Related papers: Quantum delay in the time of arrival of free-falli…
The probability distribution of a time measurement $T_x$ at position $x$ can be inferred from the probability distribution of a position measurement $X_t$ at time $t$ as given by the Born rule [Time-of-arrival distributions for continuous…
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…
Imagine an experiment where a quantum particle inside a box is released at some time in some initial state. A detector is placed at a fixed location inside the box and its clicking signifies arrival of the particle at the detector. What is…
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…
The quantum analogue of Galileo's leaning tower experiment is revisited using wave packets evolving under the gravitational potential. We first calculate the position detection probabilities for particles projected upwards against gravity…
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 propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
The uncertainty principle is one of the characteristic properties of quantum theory, where it signals the incompatibility of two types of measurements. In this paper, we argue that measurements of time-of-arrival $T_x$ at position $x$ and…
We illustrate through explicit numerical calculations how the Born-rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie-Bohm pilot-wave theory. The time evolution of a…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
We develop a general theory of the time distribution of quantum events, applicable to a large class of problems such as arrival time, dwell time and tunneling time. A stopwatch ticks until an awaited event is detected, at which time the…
The weak equivalence principle of gravity is examined at the quantum level in two ways. First, the position detection probabilities of particles described by a non-Gaussian wave-packet projected upwards against gravity around the classical…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…
The prediction of arrival time or first passage time statistics of a quantum particle is an open problem, which challenges the foundations of quantum theory. One of the most promising and insightful approaches to this problem stems from the…
We introduce a formalism for the calculation of the time of arrival t at a space point for particles traveling through interacting media. We develop a general formulation that employs quantum canonical transformations from the free to the…
We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…
This paper provides a general method for defining a generalized quantum observable (or POVM) that supplies properly normalized conditional probabilities for the time of occurrence (i.e., of detection). This method treats the time of…
I provide a simple derivation of the Born rule as giving a classical probability, that is, the ratio of the measure of favorable states of the system to the measure of its total possible states. In classical systems, the probability is due…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
We present a new method of measuring the mass density along the line of sight, based on precise measurements of the variations of the times of arrival (TOA's) of electromagnetic signals propagating between two distant regions of spacetime.…