Related papers: Detection Time Distribution for Dirac Particles
Precise measurements of both the arrival time and carrier frequency of light pulses are essential for time-frequency-encoded quantum technologies. Quantum mechanics, however, imposes fundamental limits on the simultaneous determination of…
Characterizing distinct electron wave packets is a basic task for solid-state electron quantum optics with applications in quantum metrology and sensing. A important circuit element for this task is a non-stationary potential barrier than…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity…
In this paper we introduce a new approach to the diffusive limit of the weakly random Schrodinger equation, first studied by L. Erdos, M. Salmhofer, and H.T. Yau. Our approach is based on a wavepacket decomposition of the evolution…
How long does a diffusing molecule spend in a close vicinity of a confining boundary or a catalytic surface? This quantity is determined by the boundary local time, which plays thus a crucial role in the description of various…
One solution to the so-called problem of time is to construct certain Dirac observables, sometimes called evolving constants of motion. There has been some discussion in the literature about the interpretation of such observables, and in…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…
We consider a particle diffusing outside a compact planar set and investigate its boundary local time $\ell_t$, i.e., the rescaled number of encounters between the particle and the boundary up to time $t$. In the case of a disk, this is…
To what extent can particulate random media be characterised using direct wave backscattering from a single receiver/source? Here, in a two dimensional setting, we show using a machine learning approach that both the particle radius and…
The problem of designing optimal quantization rules for sequential detectors is investigated. First, it is shown that this task can be solved within the general framework of active sequential detection. Using this approach, the optimal…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
By a detector, one has in mind a point particle with internal energy levels, which when set in motion on a generic trajectory can get excited due to its interaction with a quantum field. Detectors have often been considered as a helpful…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…
The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…
In this note we demonstrate that a quantum-like interference picture could appear as a statistical effect of interference of deterministic particles, i.e. particles that have trajectories and obey deterministic equations, if one introduces…
Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
We consider the general problem of the first passage distribution of particles whose displacements are subject to time delays. We show that this problem gives rise to a \emph{propagation-dispersion equation} which is obtained as the…
Starting from a continuous time random walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integro-differential equations for the probability density for a particle to be found at point r at…