Related papers: A New Time-Scale for Tunneling
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
In this paper, the interaction and transmission time of quantum density solitons waves representing particles passing through finite barrier potentials is investigated. Using the conservation of energy and of quantum density, it is first…
We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…
We propose a method to study the tunneling process by analyzing the time-dependent ionization yield in circularly polarized laser. A numerical calculation shows that for an atom exposed to a long laser pulse, if its initial electronic state…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
We investigate the martingale Schr\"odinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that this construction extends naturally to…
In this article, we are concerned with long-time behaviour of solutions to a semi-classical Schr\"odinger-type equation on the torus. We consider time scales which go to infinity when the semi-classical parameter goes to zero and we…
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of…
We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. Analyzing solutions with small (complex) energy, relevant for…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential…
The conundrum parameter-operator of time in quantum mechanics (QM), as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical ioniza- tion experiments. The parameter…
We propose a method for solving the time independent Schr\"odinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al., New J. Phys.…
In this paper, we focus on a general class of Schr\"odinger equations that are time-dependent and quadratic in X and P. We transform Schr\"odinger equations in this class, via a class of time-dependent mass equations, to a class of solvable…
We obtain the solution of a relativistic wave equation and compare it with the solution of the Schroedinger equation for a source with a sharp onset and excitation frequencies below cut-off. A scaling of position and time reduces to a…
Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schr\"odinger-Langevin or Kostin quantum classical transition wave equation is used and applied resulting in a scaled…
The measurement of the tunneling time (T-time) in today's attosecond and strong field (low-frequency) experiments, despite its controversial discussion, offers a fruitful opportunity to understand time measurement and the time in quantum…
Time-periodic solitons of the parametrically driven damped nonlinear Schr\"odinger equation are obtained as solutions of the boundary-value problem on a two-dimensional spatiotemporal domain. We follow the transformation of the periodic…