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We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…
The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination,…
We compute in a relativistic way the time-of-arrival and the traversal time through a region of a free particle with spin 1/2. We do this by applying the relativistic extension of the Event-Enhanced Quantum Theory which we have presented in…
We present a rigorous study of quantum diffusion of a relativistic particle subjected to a time-dependent random potential with $\delta$ correlation in time. We find that in the asymptotic time limit the particle wave packet spreads…
We suggest scattering experiments which implement the concept of ``protective measurements'' allowing the measurement of the complete wave function even when only one quantum system (rather than an ensemble) is available. Such scattering…
In this paper, we study the following detection problem. There are $n$ detectors randomly placed in the unit square $S = \left[-\frac{1}{2},\frac{1}{2}\right]^2$ assigned to detect the presence of a source located at the origin. Time is…
We follow the emergence of quantum entanglement in a scattering event between two initially uncorrelated distinguishable quantum particles interacting via a delta potential. We calculate the time dependence of the Neumann entropy of the…
We calculate the Wigner quasiprobability distribution function of quantum elliptical vortex in elliptical beam (EEV), produced by coupling squeezed coherent states of two modes. The coupling between the two modes is performed by using beam…
The electron waiting time is the time that passes between two subsequent charge transfers in an electronic conductor. Recently, theories of electron waiting times have been devised for quantum transport in Coulomb-blockade structures and…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
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…
The distribution of exit times is computed for a Brownian particle in spherically symmetric two- dimensional domains (disks, angular sectors, annuli) and in rectangles that contain an exit on their boundary. The governing partial…
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…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…
In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the ``crossing state'' concept. It is shown that only one of them has…
The time of flight distribution for a cloud of cold atoms falling freely under gravity is considered. We generalise the probability current density approach to calculate the quantum arrival time distribution for the mixed state describing…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…