The Statistics of Chaotic Tunnelling
arXiv:chao-dyn/9909046 · doi:10.1103/PhysRevLett.84.4084
Abstract
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on using the properties of a semiclassical tunnelling operator together with random matrix theory arguments about wave function overlaps. The resulting distribution depends on the stability of a specific tunnelling orbit and is therefore not universal. However it does reduce to the universal Porter-Thomas form as the orbit becomes very unstable. For some choices of system parameters there are systematic deviations which we explain in terms of scarring of certain real periodic orbits. The theory is tested in a model symmetric double well problem and possible experimental realisations are discussed.
Submitted to PRL
References in corpus (12)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Linear and Nonlinear Theory of Eigenfunction Scars
- Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering
- Dynamical Tunneling in Mixed Systems
- Wavefunction Intensity Statistics from Unstable Periodic Orbits
- Ionization via Chaos Assisted Tunneling
- A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities
- Semiclassical theory of magnetotransport through a chaotic quantum well
- Homoclinic Structure Controls Chaotic Tunnelling
- Chaos in Quantum Dots: Dynamical Modulation of Coulomb Blockade Peak Heights
- Quantum chaos with non-periodic, complex orbits in the Resonant Tunneling Diode
- Semiclassical description of resonant tunneling
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- Resonance- and Chaos-Assisted Tunneling