Numerical Evaluation of Shot Noise using Real Time Simulations

Abstract

We present a method to determine the shot noise in quantum systems from knowledge of their time evolution - the latter being obtained using numerical simulation techniques. While our ultimate goal is the study of interacting systems, the main issues for the numerical determination of the noise do not depend on the interactions. To discuss them, we concentrate on the single resonant level model, which consists in a single impurity attached to non-interacting leads, with spinless fermions. We use exact diagonalisations (ED) to obtain time evolution, and are able to use known analytic results as benchmarks. We obtain a complete characterization of finite size effects at zero frequency, where we find that the finite size corrections scale $\propto G^2$, $G$ the differential conductance. We also discuss finite frequency noise, as well as the effects of damping in the leads.

6 pages, 7 figures

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• Non-equilibrium quantum transport in presence of a defect: the non-interacting case
• The interacting resonant level model in nonequilibrium: finite temperature effects
• Real-time simulation of finite frequency noise from a single electron emitter
• Magnetic field effects on the finite-frequency noise and ac conductance of a Kondo quantum dot out of equilibrium
• Full counting statistics in the not-so-long-time limit
• Transient noise spectra in resonant tunneling setups: Exactly solvable models
• Transport through nanostructures: Finite time vs. finite size
• Out-of-equilibrium transport in the interacting resonant level model: the surprising relevance of the boundary sine-Gordon model
• Universal Entanglement Dynamics following a Local Quench
• Healing of Defects in Random Antiferromagnetic Spin Chains
• On Landauer--Büttiker formalism from a quantum quench
• Transport through two interacting resonant levels connected by a Fermi sea
• Finite-frequency noise in a non-interacting quantum dot
• Current noise of the interacting resonant level model