13,583 research outputs found

    A new coherent states approach to semiclassics which gives Scott's correction

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    We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for molecules.Comment: A misprint in the definition of new coherent states correcte

    Singlets and reflection symmetric spin systems

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    We rigorously establish some exact properties of reflection symmetric spin systems with antiferromagnetic crossing bonds: At least one ground state has total spin zero and a positive semidefinite coefficient matrix. The crossing bonds obey an ice rule. This augments some previous results which were limited to bipartite spin systems and is of particular interest for frustrated spin systems.Comment: 11 pages, LaTeX 2

    The 200 MeV Pi+ induced single-nucleon removal from 24Mg

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    Nuclear gamma-rays in coincidence with outgoing pions or protons following single nucleon removal from Mg-24 by 200 MeV pions (+) were detected with Ge(Li) detectors. Differential cross sections are reported for gamma-rays from the first excited mirror states of Na-23 and Mg-23 in coincidence with positive pions or protons detected in particle telescopes at 30, 60, 90, 120, and 150 deg; angle-integrated absolute cross sections and cross section ratios are calculated. These results are compared with the predictions of a Pauli-blocked plane-wave impulse approximation (PWIA) and the intranuclear cascade (INC) and nucleon charge exchange (NCX) reaction models. The PWIA and the INC calculations generally agree with the angular dependence of the experimental results but not the absolute magnitude. The NCX calculation does not reproduce the observed cross section charge ratios

    Bose-Einstein Condensation and Spontaneous Symmetry Breaking

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    After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein Condensation is presented. The proof is based on a rigorous validation of Bogoliubov's cc-number substitution for the k=0{\bf k}={\bf 0} mode operator a0a_{\bf 0}.Comment: Contribution to the proceedings of the 21st Max Born Symposium, Wroclaw, Poland, June 26--28, 2006. (References added. To be published in Reports on Mathematical Physics.

    Proof of Bose-Einstein Condensation for Dilute Trapped Gases

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    The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schroedinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.Comment: Revised version with some simplifications and clarifications. To appear in Phys. Rev. Let

    Ground State Asymptotics of a Dilute, Rotating Gas

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    We investigate the ground state properties of a gas of interacting particles confined in an external potential in three dimensions and subject to rotation around an axis of symmetry. We consider the so-called Gross-Pitaevskii (GP) limit of a dilute gas. Analyzing both the absolute and the bosonic ground state of the system we show, in particular, their different behavior for a certain range of parameters. This parameter range is determined by the question whether the rotational symmetry in the minimizer of the GP functional is broken or not. For the absolute ground state, we prove that in the GP limit a modified GP functional depending on density matrices correctly describes the energy and reduced density matrices, independent of symmetry breaking. For the bosonic ground state this holds true if and only if the symmetry is unbroken.Comment: LaTeX2e, 37 page

    A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas

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    We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number NN is large but ρˉa2\bar\rho a^2 is small, where ρˉ\bar\rho is the average particle density and aa the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional with a coupling constant g1/ln(ρˉa2)g\sim 1/|\ln(\bar\rho a^2)|. In contrast to the 3D case the coupling constant depends on NN through the mean density. The GP energy per particle depends only on NgNg. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a Thomas-Fermi type functional is adequate.Comment: 14 pages, no figures, latex 2e. References, some clarifications and an appendix added. To appear in Commun. Math. Phy

    Free Energy of a Dilute Bose Gas: Lower Bound

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    A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density ρ\rho and temperature TT. In the dilute regime, i.e., when a3ρ1a^3\rho \ll 1, where aa denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2ρ2[ρρc]+2)4\pi a (2\rho^2 - [\rho-\rho_c]_+^2). Here, ρc(T)\rho_c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and []+[ ]_+ denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., Tρ2/3T \sim \rho^{2/3} or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [arXiv:math-ph/0601051] for estimating correlations to temperatures below the critical one.Comment: LaTeX2e, 53 page

    Stability of Matter in Magnetic Fields

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    In the presence of arbitrarily large magnetic fields, matter composed of electrons and nuclei was known to be unstable if α\alpha or ZZ is too large. Here we prove that matter {\it is stable\/} if α<0.06\alpha<0.06 and Zα2<0.04Z\alpha^2<0.04.Comment: 10 pages, LaTe
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