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First-passage phenomena play a fundamental role in classical stochastic processes. We here exactly solve a quantum first-passage time problem for quantum diffusion driven by measurement noise, a generalization of classical Brownian motion.…
We study the tunneling zone solutions of a one-dimensional electrostatic potential for the relativistic (Dirac to Klein-Gordon) wave equation when the incoming wave packet exhibits the possibility of being almost totally transmitted through…
Electrons in atoms and molecules move on attosecond time scales. Deciphering their quantum dynamics in space and time calls for high-resolution microscopy at this speed. While scanning tunnelling microscopy (STM) driven with terahertz…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
The time dependent density matrix of a system with potential barrier is studied using path integrals. The characterization of the initial state, which is assumed to be restricted to one side of the barrier, and the time evolution of the…
We demonstrate how rate equations can be employed to find analytical expressions for the sequential tunneling current through a quantum dot as a function of the tunnel rates, for an arbitrary number of states involved. We apply this method…
Strongly correlated transport of interacting electrons through the one-dimensional tunnel contact is considered within the Luttinger liquid model of one-dimensional electrodes on arbitrary time scales $ t> \hbar /\Lambda_{g} $. Using…
Analytic solutions to the time-dependent Schr\"odinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential…
We study the tunneling through an oscillating delta barrier. Using time periodicity of the model, the time-dependent Schr\"odinger equation is reduced to a simple but infinite matrix equation. Employing Toeplitz matrices methods, the…
We investigate the tunneling time of a wave packet propagating through a non-Hermitian potential $V_{r} - iV_{i}$ in space-fractional quantum mechanics. By applying the stationary phase method, we derive a closed-form expression for the…
The transient tunneling current of single electron transistors (SETs) is theoretically investigated. The time-dependent current formula given by Jauho, Wingreen and Meir [Phys. Rev. B 50, 5528 (1994)] is applied to study the temperature…
We revisit the path integral description of quantum tunneling and lay the groundwork for its generalization to excites states through real-time path integral techniques. For clarity, we focus on the simple toy model of a point particle in a…
The transmission of wave packets through tunneling barriers is studied in detail by the method of quantum molecular dynamics. The distribution function of the times describing the arrival of a tunneling packet in front of and behind a…
We use time-resolved charge detection techniques to probe virtual tunneling processes in a double quantum dot. The process involves an energetically forbidden state separated by an energy $\delta$ from the Fermi energy in the leads. The…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
What is the nature of tunnelling? This yet unanswered question is as pertinent today as it was at the dawn of quantum mechanics. This article presents a cross section of current perspectives on the interpretation, computational modelling,…
The refinement and specifications of time-energy uncertainty relations have shown that the experimentally observed phenomena of superluminal signaling are describable by such their form: $\Delta E\Delta\tau\geq\pi\hbar$, where both standard…
Nelson's stochastic mechanics formulates quantum dynamics as a real-time conservative diffusion process in which a particle undergoes Brownian-like motion with a fluctuation amplitude fixed by Planck's constant. While being mathematically…
We report on measurements of single electron tunneling through a quantum dot using a quantum point contact as non-invasive charge detector with fast time response. We elaborate on the unambiguous identification of individual tunneling…
Electron transport through a nanoscale system is an inherently stochastic quantum mechanical process. Electric current is a time series of electron tunnelling events separated by random intervals. Thermal and quantum noise are two sources…