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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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DOI

10.1007/bf01934921

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1432-0916

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Binding of Polarons and Atoms at Threshold

Authors: Rupert L Frank Elliott H Lieb Robert Seiringer
Publish Date: 2012/02/10
Volume: 313, Issue: 2, Pages: 405-424
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Abstract

If the polaron coupling constant α is large enough bipolarons or multipolarons will form When passing through the critical α c from above does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode We prove that it is always the latter We also prove the analogous statement for the PekarTomasevich PT approximation to the energy in which case there is a solution to the PT equation at α c Similarly we show that the same phenomenon occurs for atoms eg helium at the critical value of the nuclear charge Our proofs rely only on energy estimates not on a detailed analysis of the Schrödinger equation and are very general They use the fact that the Coulomb repulsion decays like 1/r while ‘uncertainty principle’ localization energies decay more rapidly as 1/r 2

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  1. Statistics of Wave Functions for a Point Scatterer on the Torus
  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
  3. Stability and Duality in $${\mathcal{N}\,{=}\,2}$$ Supergravity
  4. Exponential Mixing for the 3 D Stochastic Navier–Stokes Equations
  5. Probabilistic Weyl Laws for Quantized Tori
  6. On Perturbations of the Schwarzschild Anti-De Sitter Spaces of Positive Mass
  7. Wall-Crossing, Free Fermions and Crystal Melting
  8. Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation
  9. Laminar Boundary Layers in Convective Heat Transport
  10. There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group
  11. Duality of 2D Gravity as a Local Fourier Duality
  12. Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities
  13. Extended Scaling Relations for Planar Lattice Models
  14. Infinite-Dimensional Schur–Weyl Duality and the Coxeter–Laplace Operator
  15. Phase Boundaries in Algebraic Conformal QFT
  16. On the Singularity of the Free Energy at a First Order Phase Transition
  17. Free Analog of Pressure and Its Legendre Transform
  18. Continuity of the Lyapunov Exponents for Quasiperiodic Cocycles
  19. On the Correlation Function of the Characteristic Polynomials of the Hermitian Wigner Ensemble
  20. Stationary Random Metrics on Hierarchical Graphs Via $${(\min,+)}$$-type Recursive Distributional Equations
  21. Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems
  22. Higgs Bundles and ( A , B , A )-Branes
  23. Inviscid Incompressible Limits of the Full Navier-Stokes-Fourier System
  24. Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data
  25. Dispersive Estimates for Schrödinger Operators in Dimension Two
  26. A Monoidal Category for Perturbed Defects in Conformal Field Theory
  27. On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System
  28. Holomorphic Factorization for a Quantum Tetrahedron
  29. High Energy Limits of Laplace-Type and Dirac-Type EigenFunctions and Frame Flows
  30. The Operator Product Expansion for Perturbative Quantum Field Theory in Curved Spacetime
  31. The Szegő Kernel on a Sewn Riemann Surface
  32. Wave Relations
  33. An Application of Mirror Extensions
  34. Diffusion in a Weakly Random Hamiltonian Flow
  35. Spherical T-Duality
  36. A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals
  37. Lax Pair Equations and Connes-Kreimer Renormalization
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  39. On the Geometry of Closed G 2 -Structures
  40. Irreducible Characters of General Linear Superalgebra and Super Duality
  41. Connecting Solutions of the Lorentz Force Equation do Exist
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  43. The Smoluchowski-Kramers Limit of Stochastic Differential Equations with Arbitrary State-Dependent Friction
  44. Dirac Reduction for Poisson Vertex Algebras
  45. Dispersive Estimates for Schrödinger Equations with Threshold Resonance and Eigenvalue
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  64. Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
  65. Periodicity and the Determinant Bundle
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