Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4
arXiv:1206.4584 · doi:10.1007/s00220-013-1813-z
Abstract
We study the cumulants and their generating functions of the probability distributions of the conductance, shot noise and Wigner delay time in ballistic quantum dots. Our approach is based on the integrable theory of certain matrix integrals and applies to all the symmetry classes beta=1,2,4 of Random Matrix Theory. We compute the weak localization corrections to the mixed cumulants of the conductance and shot noise for beta=1,4, thus proving a number of conjectures of Khoruzhenko et al. (Phys. Rev. B, Vol. 80 (2009), 125301). We derive differential equations that characterize the cumulant generating functions for all beta=1,2,4. Furthermore, we show that the cumulant generating function of the Wigner delay time can be expressed in terms of the Painleve' III' transcendant. This allows us to study properties of the cumulants of the Wigner delay time in the asymptotic limit n -> infinity. Finally, for all the symmetry classes and for any number of open channels, we derive a set of recurrence relations that are very efficient for computing cumulants at all orders.
46 pages. Minor corrections
References in corpus (18)
- Semiclassical Foundation of Universality in Quantum Chaos
- Periodic-Orbit Theory of Universality in Quantum Chaos
- Semiclassical Theory of Chaotic Conductors
- Distributions of Conductance and Shot Noise and Associated Phase Transitions
- Wigner time-delay distribution in chaotic cavities and freezing transition
- Systematic approach to statistics of conductance and shot-noise in chaotic cavities
- Nonlinear statistics of quantum transport in chaotic cavities
- Delay times and reflection in chaotic cavities with absorption
- Statistics of quantum transport in chaotic cavities with broken time-reversal symmetry
- Moments of the transmission eigenvalues, proper delay times and random matrix theory II
- Integrable theory of quantum transport in chaotic cavities
- Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
- Full counting statistics of chaotic cavities with many open channels
- Statistics of reflection eigenvalues in chaotic cavities with non-ideal leads
- Are Bosonic Replicas Faulty?
- Statistics of thermal to shot noise crossover in chaotic cavities
- Conductance Distributions in Chaotic Mesoscopic Cavities
- Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues
Cited by in corpus (39)
- Wigner time delay and related concepts -- Application to transport in coherent conductors
- Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
- Moments of the position of the maximum for GUE characteristic polynomials and for log-correlated Gaussian processes
- Efficient semiclassical approach for time delays
- Capacitance and charge relaxation resistance of chaotic cavities - Joint distribution of two linear statistics in the Laguerre ensemble of random matrices
- Generalization of Wigner Time Delay to Sub-Unitary Scattering Systems
- Moments of random matrices and hypergeometric orthogonal polynomials
- Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
- Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach
- Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities
- Correlators for the Wigner-Smith time-delay matrix of chaotic cavities
- Large- expansion for the time-delay matrix of ballistic chaotic cavities
- Recursion for the smallest eigenvalue density of -Wishart-Laguerre ensemble
- Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
- Random matrix theory of quantum transport in chaotic cavities with non-ideal leads
- Universal covariance formula for linear statistics on random matrices
- Effect of chiral symmetry on chaotic scattering from Majorana zero modes
- 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
- Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots
- Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
- Joint statistics of quantum transport in chaotic cavities
- Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials
- Painlevé V and the Hankel Determinant for a Singularly Perturbed Jacobi Weight
- Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities
- A Physical Interpretation of Imaginary Time Delay
- The Correlated Jacobi and the Correlated Cauchy-Lorentz ensembles
- Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations
- Statistics of quantum transport in weakly non-ideal chaotic cavities
- Time delay statistics for finite number of channels in all symmetry classes
- Distribution of the Wigner-Smith time-delay matrix for chaotic cavities with absorption and coupled Coulomb gases
- Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity
- A singular-potential random matrix model arising in mean-field glassy systems
- Semiclassical approach to matrix energy correlations and time delay in chaotic systems
- Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
- The probability distribution of spectral moments for the Gaussian beta-ensembles
- Spectral statistics of the uni-modular ensemble
- Integrable Aspects of Universal Quantum Transport in Chaotic Cavities
- On a distinguished family of random variables and Painlevé equations