Related papers: Absorbing Boundary Condition as Limiting Case of I…
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…
Consider detectors waiting for a quantum particle to arrive at a surface $S$ in 3-space. For predicting the probability distribution of the time and place of detection, a rule was proposed in [arXiv:1601.03715], called the absorbing…
Complex absorbing potentials are frequently imposed when simulating unbound quantum systems. While this is usually done solely in order to avoid artifacts at the numerical boundary, we show how absorbers may also be used to probe the…
The phenomenological boundary conditions for the envelope wave function, which is applicable for contacts of semiconductors with the rather different crystal symmetry are proposed. It is shown that the boundary conditions are determined by…
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…
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 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…
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
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…
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…
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…
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…
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…
We study a limiting absorption principle for the boundary-value problem describing a hybrid plasma resonance, with a regular coefficient in the principal part of the operator that vanishes on a curve inside the domain and changes its sign…
The physical origin is investigated of Robin boundary conditions for wave functions at an infinite reflecting wall. We consider both Schr\"odinger and phase-space quantum mechanics (a.k.a. deformation quantization), for this simple example…
We investigate the short-time dynamics of a delta-function potential barrier on an initially confined wave-packet. There are mainly two conclusions: A) At short times the probability density of the first particles that passed through the…
Gravity wave turbulence is studied experimentally in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are…
Motivated by recent experimental progress, we study scalar wave propagation over an imperfect draining vortex, which can serve as an analogue for rotating and non-rotating extreme compact objects (ECOs). We encapsulate the absorbing…
For each optical topology of an interferometric gravitational wave detector, quantum mechanics dictates a minimum optical power (the ``energetic quantum limit'') to achieve a given sensitivity. For standard topologies, when one seeks to…