Paper Search Console

Home Search Page About Contact

Journal Title

Title of Journal: Commun Math Phys

Search In Journal Title:

Abbravation: Communications in Mathematical Physics

Search In Journal Abbravation:

Publisher

Springer-Verlag

Search In Publisher:

DOI

10.1002/jbm.b.30299

Search In DOI:

ISSN

1432-0916

Search In ISSN:
Search In Title Of Papers:

Statistics of Wave Functions for a Point Scatterer

Authors: Zeév Rudnick Henrik Ueberschär
Publish Date: 2012/08/24
Volume: 316, Issue: 3, Pages: 763-782
PDF Link

Abstract

Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space In contrast when the classical dynamics is integrable there is concentration of eigenfunctions on invariant structures in phase space In this paper we study eigenfunction statistics for the Laplacian perturbed by a deltapotential also known as a point scatterer on a flat torus a popular model used to study the transition between integrability and chaos in quantum mechanics The eigenfunctions of this operator consist of eigenfunctions of the Laplacian which vanish at the scatterer and new or perturbed eigenfunctions We show that almost all of the perturbed eigenfunctions are uniformly distributed in configuration space

Keywords:

References

.
Search In Abstract Of Papers:
Other Papers In This Journal:
  1. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
  2. Stability and Duality in $${\mathcal{N}\,{=}\,2}$$ Supergravity
  3. Exponential Mixing for the 3 D Stochastic Navier–Stokes Equations
  4. Binding of Polarons and Atoms at Threshold
  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
  38. SNA’s in the Quasi-Periodic Quadratic Family
  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
  42. Toric G 2 and Spin (7) Holonomy Spaces from Gravitational Instantons and Other Examples
  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
  46. Multipermutation Solutions of the Yang–Baxter Equation
  47. The Shape of Expansion Induced by a Line with Fast Diffusion in Fisher-KPP Equations
  48. Quasicrystals and Almost Periodicity
  49. A Lower Bound on Blowup Rates for the 3D Incompressible Euler Equation and a Single Exponential Beale-Kato-Majda Type Estimate
  50. On the Weak Solutions to the Maxwell–Landau–Lifshitz Equations and to the Hall–Magneto–Hydrodynamic Equations
  51. Spin(7)-Instantons, Cayley Submanifolds and Fueter Sections
  52. Equivariant Comparison of Quantum Homogeneous Spaces
  53. Regular Strongly Typical Blocks of $${\mathcal{O}^{\mathfrak {q}}}$$
  54. Exponential Equations Related to the Quantum ‘ ax + b ’ Group
  55. Twisted Logarithmic Modules of Vertex Algebras
  56. Singular Continuous Spectrum for Singular Potentials
  57. How to Remove the Boundary in CFT – An Operator Algebraic Procedure
  58. Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
  59. Multidimensional Continued Fractions, Dynamical Renormalization and KAM Theory
  60. Twistor Theory on a Finite Graph
  61. Triangular Invariants, Three-Point Functions and Particle Stability on the de Sitter Universe
  62. On positive functionals on algebras of test functions for quantum fields
  63. Large Deviations for the Yang-Mills Measure on a Compact Surface
  64. Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
  65. Periodicity and the Determinant Bundle
Search Result: