Quantum-to-classical correspondence in open chaotic systems
arXiv:cond-mat/0508092 · doi:10.1088/0305-4470/38/49/013
Abstract
We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time tau_E. The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by random-matrix theory. In the semiclassical limit, tau_E becomes parametrically larger than the scattering time off the boundaries and the dwell time in the system. This results in the emergence of an increasing number of deterministic transport and escape modes, which induce strong deviations from random-matrix universality. We discuss these deviations for a variety of physical phenomena, including shot noise, conductance fluctuations, decay of quasibound states, and the mesoscopic proximity effect in Andreev billiards.
23 pages, contribution for the special issue of J.Phys.A on "Trends in Quantum Chaotic Scattering"
References in corpus (52)
- Shot Noise in Mesoscopic Conductors
- Random-Matrix Theory of Quantum Transport
- Random Matrix Theories in Quantum Physics: Common Concepts
- The Statistical Theory of Quantum Dots
- Quantum Effects in Coulomb Blockade
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach
- Universal Quantum Signatures of Chaos in Ballistic Transport
- Semiclassical Foundation of Universality in Quantum Chaos
- Weak-Localization and Integrability in Ballistic Cavities
- Divergence of the Classical trajectories and Weak Localization
- Quantum Shot Noise
- Semiclassical Theory of Chaotic Quantum Transport
- Truncations of random unitary matrices
- GENERALIZED CIRCULAR ENSEMBLE OF SCATTERING MATRICES FOR A CHAOTIC CAVITY WITH NON-IDEAL LEADS
- Fractal Weyl laws for chaotic open systems
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Induced superconductivity distinguishes chaotic from integrable billiards
- Shot noise in chaotic systems: "classical" to quantum crossover
- Universal gap fluctuations in the superconductor proximity effect
- Shot Noise by Quantum Scattering in Chaotic Cavities
- Chaos in Andreev Billiards
- Density of States and Energy Gap in Andreev Billiards
- Conductance of Open Quantum Billiards and Classical Trajectories
- Fractal Weyl laws in discrete models of chaotic scattering
- Ehrenfest time dependent suppression of weak localization
- Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems
- Quantum Disorder and Quantum Chaos in Andreev Billiards
- Dynamical model for the quantum-to-classical crossover of shot noise
- Andreev billiards
- Superconductor-proximity effect in chaotic and integrable billiards
- Quantum Andreev map: A paradigm of quantum chaos in superconductivity
- Effect of the coupling to a superconductor on the level statistics of a metal grain in a magnetic field
- Excitation spectrum of Andreev billiards with a mixed phase space
- Fingerprints of classical diffusion in open 2D mesoscopic systems in the metallic regime
- Ehrenfest-time dependence of weak localization in open quantum dots
- Noiseless scattering states in a chaotic cavity
- Semiclassical theory of the emission properties of wave-chaotic resonant cavities
- Whispering gallery modes in open quantum billiards
- Quantum interference and the formation of the proximity effect in chaotic normal-metal/superconducting structures
- Adiabatic quantization of Andreev levels
- Shot noise in the chaotic-to-regular crossover regime
- Quantum-to-classical crossover of mesoscopic conductance fluctuations
- Shot noise and transport in small quantum cavities with large openings
- Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport
- Efficient Diagonalization of Kicked Quantum Systems
- Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard
- Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
- Effective Random Matrix Theory description of chaotic Andreev billiards
- Weak localization of the open kicked rotator
- Quantum-to-classical crossover for Andreev billiards in a magnetic field
- Decomposition of Resonant Scatterers by Surfaces of Section
Cited by in corpus (46)
- Light fields in complex media: mesoscopic scattering meets wave control
- Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
- Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
- Semiclassical structure of chaotic resonance eigenfunctions
- Shot noise in semiclassical chaotic cavities
- Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting, Coherent Backscattering and Weak Localization
- Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport
- Truncations of Random Orthogonal Matrices
- Resonances in open quantum maps
- Full counting statistics of chaotic cavities from classical action correlations
- Quantum complexity in gravity, quantum field theory, and quantum information science
- From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
- Full counting statistics of chaotic cavities with many open channels
- Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots
- Fractal Weyl laws for quantum decay in generic dynamical systems
- Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport
- Shot Noise of Spin-Decohering Transport in Spin-Orbit Coupled Nanostructures
- Semiclassical approach to the ac-conductance of chaotic cavities
- Statistics of Chaotic Resonances in an Optical Microcavity
- Dephasing in quantum chaotic transport: a semiclassical approach
- Lifetime statistics in chaotic dielectric microresonators
- The density of states of chaotic Andreev billiards
- A model for chaotic dielectric microresonators
- Semiclassical Mechanism for the Quantum Decay in Open Chaotic Systems
- Quantum Corrections to Fidelity Decay in Chaotic Systems
- Conductance fluctuations in chaotic systems with tunnel barriers
- Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot
- On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
- Formation and interaction of resonance chains in the open 3-disk system
- Driven coupled Morse oscillators --- visualizing the phase space and characterizing the transport
- Asymptotic boundary layer method for unstable trajectories: Semiclassics for individual scar wavefunctions
- What can we learn about the dynamics of transported spins by measuring shot noise in spin-orbit-coupled nanostructures?
- Semiclassical transport in nearly symmetric quantum dots II: symmetry-breaking due to asymmetric leads
- Multifractality of open quantum systems
- Semiclassical theory of a quantum pump
- Chaos in circuit QED: decoherence, localization, and nonclassicality
- Quantum Localization in Open Chaotic Systems
- Semiclassical theory of chaotic quantum resonances
- Higher-order gap ratios of singular values in open quantum systems
- Semiclassical theory of non-local statistical measures: residual Coulomb interactions
- Long-time signatures of short-time dynamics in decaying quantum-chaotic systems
- A unified time scale for quantum chaotic regimes
- Macroscopic Resonant Tunneling through Andreev Interferometers
- Counting statistics of chaotic resonances at optical frequencies: theory and experiments
- Non-universal suppression of the excitation gap in chaotic Andreev billiards: Superconducting terminals as sensitive probes for scarred states
- Mode resolved travel time statistics for elastic rays in three-dimensional billiards