization group transformations. The expansions yield decoupling properties needed for a proof of exponential decay of correlations. The result of this analysis is a gauge invariant unit lattice theory with a deep Higgs potential of the shape required to exhibit the Higgs mechanism.Research partially supported by the National Science Foundation under Grant DMS-8602207 and by the Air Force Office of Scientific Research under Grant AFOSR-86-0229Alfred P. Sloan Research Fellow. Research partially supported by the National Science Foundation under Grants PHY-84-13285 and PHY-85-13554Research partially supported by the National Science Foundation under Grant PHY-85-13554     

Stability of shock waves for the Broadwell equations

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we prove asymptotic (in time) stability with respect to small perturbations of the initial data. Following the work of Liu [7] on shock wave stability for viscous conservation laws, the method consists of analyzing the solution as the sum of a shock wave, a diffusive wave, a linear hyperbolic wave and an error term. The diffusive and linear hyperbolic waves are approximate solutions of the fluid dynamic equations corresponding to the Broadwell model. The error term is estimated using a variation of the energy estimates of Kawashima and Matsumura [6] and the characteristic energy method of Liu [7].Research supported by the Office of Naval Research through grant N00014-81-0002 and by the National Science Foundation through grant NSF-MCS-83-01260Research supported by the National Science Foundation through grant DMS-84-01355     

Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems IV

We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method ofinfrared bounds and the chessboard method of estimating contour probabilities in Peierls arguments. We illustrate the ideas by applying them to models with long range interactions in one and two dimensions. Additional applications are discussed in a second paper.Research partially supported by US National Science Foundation under Grant MPS-75-11864Research partially supported by Canadian National Research Council under Grant A4015Research partially supported by US National Science Foundation under Grant MCS-75-21684-A01     

Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures

We prove that the self-avoiding walk has Ornstein-Zernike decay and some related properties for all noncritical temperatures at which the model is defined.National Science Foundation Postdoctoral Research Fellows. Work supported in part by the National Science Foundation under Grants No. PHY-82-03669 and MCS-81-20833     

The Hartree-Fock theory for Coulomb systems

For neutral atoms and molecules and positive ions and radicals, we prove the existence of solutions of the Hartree-Fock equations which minimize the Hartree-Fock energy. We establish some properties of the solutions including exponential falloff.Research partially supported by U.S. National Science Foundation Grant MCS-75-21684Research partially supported by U.S. National Science Foundation under Grants MPS-75-11864 and MPS-75-20638. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, NJ08540, USA     

Quantum coherent operators: A generalization of coherent states

We introduce a technique to compare different, but related, quantum systems, thereby generalizing the way that coherent states are used to compare quantum systems to classical systems in semiclassical analysis. We then use this technique to estimate the dependence of the free energy of the quantum Heisenberg model on the spin value, and to estimate the relation between the ferromagnetic and antiferromagnetic free energies.Work supported in part by the U.S. National Science Foundation grant PHY-9019433.Work supported in part by the U.S. National Science Foundation grant DMS-9002416.     

Tunneling spectra of underdoped Bi_2Sr_2Ca_(1-x)Y_xCu_2O_(8+δ) intrinsic Josephson junctions

<正>Mesa-structured submicron intrinsic Josephson junctions are successfully fabricated and well characterized on underdoped Bi_2Sr_2Ca_(1-x)Y_xCu-2O_(8+δ) single crystals with a T_c of 80 K.Tunneling spectra at the temperatures ranging from 4.2 K to 295 K are measured.A pulse technique is used to reduce sample heating for the measurement near pseudogap opening temperature T~*~280 K.Our experimental results show that the superconducting gap,the peak-dip separation,and the pseudogap opening temperature are all increased as compared with those from near optimally doped samples,which requires further theoretical analysis in the future.     

First-principles study of interphase Ni3Sn in Sn--Ni alloy for anode of lithium ion battery

This paper investigates the mechanism of Li insertion into interphase Ni3Sn in Ni-Sn alloy for the anode of lithium ion battery by means of the first-principles plane-wave pseudopotential. Compared with other phases, it is found that the Ni3Sn has larger relative expansion ratio and lower electrochemical potential, with its specific plateaus voltage around 0.3 eV when lithium atoms are filled in all octahedral interstitial sites, and the relative expansion ratio increasing dramatically when the lithiated phase transits from octahedral interstitial sites to tetrahedral interstitial sites. So this phase is a devastating phase for whole alloy electrode materials.     

