Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula
arXiv:cond-mat/0701620 · doi:10.1103/PhysRevB.75.205329
Abstract
Exact numerical results for the full counting statistics (FCS) for a one-dimensional tight-binding model of noninteracting electrons are presented without using an idealized measuring device. The two initially separate subsystems are connected at t=0 and the exact time evolution for the large but finite combined system is obtained numerically. At zero temperature the trace formula derived by Klich is used to to calculate the FCS via a finite dimensional determinant. Even for surprisingly short times the approximate description of the time evolution with the help of scattering states agrees well with the exact result for the local current matrix elements. An additional approximation has to be made to recover the Levitov-Lesovik formula in the limit where the system size becomes infinite and afterwards the long time limit is addressed. The new derivation of the Levitov-Lesovik formula is generalized to more general geometries like a Y-junction enclosing a magnetic flux.
former section 2-> appendix A, add. references; to appear in PRB
References in corpus (15)
- Shot Noise in Mesoscopic Conductors
- Electron Counting Statistics and Coherent States of Electric Current
- Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
- Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects
- Towards full counting statistics for the Anderson impurity model
- Spin-charge separation in cold Fermi-gases: a real time analysis
- Full Counting Statistics of a Superconducting Beam Splitter
- Impurity and correlation effects on transport in one-dimensional quantum wires
- Circuit Theory for Full Counting Statistics in Multi-Terminal Circuits
- DMRG evaluation of the Kubo formula -- Conductance of strongly interacting quantum systems
- A junction of three quantum wires: restoring time-reversal symmetry by interaction
- Scattering Approach to Counting Statistics in Quantum Pumps
- Full Counting Statistics: An elementary derivation of Levitov's formula
- Quantum and Classical Binomial Distributions for the Charge Transmitted through Coherent Conductor
- Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at non-zero temperatures
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