相关论文: On a Derivation of the Absorbing Boundary Rule

We address the question of how to compute the probability distribution of the time at which a detector clicks, in the situation of $n$ non-relativistic quantum particles in a volume $\Omega\subset \mathbb{R}^3$ in physical space and…

The problem of detection time distribution concerns a quantum particle surrounded by detectors and consists of computing the probability distribution of where and when the particle will be detected. While the correct answer can be obtained…

Consider a non-relativistic quantum particle with wave function inside a region $\Omega\subset \mathbb{R}^3$, and suppose that detectors are placed along the boundary $\partial \Omega$. The question how to compute the probability…

We consider the problem of computing, for a detector surface waiting for a quantum particle to arrive, the probability distribution of the time and place at which the particle gets detected, from the initial wave function of the particle in…

There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary…

We consider particles emanating from a source point inside an interval in one-dimensional space and passing through detectors situated at the endpoints of the interval that register their arrival time. Unambiguous measurements of arrival or…

Any proposed solution to the "screen problem" in quantum mechanics -- the challenge of predicting the joint distribution of particle arrival times and impact positions -- must align with the extensive data obtained from scattering…

Absorbing boundary conditions are presented for three-dimensional time-dependent Schr\"odinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a…

Absorbing boundaries are frequently employed in real-time propagation of the Schr\"odinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an…

We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined to the non-absorbing region. Trajectories that reach the absorbing wall are…

A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary…

Suppose that particle detectors are placed along a Cauchy surface $\Sigma$ in Minkowski space-time, and consider a quantum theory with fixed or variable number of particles (i.e., using Fock space or a subspace thereof). It is…

We prove the uncertainty relation $\sigma_T \, \sigma_E \geq \hbar/2$ between the time $T$ of detection of a quantum particle on the surface $\partial \Omega$ of a region $\Omega\subset \mathbb{R}^3$ containing the particle's initial wave…

Imaginary potentials such as $V(x)=-iv 1_\Omega(x)$ (with $v>0$ a constant, $\Omega$ a subset of 3-space, and $1_\Omega$ its characteristic function) have been used in quantum mechanics as models of a detector. They represent the effect of…

We propose an adaptive approach in picking the wave-number parameter of absorbing boundary conditions for Schr\"{o}dinger-type equations. Based on the Gabor transform which captures local frequency information in the vicinity of artificial…

We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the…

How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a…

We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined by the absorbing boundary. Trajectories that reach the absorbing wall are…

Consider a particle which is randomly accelerated by Gaussian white noise on the line segment $0<x<1$ and is absorbed as soon as it reaches $x=0$ or $x=1$. The mean absorption time $T(x,v)$, where $x$ and $v$ denote the initial position and…

We investigate state estimation in discrete-time quantum walks with a single absorbing boundary. Using a spectral approach, we obtain closed expressions for the escape probability as a function of the initial coin state and the boundary…