Entangled State in Quantization of Magnetic Flux Qubits with Mutual Inductance Coupling

Via the Hamilton dynamical approach we have constructed Hamiltonian for the mutual inductance coupling magnetic flux qubits. The entangled state representation is used to propose Cooper-pair number-phase quantization and the Hamiltonian operator for the whole system. The dynamical evolution of the phase difference operator and the Cooper-pairs number operator is investigated by virtue of Heisenberg equations. Project 10574060 supported by the National Natural Science Foundation of China and project X071045 supported by the Science Foundation of Liaocheng University.     

Stochastic variational problems with constraints

Two theorems in stochastic variational problems with constraints are presented.Partially supported by the Swiss National Science Foundation.     

Superconductivity without dependence on valenceelectron density in Zn doped YBCO systems

This paper reports that the YBa2Cu3-xZnxO7-δ （x = 0-0.4） samples are researched by means of x-ray diffraction, calculations of binding energy, the positron experiments and variations of oxygen content. The results of simulated calculations, positron experiments and variations of oxygen content support the existence of cluster effect. Moreover, it is concluded that the cluster effect is an important factor on suppression of high-Tc cuprate superconductivity and the Tc does not depend on the density of valence electron directly.     

Self-organization effect in poly（3-hexylthiophene）： methanofullerenes solar cells

This paper studies the self-organization of the polymer in solar cells based on poly（3-hexylthiophene）： [6, 6]-phenyl C61-butyric acid methyl ester by controlling the growth rate of active layer. These blend films are characterized by UV-vis absorption spectroscopy, charge-transport dark J - V curve, x-ray diffraction pattern curve, and atomic force microscopy. The results indicate that slowing down the drying process of the wet films leads to an enhanced selforganization, which causes an increased hole transport. Increased incident light absorption, higher carrier mobility, and balanced carrier transport in the active layer explain the enhancement in the device performance, the power conversion efficiency of 3.43% and fill factor up to 64.6% are achieved under Air Mass 1.5, 100 mW/cm^2.     

Gravitational collapse and related phenomena from an empirical point of view,or, Black holes are where you find them

Conclusions There can be no conclusions until we find a black hole.Research supported in part by the National Science Foundation and by the Alfred P. Sloan Foundation.Presented at the International Conference on Gravitation and Relativity, Copenhagen, 5–10 July 1971.     

Hausdorff Measure of the Singular Set of Landau-Lifshitz Equations with a Nonlocal Term

This paper is concerned with the partial regularity of the stationary solutions to the Landau-Lifshitz system of ferromagnetic spin chain with Gilbert damping and a nonlocal term in 3-dimensions. The Hausdorff measure of the singular set is discussed.The author is partially supported by the National Natural Science Foundation of China (Grant No.19971030) and by Guangdong Provincial Natural Science Foundation (Grant No.000671 and No.031495).     

Topology of monopole catalysis

We give the necessary mathematical conditions for strong monopole catalysis.Researach supported in part by the National Science Foundation under Grant No PHY 82-15249.     

The power counting theorem for Minkowski metric

Dyson's power counting theorem is proved for the case of Minkowski metric.The research reported in this paper was supported in part by the National Science Foundation.     

Well-Posedness for the Dumbbell Model of Polymeric Fluids

The dumbbell model is a coupled hydrodynamic-kinetic model for polymeric fluids in which the configurations of the dumbbells are described by stochastic differential equations. We prove well-posedness of this model by deriving directly a priori estimates on the stochastic model. Our results can be used to analyze stochastic simulation methods such as the ones that are based on Brownian configuration fields.Supported by ONR grant N00014-01-1-0674 and National Science Foundation of China through a Class B Award for Distinguished Young Scholars 10128102.Partially supported by the special funds for Major State Research Projects G1999032804 and National Science Foundation of China for Distinguished Young Scholars 10225103.