Out of equilibrium correlations in the XY chain
We study the transversal XY spin-spin correlations in the non-equilibrium steady state constructed in \cite{AP03} and prove their spatial exponential decay close to equilibrium.
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arXiv subjects
Jean-Marie Barbaroux
Publications and source records attributed to Jean-Marie Barbaroux.
Quantitative estimates on the enhanced binding for the Pauli-Fierz operator
For a quantum particle interacting with a short-range potential, we estimate from below the shift of its binding threshold, which is due to the particle interaction with a quantized radiation field.
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Some connections between Dirac-Fock and Electron-Positron Hartree-Fock
We study the ground state solutions of the Dirac-Fock model in the case of weak electronic repulsion, using bifurcation theory. They are solutions of a min-max problem. Then we investigate a max-min problem coming from the electron-positron field theory of Bach-Barbaroux-Helffer-Siedentop. We show that given a radially symmetric nuclear charge, the ground state of Dirac-Fock solves this max-min problem for certain numbers of electrons. But we also exhibit a situation in which the max-min level does not correspond to a solution of the Dirac-Fock equations together with its associated self-consistent projector.
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Binding conditions for atomic N-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.
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Dynamical properties of random Schrödinger operators
We study dynamical properties of random Schrödinger operators $H^{(ω)}$ defined on the Hilbert space $\ell^2(\bbZ^d)$ or $L^2(\bbR^d)$. Building on results from existing multi-scale analyses, we give sufficient conditions on $H^{(ω)}$ to obtain the vanishing of the diffusion exponent $$ σ_{\rm diff}^+ := \limsup_{T\rightarrow\infty } \frac{\log \bbE \left(\la\la\vert X \vert^2\ra\ra_{T,f_I(H^{(ω)})ψ}\right) }{\log T}=0. $$ Here $\bbE$ is the expectation over randomness, $f_{I}$ is any smooth characteristic function of a bounded energy-interval $I$ and $ψ$ is a state vector in the domain of $H^{(ω)}$ with compact spatial support. The quantity $\la\la |X|^2 \ra\ra_{T,φ}$ denotes the Cesaro mean up to time $T$ of the second moment of position $\la |X|^2\ra_{t,φ}$ at times $0\le t\le T$ of an initial state vector $φ$. If the Hilbert space is $\ell^2(\bbZ^d)$, the method of proof can be strengthened to yield dynamical localization. Under weaker assumptions, we also prove a theorem on the absence of diffusion. The results are applied to a randomly perturbed periodic Schrödinger operator on $L^2(\bbR^d)$, to a simple Anderson-type model on the lattice and to a model with a correlated random potential in continuous space.
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