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     

Phase transition in a class of Hamiltonians

We consider a class of Hamiltonians for a system of one localized spin-1/2 particle per lattice site with the total spin as a good quantum number. We introduce a set of conditions in the form of a hypothesis relating the subpartition function, which is the partition function defined by the subset of energies with a specific value of spin. If the equality in the hypothesis is satisfied, then the system undergoes a phase transition as a consequence of Yang-Lee theorem. As an application, we estimate the bounds on the spectrum of the Heisenberg Hamiltonian. Supported by the National Science Foundation, Washington D.C. and the Robert A. Welch Foundation, Houston, Texas and partly supported by the United States Atomic Energy Commission, Contract Grant AT (40-1) 3992.     

O(3) symmetric merons in an SU(3) Yang-Mills theory

We investigate irreducible, O(3) symmetric multiple-meron solutions to the classical SU(3) Yang-Mills equations in four-dimensional Euclidean space. The solutions have topological charge density equal to a sum of delta-functions with integer coefficients, and correspond to solutions of a system of two coupled singular elliptic equations. We prove the existence of twomeron solutions of the coupled system.Supported in part by the National Science Foundation under Grant No. PHY77-18762.     

Heat kernel regularization of quantum fields

We discuss some consequences of the existence of a heat kernel regularization (HKR) for quantum fields. We demonstrate that HKR applies in certain examples, using methods which should be useful more generally.Supported in part by the National Science Foundation under Grant PHY/DMS 86-45122Supported in part by a German National Scholarship Foundation fellowship     

On the Topological Multivortex Solutions of the Self-Dual Maxwell-Chern-Simons Gauged <Emphasis Type="Italic">O</Emphasis>(3) Sigma Model

We consider the self-dual Maxwell-Chern-Simons gauged O(3) sigma model in the whole plane . After reducing to a system of semilinear elliptic equations, we construct a topological solution pair via iteration method and compute the conserved energy explicitly using the exponential decay property of the solution.Jongmin Han: Supported by grant No. R01-2002-000-00390-0 from the Basic Research Program of the Korea Science and Engineering Foundation.Hee-seok Nam: Supported by Korea Research Foundation Grant (KRF-2004-003-C00017).Mathematics Subject Classification: 81T13, 35B40.     

Axioms for Euclidean Green's functions II

We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper.with an Appendix by Stephen SummersSupported in part by the National Science Foundation under Grant MPS 73-05037 A01.Alfred P. Sloan Foundation Fellow.     

Space-dependent dirac operators and effective quantum field theory for fermions

For the operator, wherem(x) can change sign, we develop a cluster expansion for computing the determinant and Green's functions. We use a local chiral transformation to relate the space-dependent case to the ordinary Dirac operator.Supported in part by National Science Foundation grant PHY/DMS 88-16214Supported in part by National Science Foundation grants DMS 90-08827 and DMS 88-580873Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291     

On Scattering of Solitons for the Klein–Gordon Equation Coupled to a Particle

We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein–Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of the soliton solutions. We show that in the large time approximation any finite energy solution, with the initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution of the free Klein–Gordon equation. It is assumed that the charge density satisfies the Wiener condition which is a version of the “Fermi Golden Rule”. The proof is based on an extension of the general strategy introduced by Soffer and Weinstein, Buslaev and Perelman, and others: symplectic projection in Hilbert space onto the solitary manifold, modulation equations for the parameters of the projection, and decay of the transversal component. Supported partly by Austrian Science Foundation (FWF) Project P19138-N13, by research grants of DFG (436 RUS 113/615/0-1(R)) and RFBR (01-01-04002). On leave Department Mechanics and Mathematics of Moscow State University. Supported partly by Austrian Science Foundation (FWF) Project P19138-N13 by Max-Planck Institute of Mathematics in the Sciences (Leipzig), and Wolfgang Pauli Institute of Vienna University. Supported partially by the NSF grant DMS-0405927     

Complex free energies and metastable lifetimes

For two simple models we consider the analytic continuation of the free energy across a first-order phase transition. For each system we also study an associated stochastic dynamics and decay rates for passage to the stable equilibrium. We then investigate the relation between the imaginary part of the free energy and the decay rate per unit volume.Supported in part by U.S.-Israel Binational Science Foundation and by National Science Foundation Grant MCS 77-20683.Alfred P. Sloan Research Fellow. On leave from Indiana University, Bloomington, Indiana.     

