260 research outputs found

    Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems

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    We consider a finite chain of non-linear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for arbitrary temperature differences and arbitrary couplings, such a system has a unique stationary state. (This extends our earlier results for small temperature differences.) In all these cases, any initial state will converge (at an unknown rate) to the stationary state. We show that this stationary state continually produces entropy. The rate of entropy production is strictly negative when the temperatures are unequal and is proportional to the mean energy flux through the system

    Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures

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    We study the statistical mechanics of a finite-dimensional non-linear Hamiltonian system (a chain of anharmonic oscillators) coupled to two heat baths (described by wave equations). Assuming that the initial conditions of the heat baths are distributed according to the Gibbs measures at two different temperatures we study the dynamics of the oscillators. Under suitable assumptions on the potential and on the coupling between the chain and the heat baths, we prove the existence of an invariant measure for any temperature difference, i.e., we prove the existence of steady states. Furthermore, if the temperature difference is sufficiently small, we prove that the invariant measure is unique and mixing. In particular, we develop new techniques for proving the existence of invariant measures for random processes on a non-compact phase space. These techniques are based on an extension of the commutator method of H\"ormander used in the study of hypoelliptic differential operators.Comment: 43 page

    Generating non-Gaussian states using collisions between Rydberg polaritons

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    We investigate theoretically the deterministic generation of quantum states with negative Wigner functions, by using giant non-linearities due to collisional interactions between Rydberg polaritons. The state resulting from the polariton interactions may be transferred with high fidelity into a photonic state, which can be analyzed using homodyne detection followed by quantum tomography. Besides generating highly non-classical states of the light, this method can also provide a very sensitive probe for the physics of the collisions involving Rydberg states.Comment: 5 pages, 3 figure

    Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains

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    International audienceWe generalize earlier studies on the Laplacian for a bounded open domain Ω⊂R2\Omega\subset\mathbb R^2 with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical scattering operator for the exterior of this same domain. Using single layer and double layer potentials we can prove a number of new relations which hold when one chooses independently Dirichlet or Neumann boundary conditions for the interior and exterior problem. This relation is provided by a very simple set of ζ\zeta-functions, which involve the single and double layer potentials. We also provide Krein spectral formulas for all the cases considered and give a numerical algorithm to compute the ζ\zeta-function

    Inside-Outside Duality for Planar Billiards -- A Numerical Study

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    This paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There is a close connection between eigenvalues of the billiard Laplacian and the scattering phases, basically that every energy at which a scattering phase is 2Ï€2\pi corresponds to an eigenenergy of the Laplacian. Interesting phenomena appear when the shape of the domain does not allow an extension of the eigenfunction to the exterior. In this paper these phenomena are studied and illustrated from several points of view.Comment: uuencoded tar-compressed (using uufiles) postscript file, 15 page

    Efficient formation of deeply bound ultracold molecules probed by broadband detection

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    Using a non-selective broadband detection scheme we discovered an efficient mechanism of formation of ultracold Cs2_2 molecules in deeply bound levels (v=1−9v=1-9) of their electronic ground state X1Σg+^1 \Sigma_g^+. They are formed by a one-photon photoassociation of ultracold cesium atoms in a manifold of excited electronic states, followed by a two-step spontaneous emission cascade. We were able to form about 105−10610^5-10^6 molecules per second in these low vibrational levels of the ground state. This detection scheme could be generalized to other molecular species for the systematic investigation of cold molecule formation mechanisms.Comment: 4 page
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