Paper Search Console

Home Search Page About Contact

Journal Title

Title of Journal: J Stat Phys

Search In Journal Title:

Abbravation: Journal of Statistical Physics

Search In Journal Abbravation:

Publisher

Springer US

Search In Publisher:

ISSN

1572-9613

Search In ISSN:
Search In Title Of Papers:

Ground State Energy of the OneDimensional Discret

Authors: Michael Bishop Jan Wehr
Publish Date: 2012/04/20
Volume: 147, Issue: 3, Pages: 529-541
PDF Link

Abstract

In this paper we show the that the ground state energy of the onedimensional discrete random Schrödinger operator with Bernoulli potential is controlled asymptotically as the system size N goes to infinity by the random variable ℓ N the length the longest consecutive sequence of sites on the lattice with potential equal to zero Specifically we will show that for almost every realization of the potential the ground state energy behaves asymptotically as fracpi2ell N +12 in the sense that the ratio of the quantities goes to oneWe would like to thank W Faris for the suggestion to look at potentials with Bernoulli distributions which turned out to be a great starting point We would like to thank R Sims for useful discussions in particular of the broader context of random Schrödinger operator theory We would like to thank M Lewenstein A Sanpera P Massignan and J Stasińska for collaborating with us on related projects as well as providing supporting numerical results The first idea of the present paper grew out of discussions with J Xin Both authors were supported in part by NSF grant DMS1009508 and M Bishop was in addition funded by NSF VIGRE grant DMS0602173 at the University of Arizona and by the NSF under Grant No DGE0841234

Keywords:

References

.
Search In Abstract Of Papers:
Other Papers In This Journal:
  1. Mean Field Dilute Ferromagnet: High Temperature and Zero Temperature Behavior
  2. Probabilistic Cellular Automata for Low-Temperature 2-d Ising Model
  3. Random Birth-and-Death Networks
  4. Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma
  5. On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices
  6. Products of Random Matrices and Generalised Quantum Point Scatterers
  7. Symmetry of the Linearized Boltzmann Equation and Its Application
  8. Activity of Excitatory Neuron with Delayed Feedback Stimulated with Poisson Stream is Non-Markov
  9. Replica Symmetry Breaking Condition Exposed by Random Matrix Calculation of Landscape Complexity
  10. Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System
  11. Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties
  12. New Horizons in Multidimensional Diffusion: The Lorentz Gas and the Riemann Hypothesis
  13. Clustering of Fermionic Truncated Expectation Values Via Functional Integration
  14. Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry–Mather Theory
  15. Revisiting the Glansdorff–Prigogine Criterion for Stability Within Irreversible Thermodynamics
  16. A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths
  17. The More the Merrier?
  18. Non-equilibrium Phase Diagram for a Model with Coalescence, Evaporation and Deposition
  19. Real Spin Glasses Relax Slowly in the Shade of Hierarchical Trees
  20. Galton–Watson Trees with Vanishing Martingale Limit
  21. A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings
  22. Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians
  23. Dynamics of Infinitely Many Particles Mutually Interacting in Three Dimensions via a Bounded Superstable Long-Range Potential
  24. Statistical Mechanics of Nucleosomes Constrained by Higher-Order Chromatin Structure
  25. Large Deviations for the Branching Brownian Motion in Presence of Selection or Coalescence
  26. Clustering Bounds on n -Point Correlations for Unbounded Spin Systems
  27. Dissipative Diamagnetism—A Case Study for Equilibrium and Nonequilibrium Statistical Mechanics
  28. On the Transfer of Energy Towards Infinity in the Theory of Weak Turbulence for the Nonlinear Schrödinger Equation
  29. Finite-Time Fluctuations in the Degree Statistics of Growing Networks
  30. Exotic Ground States of Directional Pair Potentials via Collective-Density Variables
  31. Strong Asymmetric Coupling of Two Parallel Exclusion Processes
  32. Repeated Interaction Quantum Systems: Van Hove Limits and Asymptotic States
  33. On the Dynamics of the Glass Transition on Bethe Lattices
  34. Coarsening Dynamics on $$\mathbb {Z}^d$$ with Frozen Vertices
  35. A Class of Random Walks in Reversible Dynamic Environments: Antisymmetry and Applications to the East Model
  36. Power-law Decay and the Ergodic–Nonergodic Transition in Simple Fluids
  37. Rigorous Treatment of the Liquid-Vapor Transition in a Polydisperse System with Kac Interaction
  38. R -Local Delaunay Inhibition Model
  39. Patterns and Symmetries in the Visual Cortex and in Natural Images
  40. Parameter Estimation for Multiscale Diffusions
  41. Onsager and Kaufman’s Calculation of the Spontaneous Magnetization of the Ising Model: II
  42. Injected Power Fluctuations in 1D Dissipative Systems
  43. Anomalies in Conductance and Localization Length of Disordered Ladders
  44. Finite-Size Scaling in the Energy-Entropy Plane for the 2D ± Ising Spin Glass
Search Result: