Related papers: Detection time of Dirac particles in one space dim…
Using standard results from statistics, we show that for any continuous quantum system (Gaussian or otherwise) and any observable $\widehat{A}$ (position or otherwise), the distribution $\pi_{a}\left(t\right)$ of time measurement at a fixed…
A literature review of related articles, either by affinity or by contrast, to a fundamental theory of time and space - time previously developed. It shows how from a primitive concept of preparticle and membership relation of set theory,…
Previous numerical analyses on the Aharonov-Bohm (AB) operator representing the quantum time-of-arrival (TOA) observable for the free particle have indicated that its eigenfunctions represent quantum states with definite arrival time at the…
Inspired by Mott's (1929) analysis of particle tracks in a cloud chamber, we consider a simple model for quantum cosmology which includes, in the total Hamiltonian, model detectors registering whether or not the system, at any stage in its…
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…
A phenomenological model for a measurement of barrier traversal times for particles is proposed. Two idealized detectors for passage and arrival provide entrance and exit times for the barrier traversal. The averaged traversal time is…
Jacobi's action principle is known to lead to a problem of time. For example, the timelessness of the Wheeler-DeWitt equation can be seen as resulting from using Jacobi's principle to define the dynamics of 3-geometries through superspace.…
The extended Dirac's principle describes the interference between different particles as an effect of the multiparticle system with itself. In this paper we present a novel example, based on the detection of particles emitted in multimode…
The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…
We construct a boundary integral representation for the low-Reynolds-number flow in a channel in the presence of freely-suspended particles (or droplets) of arbitrary size and shape. We demonstrate that lubrication theory holds away from…
It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie-Bohm theory) offers a distinct conceptual advantage…
The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that…
A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function.…
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's…
It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta…
We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is…
Although position and time have different mathematical roles in quantum mechanics, with one being an operator and the other being a parameter, there is a space-time duality in quantum phenomena: a lot of quantum phenomena that were first…
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…
Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their…
We consider the quantum first detection problem for a particle evolving on a graph under repeated projective measurements with fixed rate $1/\tau$. A general formula for the mean first detected transition time is obtained for a quantum walk…