Related papers: Early times in tunneling
Solutions to explicit time-dependent problems in quantum mechanics are rare. In fact, all known solutions are coupled to specific properties of the Hamiltonian and may be divided into two categories: One class consists of time-dependent…
Starting with the equivalence of the rest energy of a particle to an amount of the radiant energy characterized by a frequency, in addition to the usual relativistic transformation rules leading to the wave-particle duality, we investigate…
Tunneling in the presence of an opaque barrier, part of which varies in time, is investigated numerically and analytically in one dimension. Clearly, due to the varying barrier a tunneling particle experiences spectral widening. However, in…
The classical problem of a time-modulated barrier, inspired by the Buttiker and Landauer model to study the tunneling times, is analyzed. We show that the traversal-time distribution of an ensemble of non-interacting particles that arrives…
In this article, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles, by a careful treatment of temporal observables in quantum theory and through a precise application of the duality between…
In this paper we study the tunneling using a background independent (polymer) quantization scheme. We show that at low energies, for the tunneling through a single potential barrier, the polymer transmission coefficient and the polymer…
We introduce the concept of partial and full tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a…
For drifted Brownian motion $X(t)= x - \mu t + B_t \ (\mu >0)$ starting from $x>0,$ we study the joint distribution of the first-passage time below zero, $\tau(x),$ and the first-passage area, $A(x),$ swept out by $X$ till the time…
We show the equivalence of the functions $G_{\rm p}(t)$ and $|\Psi(d,t)|^2$ for the ``passage time'' in tunneling. The former, obtained within the framework of the real time Feynman histories approach to the tunneling time problem, using…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…
We provide a full account of our recent report (EPL, 141 (2023) 10001}) which constructed a quantized relativistic time-of-arrival operator for spin-0 particles using a modified Weyl-ordering rule to calculate the traversal time across a…
Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…
Tunnelling is one of the most paradigmatic and evocative phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from SQUID magnetometers to superconducting qubits for quantum…
Semiclassical approximations for tunneling processes usually involve complex trajectories or complex times. In this paper we use a previously derived approximation involving only real trajectories propagating in real time to describe the…
Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The…
In electron transport, the tunnelling time is the time taken for an electron to tunnel out of a system after it has tunnelled in. We define the tunnelling time distribution for quantum processes in a dissipative environment and develop a…
A one-dimensional scattering problem off a $\delta$-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schr\"odinger equation. The exact and explicit expression of the…
We numerically study two methods of measuring tunneling times using a quantum clock. In the conventional method using the Larmor clock, we show that the Larmor tunneling time can be shorter for higher tunneling barriers. In the second…
Time evolution of tunneling phenomena in medium is studied using a standard model of environment interaction. A semiclassical formula valid at low, but finite temperatures is derived in the form of integral transform for the reduced Wigner…