Out of Equilibrium Correlations in the XY Chain

We study the transversal spin–spin correlations in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right acting as thermal reservoirs at different temperatures. We prove that the spatial decay of these correlations is at least exponentially fast.     

The carbon isotope composition of CO2 respired by trunks: comparison of four sampling methods

The (13)C natural abundance of CO(2) respired by plants has been used in the laboratory to examine the discrimination processes that occur during respiration. Currently, field measurements are being expanded to interpret the respiration delta(13)C signature measured at ecosystem and global levels. In this context, forests are particularly important to consider as they represent 80% of the continental biomass. The objective of this investigation was to compare four methods of sampling the CO(2) respired by trunks for the determination of its carbon isotope composition: three in situ methods using chambers placed on the trunk, and one destructive method using cores of woody tissues. The in situ methods were based either on a Keeling plot approach applied at the tissue level or on an initial flush of the chamber with nitrogen or with CO(2)-free air. In parallel, we investigated the possibility of an apparent discrimination during tissue respiration by comparing the delta(13)C signature of the respired CO(2) and that of the organic matter. The study was performed on six tree species widely distributed in temperate and mediterranean areas. The four methods were not significantly different when overall means were considered. However, considering the individual data, the Keeling plot approach and the nitrogen flush methods gave fairly homogeneous results, whereas the CO(2)-free air method produced more variable results. The core method was not correlated with any of the chamber methods. Regardless of the methodology, the respired CO(2) generally was enriched in (13)C relative to the total organic matter. This apparent enrichment during respiration was variable, reaching as much as 3-5 per thousand. This study showed that, on the whole, the different sampling techniques gave similar results, but one should be aware of the variability associated with each method.     

Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED

In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli–Fierz model up to the order α ⁵ log α ⁻¹, where α denotes the fine structure constant, and prove rigorous bounds on the remainder term of the order o(α ⁵ log α ⁻¹). As a consequence, we prove that the binding energy is not a real analytic function of α, and verify the existence of logarithmic corrections to the expansion of the ground state energy in powers of α, as conjectured in the recent literature.     

Landau Hamiltonians with Unbounded Random Potentials

We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to , and satisfies , for some > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum is , provided the magnetic field B0. We prove that for each positive integer n, there exists a field strength B _n , such that for all B>B _n , the almost sure spectrum is pure point at all energies except in intervals of width about each lower Landau level , for m < n. We also prove that for any B0, the integrated density of states is Lipschitz continuous away from the Landau energiesE _n (B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials.     

Binding Conditions for AtomicN-electron Systems in Non-Relativistic QED

We examine the binding conditions for atoms in non-relativistic QED, and prove that removing one electron from an atom requires a positive energy. As an application, we establish the existence of a ground state for the Helium atom. Communicated by Bernard Helffer submitted 14/07/03, accepted: 18/08/03     

On the Stability of the Relativistic Electron-Positron Field

We study the energy of relativistic electrons and positrons interacting through the second quantized Coulomb interaction and a self-generated magnetic field. As states we allow generalized Hartree-Fock states in the Fock space. Our main result is the assertion of positivity of the energy, if the atomic numbers and the fine structure constant are not too big. We also discuss the dependence of the result on the dressing of the electrons (choice of subspaces defining the electrons).     

Spectral Theory for a Mathematical Model of the Weak Interaction: The Decay of the Intermediate Vector Bosons W ��, II

We do the spectral analysis of the Hamiltonian for the weak leptonic decay of the gauge bosons W ^±. Using Mourre theory, it is shown that the spectrum between the unique ground state and the first threshold is purely absolutely continuous. Neither sharp neutrino high-energy cutoff nor infrared regularization is assumed.     

Generalized fractal dimensions: equivalences and basic properties

Given a positive probability Borel measure μ on , we establish some basic properties of the associated functions τ_μ^±(q) and of the generalized fractal dimensions D_μ^±(q) for . We first give the equivalence of the Hentschel–Procaccia dimensions with the Rényi dimensions and the mean-q dimensions, for q>0. We then use these relations to prove some regularity properties for τ_μ^±(q) and D_μ^±(q); we also provide some estimates for these functions, in particular estimates on their behaviour at ±∞, as well as for the dimensions corresponding to convolution of two measures. We finally present some calculations for specific examples illustrating the different cases met in the article.