Compositions of Sasaki projections

In an orthomodular lattice (abbreviated OML) L, a Sasaki projection is a mappinga _x(a)=x(x va) fromL toL, wherexL. We study compositions of finite numbers of Sasaki projections and of the same Sasaki projections composed in inverse order. By using the Baer-semigroup of all finite compositions of Sasaki projections, we establish a new characterization of kernels of congruences in OMLs and a generalization of the parallelogram law for dimension OMLs. Our results are also related to quantum measurements via Pool's definition of the change of the support of a state after a measurement.     

Uniform boundedness of the solutions for a one-dimensional isentropic model system of compressible viscous gas

This paper studies an initial boundary value problem for a one-dimensional isentropic model system of compressible viscous gas with large external forces, represented by v _t –u _x =0,u _t +(av ^–) _x =(u _x /v) _x +f( ₀ ^x vdx,t), with (v(x, 0),u(x, 0))= (v ₀(x),u ₀(x)),u(0,t)=u(1,t)=0. Especially, the uniform boundedness of the solution in time is investigated. It is proved that for arbitrary large initial data and external forces, the problem uniquely has an uniformly bounded, global-in-time solution with also uniformly positive mass density, provided the adiabatic constant (>1) is suitably close to 1. The proof is based on L ²-energy estimates and a technique used in [9].     

On the Initial Boundary Value Problems for the Enskog Equation in Irregular Domains

The paper is concerned with the Enskog equation with a constant high density factor for large initial data in L ¹(R ⁿ). The initial boundary value problem is investigated for bounded domains with irregular boundaries. The proof of an H-theorem for the case of general domains and boundary conditions is given. The main result guarantees the existence of global solutions of boundary value problems for large initial data with all v-moments initially finite and domains having boundary with finite Hausdorff measure and satisfying a cone condition. Existence and uniqueness are first proved for the case of bounded velocities. The solution has finite norm where q = (t ₀, x) is taken on all possible n-dimensional planes Q(v) in R ^n+l intersecting a fixed point and orthogonal to vectors (1, v), v R ⁿ.     

The equation curl 73-173-173-1(x)=0 in quantum field theory

In one time and arbitrarily many space dimensions we obtain necessary and sufficient conditions for the existence of a local operator solution of the equation _v =W _v . Here the given local fieldsW _v satisfy _µ W _v - _v W _µ=0 and the spectrum of the two point function (,W _µ(x)W _v (y)) is assumed to have a mass gap.Research supported in part by Stiftung Volkswagenwerk and the Alfred P. Sloan Foundation.On leave from II. Institut für Theoretische Physik der Universität Hamburg, Germany.     

Conservation of Energy,Entropy Identity,and Local Stability for the Spatially Homogeneous Boltzmann Equation

For nonsoft potential collision kernels with angular cutoff, we prove that under the initial condition f ₀(v)(1+|v|²+|logf ₀(v)|)L ¹(R ³), the classical formal entropy identity holds for all nonnegative solutions of the spatially homogeneous Boltzmann equation in the class L ([0, ); L ¹ ₂(R ³))C ¹([0, ); L ¹(R ³)) [where L ¹ _s (R ³)={ff(v)(1+|v|²) ^s/2L ¹(R ³)}], and in this class, the nonincrease of energy always implies the conservation of energy and therefore the solutions obtained all conserve energy. Moreover, for hard potentials and the hard-sphere model, a local stability result for conservative solutions (i.e., satisfying the conservation of mass, momentum, and energy) is obtained. As an application of the local stability, a sufficient and necessary condition on the initial data f ₀ such that the conservative solutions f belong to L ¹ _loc([0, ); L ¹ ₂₊ (R ³)) is also given.     

Un phénomène de concentration évanescente pour des flots non-stationnaires incompressibles en dimension deux

We consider a sequencev of non-stationary solutions of the incompressible 2D-Euler equation, locally bounded inL ². We prove that if the defect measure is supported in a one-dimensional set (³) of some special type (which we call finite type), the weak limitv ofv is a solution of the Euler equations: our theorem is of the type concentration-cancellation.     

On the Existence of a Maximizer for the Strichartz Inequality

It is shown that a maximizing function u _*L ² does exist for the Strichartz inequality e ^it _x ² u _L ⁶ _t (L ⁶ _x )Su _L ², with S>0 being the sharp constant.     

Band-gap structure of the spectrum of periodic Maxwell operators

We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR ³, is considered. The medium is assumed to consist of two components: the background, where (x) = _b , and the embedded component composed of periodically positioned disjoint cubes, where (x) = _a . We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast = _b / _a are chosen in such a way thatL ^–2, and quantities ^-1-3/2 and ² are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(^3/2)^-1 of the set {² L ^-2 k ²:kZ³}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum.     

The Hermite-like description of two-magnon states of 1D quantumS = 1/2 chains with elliptic exchange is complete

In this Letter, we give an example of Navier-Stokes flow with a viscosityv, which converges to Euler flow inL ² norm asv 0. Our Navier-Stokes flow has a discontinuity on the boundary at the initial time, the so-called initial layer, and its initial data has singularity asymptotically asv 0 near the boundary. Even with these singularities, it can be said that our Navier-Stoke flow can converge to some Euler flow inL ² norm.     

Critical Region for Droplet Formation in the Two-Dimensional Ising Model

We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L ² , inverse temperature > _c and overall magnetization conditioned to take the value m L ² –2m v _L , where _c ^–1 is the critical temperature, m =m () is the spontaneous magnetization and v _L is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when v _L ^3/2 L ^–2 tends to a definite limit. Specifically, we identify a dimensionless parameter , proportional to this limit, a non-trivial critical value _c and a function such that the following holds: For < _c , there are no droplets beyond log L scale, while for > _c , there is a single, Wulff-shaped droplet containing a fraction _c =2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, and are related via a universal equation that apparently is independent of the details of the system.     

Absence of highest-spin ground states in the Hubbard model

The Hubbard modelH=–tc _x c _y +U n _x n _x withN electrons and periodic boundary condition is studied onv-dimensionalL ₁ × ... ×L _v lattices. It is shown that for any value ofU there is no ground state with maximal spin (S=N/2) in the following cases: (i) ^v (v2) at low electron densities; with one hole ift>0 andL _i is odd for somei; with two holes ift<0, or ift>0 and all theL _i are even. (ii) Thebcc lattice at low densities; with two holes ift<0, or ift>0 and all theL _i are even; with 2, ..., 6 holes ifL _i =L andt<0, or ift>0 andL is even. (iii) The triangular lattice at densities near 0 and 1 ift>0; with two holes ift<0; with 2, 3, 4 holes ift<0 andL ₁=L ₂. (iv) Thefcc lattice at densities near 0 and 1 ift>0; with two holes ift<0. Some results for the one dimensional model are also presented.     

A sharp decrease of resistivity in La0.7Ca0.3Mn0.96Cu0.04O3: Evidence for Cu-assisted coherent tunneling of spin Polarons

Nearly a 50% decrease of the resistivity ρ(T, x) is observed upon just 4% Cu doping at the Mn site of La_2/3Ca_1/3Mn_1−x Cu_xO₃. When the observed phenomenon is attributed to a decrease of the spin-polaron energy E _σ(x) below T _C (x), all of the data are found to be well fitted by the nonthermal coherent tunneling expression , assuming that the magnetization in the ferromagnetic state is given by the expression . The best fits through all the data points suggest and E _σ(x)≃E _σ(0)(1−x)⁴ for the explicit x dependence of the Cu-induced modifications of the Mn-spin-dominated zero-temperature spontaneous magnetization, residual paramagnetic contribution, and spin-polaron tunneling energy, respectively, with E _σ(0)=0.12 eV. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 812–815 (10 June 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The effect of a constant number of particles on the pair correlation function and the density profile in a one-dimensional lattice gas

A one-dimensional lattice gas (Ising model) of lengthL and with nearest-neighbor couplingJ is considered in a canonical ensemble with fixed number of particlesN=L/2. Exact expressions and asymptotic forms for largeL are derived for the density-density correlation function, using periodic boundary conditions, and for the density (magnetization) profile, using antisymmetric boundary conditions. The density-density correlation function,g, assumes for temperaturesT> T, withT = 2J(_BlnL)^–1 and forL large, the formg(x) =g ^gc(x) +BL ^–1 +a(x)L ^–1 +O(L^–2) wherex is a distance between considered lattice sites,B is known from earlier work of Lebowitz and Percus,(1b) anda(x) decays exponentially forx . For TT, the correlation function and the density profile behave differently, the latter exhibiting a step in the middle of the interface.     

The12C(2 1 + ) state as probe for transient magnetic fields in polarized iron

PAC measurements on the 4.43 MeV¹²C(2⁺) state on recoil in magnetized iron at velocitiesv _ion=2.1v ₀, 6.0v ₀, 7.4v ₀ yield integral precession angles of =+0.72(18), +0.94(16) and +0.71(18) mrad, respectively. The results supplementary to existing precession data are interpreted by a distribution of C⁵⁺ ions implying a K-shell polarization of 28% and an effective charge larger than measured after emergence from the solid. The low-velocity precession tends to disagree with the empirical law of linear relationship between transient field and ion velocity. The presence of molecular orbital effects is discussed.     

Global existence of solutions for a model Boltzmann equation

A model recently introduced by Ianiro and Lebowitz is shown to have a global solution for initial data having a finiteH-functional and belonging toL ¹ (L _x ). Methods previously introduced by Tartar to deal with discrete velocity models are used.     

Scattering approach to the von Klitzing effect

Earlier results of the scattering theoretical approach to the quantum Hall effect are simplified and generalized. Finite size corrections to the plateau values are found to be not of order (l/L _x ) but (l ² /L _x L _y )²,l,L _x ,L _y being the magnetic length, and the sample dimensions inx andy-direction respectively. An expression for the current parallel to the electric field in terms of a scattering matrix is derived. In the weak scattering regime this expression leads to a vanishing diagonal conductivity _xx .     

Difference-frequency source for very low optical frequencies spectroscopy: CO2 induced spectra

In a previous paper [1] the manufacturing, development and testing of a coherent submillimetric source was exposed. This source was obtained by difference frequency mixing of two CO₂ TEA lasers.In this present work, are presented the first results obtained with this mounting and concerning the collision induced spectrum of gaseous carbon dioxide at room temperature in the 4–40 cm^–1 region.The absorption coefficient is calculated together with the first coefficients of its development as a function of density.The curves ₂/v ²=f(v) and ₃/v ²=f(v), wherev is the frequency, are presented. They permit the calculation of the virial coefficients.The results are then compared with those determined by an extrapolation in this frequency range, of measurements already made in CO₂ in higher (optical) or lower (microwaves) frequencies.     

Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph

For the kernel of the Laplace operator Δ^Λ with potential Σ _j=1 ^k c _j δ _{q j} (x) on a manifold, (the operator is given by a Lagrangian plane Λ ⊂ ℂ ^k ⊕ ℂ ^k ), an isomorphism Γ: ker Δ^Λ → Λ ∩ L is described, where L is a special Lagrangian plane (whose explicit form is evaluated). A similar assertion holds for the Laplace operator on a decorated graph; for such a graph (obtained by decorating a connected finite graph with n edges and v vertices) with “continuity” conditions, the inequality 1 ≤ dimker ≤ n − v + 2 is obtained. It is also proved that the quantity n − v + 1-dim ker cannot reduce when adding new edges and manifolds. The first terms of the expansion of Tr(exp(-tH ^Λ)) are found. Dedicated to the memory of V. A. Geyler     

Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2^– state in¹⁴⁵Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency _L=g_NN¹ (T)B_ext. The paramagnetic correction factor strictly follows the Curie-Weiss relation =1+C/(T-), withC=–50(2) K and =–29(5) K. This is compatible with a hyperfine field ofB _int(0)=–25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.The temperature dependence of the electric quandrupole coupling constant v_Q, investigated between 100 K and 400 K, can be reproduced by a linear temperature variation v_Q(T)=v_Q(0) (1-AT), with v_Q(0)=16.2(4) MHz andA=7.2(8)·10^–4 K^–1.The paramagnetic relaxation time _rel of the nuclear alignment is proportional to the temperature of the sample, with _rel T^–1=3.7(2) ·10^–9s K^–1.This leads to the Korringa relation _J T=const=5.1(5)·10^–11s K for the relaxation time of the 4f electronic spinJ. Assuming that the relaxation ofJ is mainly caused by exchange interaction between conduction electrons and localized 4f electrons at the Eu site, an exchange integral of |J _eff|=0.10(2) eV can be deduced.     

Decay of Weak Solutions to the 2D Dissipative Quasi-Geostrophic Equation

We address the decay of the norm of weak solutions to the 2D dissipative quasi-geostrophic equation. When the initial data θ₀ is in L ² only, we prove that the L ² norm tends to zero but with no uniform rate, that is, there are solutions with arbitrarily slow decay. For θ₀ in L ^p ∩ L ², with 1 ≤ p < 2, we are able to obtain a uniform decay rate in L ². We also prove that when the norm of θ₀ is small enough, the L ^q norms, for , have uniform decay rates. This result allows us to prove decay for the L ^q norms, for , when θ₀ is in . The second author was partially supported by NSF grant DMS-0600692.