Wave emission from a VLF plasma-waveguide antenna system under ionospheric conditions

We study a VLF plasma-waveguide antenna system having the form of a field-aligned quasicylindrical enchancement of plasma density, which relaxes gradually to the background magnetoplasma with distance from the given source. A model enabling one to calculate both the total radiated power and the power distribution over the spatial spectrum of radiated waves is proposed. It is shown that this plasma antenna is useful for increasing the power going to the long-wave part of the spatial spectrum of whistler waves excited in the ambient plasma. Concrete estimates for terrestrial ionospheric conditions are given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 2, pp. 210–225, February, 1996.The work of the first two authors was supported in part by the Russian Foundation for Fundamental Research (Project codes No. 95-02-05001 and No. 94-02-05447-a, respectively). The work of the third author (A. V. Kudrin) was supported by the Russian Foundation for Fundamental Research under Grant No. 96-02-18666.     

Exact Analytical Solution to Equations of Perihelion Advance in General Relativity

Previously the perihelion advance in binary system was computed approximately. We will present an exact analytical solution to nonlinear differential equation of perihelion advance by method of Jacobian elliptic function and the advanced angle between successive perihelions. Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars from Ministry of Education, China (Grant No. [2004]527) and the Natural Science Foundation of Hunan Province, China (Grant No. 06JJ2026)     

A note on reflection positivity

We establish reflection positivity of covariance operators, using properties of Dirichlet or Neumann boundary data.Supported in part by National Science Foundation Grant No. PHY 78-08066.Supported in part by National Science Foundation Grant No. PHY 77-18762.     

Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions

We prove a functional central limit theorem for additive functionals of stationary reversible ergodic Markov chains under virtually no assumptions other than the necessary ones. We use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk.Supported by NSF Grant MCS-8301364, ONR Contract N00014-81-K-0012 and a Fellowship from John S. Guggenheim Memorial Foundation     

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     

A system of one dimensional balls with gravity

We introduce a Hamiltonian system with many degrees of freedom for which the nonvanishing of (some) Lyapunov exponents almost everywhere can be established analytically.Supported in part by the Sloan Foundation and the NSF Grant DMS-8807077     

Electron spin resonance study of the Ba-doping manganite Nd0.5Sr0.5MnO3

We have performed magnetization measurements and electron spin resonance （ESR） on polycrystalline manganites of Nd0.5Sr0.5-xBaxMnO3 （x = 0.1）. Phase separation and phase transitions are observed from the susceptibility and the ESR spectra data. Between 260 K （～ Tc） and 185 K （～ TN）, the system coexists of the paramagnetic phase and the ferromagnetic （FM） phase. Between 185 K and 140 K, the system coexists of the FM phase and the antiferromagnetic （AFM） phase. These results indicate that the system has a very complex magnetic state due to the origin of the instability stemming from manganite Nd0.5Sr0.4Ba0.1MnO3 by partially substituting the larger Ba^2＋ ions for the smaller Sr^2＋ ions.     

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     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Functional determinants in euclidean Yang-Mills theory

We study functional determinants entering the path integral for topologically non-trivial sectors of Euclidean SU(2) Yang-Mills theory and we derive some results in exact closed form.This work is supported through funds provided by the US Department of Energy (DOE) under Contract EY-76-C-02-3069 and by the National Science Foundation through funds provided under Contract PHY 79-16812     

The phase structure of the two-dimensionalN=2 Wess-Zumino model

We construct a convergent cluster expansion for the two-dimensionalN=2 Wess-Zumino model, in a region of parameter space where there are multiple phase. As a result of this expansion, we are able to construct the infinite volume field theory and demonstrate exponential decay of correlations. We are also able to investigate the different phases of the model, develop the phase diagram, and show that the free energy of each phase vanishes.Supported in part by National Science Foundation grants DMS 90-08827, PHY/DMS 88-16214 and DMS 88-58073Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291