Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory
arXiv:0712.0225 · doi:10.1103/PhysRevLett.100.164101
Abstract
New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. The dominant features come from the region near the boundary where there is an interplay between Friedel oscillations and fluctuations in the eigenstates. Quite naturally, the fluctuation scale is significantly enhanced for Neumann boundary conditions as compared to Dirichlet. Elements missing from random plane wave modeling of chaotic eigenstates lead surprisingly to significant errors, which can be corrected within a purely semiclassical approach.
References in corpus (8)
- Statistics of energy levels and eigenfunctions in disordered systems
- On the rate of quantum ergodicity in Euclidean billiards
- Correlations in Chaotic Eigenfunctions at Large Separation
- Spectral Statistics in the Quantized Cardioid Billiard
- Comment on "Spatial Correlation in Quantum Chaotic Systems with Time-Reversal Symmetry: Theory and Experiment" by V. N. Prigodin et al [cond-mat/9504089]
- Autocorrelation function of eigenstates in chaotic and mixed systems
- Semiclassical Construction of Random Wave Functions for Confined Systems
- Current and vorticity auto correlation functions in open microwave billiards
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