Related papers: Detection Time Distribution for Dirac Particles
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
A random sequence having two segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each…
We study a monitoring system in which the distributions of sensors' observations change from a nominal distribution to an abnormal distribution in response to an adversary's presence. The system uses the quickest change detection procedure,…
We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material…
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…
The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterisation, that have been…
Even after decades of research the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time $\tau$, we…
An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This new method is based on a method we developed previously, but with an essential change in solving the Schrodinger's equation.…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements…
A relativistic transient absorption theory is derived, implemented and validated within the dipole approximation based on the time-dependent Dirac equation. Time-dependent simulations have been performed using the Dirac equation and the…
We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…
In the field of state-of-the-art object detection, the task of object localization is typically accomplished through a dedicated subnet that emphasizes bounding box regression. This subnet traditionally predicts the object's position by…
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…
Let $Z=(Z_t)_{t\ge0}$ be a regular diffusion process started at $0$, let $\ell$ be an independent random variable with a strictly increasing and continuous distribution function $F$, and let $\tau_{\ell}=\inf\{t\ge0\vert Z_t=\ell\}$ be the…
We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
Motivated by a recent prediction [Com. Phys., 6, 195 (2023)] that time-of-flight experiments with ultracold atoms could test different interpretations of quantum mechanics, this work investigates the arrival times predicted by the…
Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational-wave interferometers and…