Systematic approach to statistics of conductance and shot-noise in chaotic cavities
arXiv:0906.0161 · doi:10.1103/PhysRevB.80.125301
Abstract
Applying random matrix theory to quantum transport in chaotic cavities, we develop a novel approach to computation of the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open channels. The method is based on the Selberg integral theory combined with the theory of symmetric functions and is applicable equally well for systems with and without time-reversal symmetry. We also compute higher-order cumulants and perform their detailed analysis. In particular, we establish an explicit form of the leading asymptotic of the cumulants in the limit of the large channel numbers. We derive further a general Pfaffian representation for the corresponding distribution functions. The Edgeworth expansion based on the first four cumulants is found to reproduce fairly accurately the distribution functions in the bulk even for a small number of channels. As the latter increases, the distributions become Gaussian-like in the bulk but are always characterized by a power-law dependence near their edges of support. Such asymptotics are determined exactly up to linear order in distances from the edges, including the corresponding constants.
arXiv comment14 pages, 4 figures, 3 tables
References in corpus (32)
- Shot Noise in Mesoscopic Conductors
- Random-Matrix Theory of Quantum Transport
- The Statistical Theory of Quantum Dots
- Mesoscopic Transport Through Ballistic Cavities: A Random S-Matrix Theory Approach
- Universal Quantum Signatures of Chaos in Ballistic Transport
- Expansions for nearly Gaussian distributions
- Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems
- Semiclassical Theory of Chaotic Quantum Transport
- Voltage-probe and imaginary potential models for dephasing in a chaotic quantum dot
- Electron counting in quantum dots
- Distributions of the Conductance and its Parametric Derivatives in Quantum Dots
- Charge Fluctuations in Quantum Point Contacts and Chaotic Cavities in the Presence of Transport
- Distributions of Conductance and Shot Noise and Associated Phase Transitions
- Shot Noise by Quantum Scattering in Chaotic Cavities
- Semiclassical Approach to Chaotic Quantum Transport
- Character Expansions, Itzykson-Zuber Integrals, and the QCD Partition Function
- Semiclassical Prediction for Shot Noise in Chaotic Cavities
- Shot noise in chaotic cavities with an arbitrary number of open channels
- Universal Conductance Distributions in the Crossover between Diffusive and Localization Regimes
- Interference Phenomena in Electronic Transport Through Chaotic Cavities: An Information-Theoretic Approach
- Nonlinear statistics of quantum transport in chaotic cavities
- Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
- General Eigenvalue Correlations for the Real Ginibre Ensemble
- Integrable theory of quantum transport in chaotic cavities
- Experimental Test of Universal Conductance Fluctuations by means of Wave-Chaotic Microwave Cavities
- Full counting statistics of chaotic cavities with many open channels
- A few remarks on Colour-Flavour Transformations,truncations of random unitary matrices, Berezin reproducing kernels and Selberg type integrals
- Effect of Dephasing on Charge-Counting Statistics in Chaotic Cavities
- Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes
- Transport in chaotic quantum dots: effects of spatial symmetries which interchange the leads
- The effect of symmetry class transitions on the shot noise in chaotic quantum dots
- Full counting statistics of a chaotic cavity with asymmetric leads
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- Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4
- Moments of the transmission eigenvalues, proper delay times and random matrix theory I
- Moments of the transmission eigenvalues, proper delay times and random matrix theory II
- Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
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- Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities
- Truncated linear statistics associated with the top eigenvalues of random matrices
- Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes
- Transport moments beyond the leading order
- Random-matrix theory of thermal conduction in superconducting quantum dots
- Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach
- Statistics of thermal to shot noise crossover in chaotic cavities
- Recursion scheme for the largest -Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport
- Random matrix theory of quantum transport in chaotic cavities with non-ideal leads
- Distribution of spectral linear statistics on random matrices beyond the large deviation function -- Wigner time delay in multichannel disordered wires
- Universal covariance formula for linear statistics on random matrices
- Random matrix ensembles involving Gaussian Wigner and Wishart matrices, and biorthogonal structure
- Transport moments and Andreev billiards with tunnel barriers
- Statistics of time delay and scattering correlation functions in chaotic systems I. Random Matrix Theory
- Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
- Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula
- Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots
- Conductance Distributions in Chaotic Mesoscopic Cavities
- Joint statistics of quantum transport in chaotic cavities
- Largest Schmidt eigenvalue of entangled random pure states and conductance distribution in chaotic cavities
- Energy-dependent correlations in the -matrix of chaotic systems
- Semiclassical treatment of quantum chaotic transport with a tunnel barrier
- Entanglement production in non-ideal cavities and optimal opacity
- Asymptotics of Selberg-like integrals by lattice path counting
- Transport through open quantum dots: making semiclassics quantitative
- An exact formula for the variance of linear statistics in the one-dimensional jellium mode
- Nonlinear Random Matrix Statistics, symmetric functions and hyperdeterminants
- Statistics of quantum transport in weakly non-ideal chaotic cavities
- Entanglement is Necessary for Optimal Quantum Property Testing
- Combinatorial problems in the semiclassical approach to quantum chaotic transport
- Joint probability distributions for projection probabilities of random orthonormal states
- Full counting statistics of 1d short-range Riesz gases in confinement
- Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
- General truncated linear statistics for the top eigenvalues of random matrices
- Chaotic Transport in the Symmetry Crossover Regime with a Spin-orbit Interaction
- Integrable Aspects of Universal Quantum Transport in Chaotic Cavities
- How to compute Selberg-like integrals?
- Transport statistics in asymmetric coupled chaotic dots in series: Brownian motion model
- Electronic transport in three-terminal chaotic systems with a tunnel barrier